From f923e8d41ca5953d9793fadcc3730cfe9fc70b3a Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:35:12 -0400 Subject: [PATCH 01/21] research: freeze five post-certificate hypotheses before execution --- graph_synthesis/post_certificates/PROTOCOL.md | 120 ++++++++++++++++++ 1 file changed, 120 insertions(+) create mode 100644 graph_synthesis/post_certificates/PROTOCOL.md diff --git a/graph_synthesis/post_certificates/PROTOCOL.md b/graph_synthesis/post_certificates/PROTOCOL.md new file mode 100644 index 0000000..481119d --- /dev/null +++ b/graph_synthesis/post_certificates/PROTOCOL.md @@ -0,0 +1,120 @@ +# Frozen protocol: five post-certificate improvements + +Baseline: `9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98` (merged PR #20), inspected September 18, 2026. + +This protocol is committed before implementation or execution. The new hypotheses are motivated by the merged evidence: source-random-effects forecasting improved Brier only 6.39% versus its same-marginal comparator and still lost to the prior feature-risk forecast, while dependence-safe bounds, bipartite flow certificates, repair-invariant queries and local delta maintenance passed their controlled targets. The present suite asks whether the remaining failure boundaries can be narrowed without changing the production graph policy. + +The repository audit covered CURRENT_RESULTS.md plus adaptive, risk-control, reliability, structural, source-structural, assumption-aware, uncertainty, novel-mechanisms, frontier and certificate studies. Related ingredients exist, including relation-level stacking, pairwise-constrained sensitivity analyses, bipartite flow, repair ambiguity and fixed-marginal credal bounds. The exact five tests below were not found in that inventory. This is a repository-scoped experiment distinction, not a worldwide novelty claim. Established calibration, active-information selection, separator conditioning, sensitivity analysis and linear programming have prior art. + +Fresh Jev service calls: **0**. H1 reuses the already authenticated saved-response development/test capture. H2-H5 are controlled algorithmic experiments. No new semantic-accuracy claim, production policy change, human-review claim, external-system superiority claim or independent preregistration claim is authorized. + +All primary targets below are frozen conjunctions. Do not retune a threshold, generator, comparator, tie rule, cap or evaluation population after observing the results. + +## H1 — Exposure-stratified stacking of source-contamination forecasts + +**Motivation.** Certificate H1 selected a beta-binomial source random-effect model and improved Brier relative to same-marginal independence, but 60/98 nonempty evaluation groups were singletons and the richer pre-existing feature-risk forecast still had lower Brier. Random effects and per-edge feature risk may contain complementary information. + +**Method.** +- Reuse exactly the certificate input loader: 73 development candidates / 40 source groups and 263 test candidates / 149 source groups, with source-group disjointness enforced. +- Accepted edges remain base1 SUPPORTS/REFUTES only. +- Build two development-only leave-one-source-group-out forecasts for each nonempty held-out group: + 1. the existing feature-risk group forecast from `reliability.calibration`; + 2. the beta-binomial random-effects forecast fitted without that group. +- Partition folds by accepted-edge exposure: singleton (`n == 1`) and multi-edge (`n > 1`). +- Within each stratum, if at least 8 folds are available, select a convex feature weight `w` from `{0.0, 0.1, ..., 1.0}` minimizing development Brier of `w * feature + (1-w) * random_effects`; ties prefer the smaller distance to 0.5, then smaller `w`. Otherwise use the globally selected weight. +- Refit both constituent models on all development rows and apply the frozen weights to test features/exposures before scoring test labels. +- No test gold, test-group outcomes or test-derived tuning may enter the fit. + +**Comparators.** Certificate random effects and prior feature-risk forecast, on the identical nonempty test-group denominator. + +**Primary target.** Stacked Brier must be no worse than feature-risk Brier, at least 3% lower than certificate random-effects Brier, and absolute mean bias must be <= 0.03. + +**Required reporting.** Brier, clipped log loss, bias, selected global/stratum weights, fold counts, singleton/multi test counts, paired source-group bootstrap intervals (4,000 draws, seed 20260923), and the unfavorable result if the conjunction fails. + +## H2 — Greedy acquisition of dependence constraints + +**Motivation.** Certificate H2 proves valid bounds under supplied marginals/joint constraints, but wide intervals can withhold useful admissions. Earlier studies tested fixed pairwise-constraint panels, not a frozen policy for deciding which pairwise intersections are most valuable to obtain. + +**Population.** Reuse the 128 arbitrary-joint random fixtures generated by certificate H2. The supplied full joint distribution is a controlled oracle only; it is not a measured Jev probability. + +**Method.** +- Start from marginal-only DNF bounds. +- Candidate observations are all pairwise atom-conjunction probabilities calculated from the fixture's supplied joint table. +- Budget = 3 pairwise constraints. +- At each step, evaluate every still-unobserved candidate by adding that exact controlled value and recomputing the certified interval; choose the candidate minimizing interval width. Ties are lexicographic on atom IDs. +- Comparator: add the first three lexicographic pair constraints, or all available pairs when fewer than three exist. +- Retain every intermediate interval and selected pair. + +**Primary target.** Zero truth-containment failures; no chosen step may widen its prior interval by >1e-8; mean final width must be <=75% of marginal-only mean width and <=90% of the lexicographic same-budget mean width. + +**Boundary.** This is an oracle value-of-information experiment. It does not establish that the selected intersections are cheaply or accurately estimable in production. + +## H3 — Separator-conditioned near-bipartite exact optimization + +**Motivation.** Certificate H3 exactly solves large bipartite conflict graphs, while large non-bipartite components still stage. A small supplied odd-cycle-transversal/separator can make the residual graph bipartite. + +**Method.** +- Input includes nonnegative integer priorities, conflict edges and a supplied separator `S` of at most 4 vertices. +- Verify that deleting `S` leaves a bipartite graph. Invalid hints stage; they are never trusted silently. +- Enumerate every independent subset `I` of `S`. Treat `I` as selected, remove all other separator vertices and every residual neighbor of `I`, then solve each remaining residual component with the existing certified bipartite-flow solver. +- Verify each returned flow certificate. Add the separator utility and select the maximum-utility feasible branch with deterministic lexical tie breaking. +- This is exact conditional on verified graph input and separator, not a semantic truth guarantee. + +**Small oracle test.** 128 seeded graphs with 6–12 vertices, separator size 1–3 and bipartite residuals; compare with independent exhaustive maximum-weight independent-set enumeration. Include order/duplicate invariance. + +**Large analytic test.** Even cycles of residual size 512, 1024 and 2048 plus one apex separator connected to two adjacent cycle vertices, with cycle weights 1 and apex weight 3. Expected optimum is `n/2 + 2`. The current generic solver must be recorded as comparator, including whether it stages. + +**Primary target.** Zero small-oracle/certificate/invariance failures; solve all three large fixtures at the analytic optimum; current generic solver stages every large fixture; malformed/non-transversal controls stage safely. + +## H4 — Reusable repair-margin query index + +**Motivation.** Certificate H4 gives correct repair-invariant query answers, but repeated queries repeatedly re-solve forced-in/forced-out optimization problems. For singleton assertions, those optimization margins can be precomputed once. + +**Method.** +- For a graph whose base optimum is not staged, compute for every vertex `v`: + - best utility with `v` forced in; + - best utility with `v` forced out. +- For tolerance `epsilon`, threshold = optimum - epsilon. +- Singleton query classification: + - impossible if forced-in utility < threshold; + - certain if forced-out utility < threshold; + - ambiguous otherwise. +- Preserve a possible witness and, where ambiguous, a counterexample witness. +- This index explicitly supports singleton queries only; conjunctions continue to use the existing query path. + +**Population.** 128 seeded weighted graphs with 4–10 vertices and finite exact behavior. For every vertex evaluate the distinct epsilon set `{0,1,2,floor(.05*optimum),floor(.10*optimum)}` after removing duplicates/nonpositive excess values. + +**Comparator.** Existing `certificates.graphs.query` on the same singleton query and epsilon. + +**Primary target.** Zero classification/witness mismatches and at least 70% fewer top-level optimization invocations over the repeated-query workload, counting baseline query execution as base + forced-in + forced-out solves and index construction as one base + two per vertex. + +**Boundary.** This is repeated-query work reduction, not database latency or semantic validation. + +## H5 — Interval-marginal dependence certificates + +**Motivation.** Every dependence-safe study retains the same falsifying control: if a supplied marginal itself is wrong, a mathematically correct point-marginal certificate can still make a false admission. Treating the marginal as an interval can represent bounded premise uncertainty explicitly. + +**Method.** +- Extend the possible-world LP so each atom probability is constrained by `lower <= P(atom) <= upper` rather than an equality; exact point marginals are the special case lower=upper. +- Objective remains min/max probability of the monotone DNF. Normalization is exact; interval rows are linear inequalities. +- Solver failure, infeasible intervals, nonfinite values, lower>upper, or atom-cap excess return an explicit non-certifying [0,1] staged result. +- Outward numerical padding and primal feasibility checks are required before a bound may certify. + +**Random containment population.** 128 seeded arbitrary joint distributions over 2–6 atoms and 1–6 proofs. For each true atom marginal, construct a seeded interval of radius 0.02–0.10 that contains the true value and a perturbed point estimate inside that interval. Require the true supplied joint fact probability to lie inside the interval-marginal result. + +**False-premise controls.** 20 singleton facts whose actual probability is below 0.95, whose biased point estimate is >=0.97, and whose supplied uncertainty interval contains the actual probability with lower endpoint <0.95. The exact-point method should admit; the interval method should withhold. + +**Primary target.** Zero random truth-containment failures, prevent all 20 designed point-estimate false admissions, and zero malformed/infeasible inputs returning a certifying interval. + +**Required reporting.** Mean point-bound width versus interval-bound width, prevented admissions, staging counts and explicit statement that interval validity itself is a supplied assumption. + +## Global validation and publication + +- Seed for new controlled generators: 20260923. +- No network access during benchmark replay. +- Add unit/adversarial tests for all five mechanisms. +- Store machine-readable results, summary CSV and five evidence-derived SVG/PNG figure pairs. +- Update `CURRENT_RESULTS.md` and append an additive section to `manuscript/paper-current.md`; regenerate HTML/PDF using the repository renderer. +- Preserve all pre-existing experiment artifacts and prior manuscript text byte-for-byte outside the additive section. +- CI must replay results and fail on generated-artifact drift. +- Report passes and failures exactly as observed. Do not pool controlled fixture counts into a semantic success rate. From 1d5ceee35bada50392be92b7f73194a4d6e41949 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:35:44 -0400 Subject: [PATCH 02/21] research: freeze five post-certificate hypotheses before execution --- graph_synthesis/post_certificate/PROTOCOL.md | 149 +++++++++++++++++++ 1 file changed, 149 insertions(+) create mode 100644 graph_synthesis/post_certificate/PROTOCOL.md diff --git a/graph_synthesis/post_certificate/PROTOCOL.md b/graph_synthesis/post_certificate/PROTOCOL.md new file mode 100644 index 0000000..8b20e6a --- /dev/null +++ b/graph_synthesis/post_certificate/PROTOCOL.md @@ -0,0 +1,149 @@ +# Frozen protocol: post-certificate graph-synthesis improvements + +Baseline: `9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98` (merged PR #20) +Protocol date: 2026-09-18 +Status: frozen before implementation/execution +Fresh Jev service calls planned: 0 +New scientific documents planned: 0 +Seed: 20260923 + +## Scope and evidence boundary + +The merged evidence separates semantic extraction quality from structural correctness. Repeated prompt/routing/calibration variants have not established a robust semantic advantage, while bounded exact graph algorithms, dependence-aware certificates, repair semantics and delta maintenance have repeatedly passed controlled tests. This protocol therefore tests five **structural / decision-theoretic extensions** suggested by those results rather than another prompt variant. + +The five mechanisms below were not found as executed implementations in the baseline repository inventory. That is a repository-scope statement, not a worldwide novelty claim. Their ingredients have substantial prior art: treewidth/variable-elimination dynamic programming, incremental view maintenance and transactions, query resilience/deletion propagation, robust/minimax decision making under imprecise probabilities, and weighted constraint/hypergraph optimization. + +No experiment changes candidate extraction, accepted Jev edges, production defaults, or the frozen original evidence. Controlled priorities, probabilities, costs and constraints are supplied inputs and must not be reinterpreted as calibrated factual truth. + +## H1 - Induced-width exact conflict optimization + +### Motivation +Prior studies established exact handling for bounded enumeration, forests, cutsets and bipartite conflict graphs. A remaining gap is connected non-bipartite cyclic structure that is still tractable because its induced width is small. + +### Method +Implement max-sum variable elimination for maximum-weight compatible assertion selection over pairwise conflict factors. A deterministic min-fill elimination order is computed without using assertion weights. Execution is allowed only when: +- induced width <= 4; +- every factor scope is <= 5 variables; +- cumulative materialized factor states <= 250,000. + +Otherwise the component is staged without a partial write. The returned assignment includes objective value, selected assertion IDs, elimination order, induced width and a direct feasibility check. + +### Frozen test +- 160 seeded small connected graphs, 8-16 vertices, generated from bounded-width constructions with random non-negative integer weights. +- Independent exhaustive subset oracle for every small fixture. +- 8 connected large triangle-chain / partial-2-tree fixtures from 33 through 1,025 vertices, checked by an independently implemented chain dynamic program. +- 5 over-width clique controls (K6-K10) that must stage. +- 8 input-order permutations per first 64 small fixtures. + +### Primary target +Zero objective, feasibility, witness or permutation failures; all 8 large tractable fixtures solved; all 5 over-width controls staged. On the 12-16 vertex small subset, counted max-sum table states must be at least 90% below the full 2^n assignment count in aggregate. + +## H2 - Transactional batch delta maintenance + +### Motivation +Merged studies validate local incremental maintenance and revision checks, but explicitly stop at sequential in-memory updates. Real graph changes often arrive as batches whose derived consequences must be all-or-nothing. + +### Method +Implement an in-memory transactional dependency engine for Boolean primitives and derived facts over an acyclic dependency graph. A transaction: +1. validates expected revision and every primitive change; +2. computes the affected reverse-dependency closure; +3. evaluates the new values in topological order against a copy-on-write overlay; +4. commits the complete overlay only if every evaluation succeeds. + +Injected evaluation failure, malformed update, or stale revision must leave both values and revision unchanged. This is atomic batch behavior only; no crash durability or concurrent database-isolation claim is made. + +### Frozen test +- 128 seeded modular DAGs with 64 primitive nodes and 256 derived nodes. +- Five 1-4 primitive transactions per DAG (640 accepted local transactions total), each compared with independent full recomputation from the post-transaction primitive snapshot. +- 64 injected evaluation-failure controls, 64 stale-revision controls and 64 malformed-update controls. +- 16 connected-control DAGs in which one primitive intentionally reaches nearly every derived node. + +### Primary target +Zero snapshot mismatches and zero partial-write/revision failures. Local transactions must perform at least 80% fewer derived-node evaluations than full recomputation in aggregate. The connected control must remain reported separately and must not be used to infer universal savings. + +## H3 - Exact query-resilience certificates + +### Motivation +The repository can classify query answers across repairs, but binary certainty does not quantify how much evidence must change before a currently true monotone query becomes false. A robustness margin can distinguish a query supported by many independent proof paths from one resting on a single fragile atom. + +### Method +For a monotone DNF lineage with positive integer evidence-removal costs, compute the minimum-cost evidence set whose deletion hits every active proof clause. The implementation uses: +- incidence-component decomposition; +- forced singleton reductions; +- branch-and-bound with deterministic branching; +- a disjoint-clause lower bound; +- explicit deletion witness validation. + +Connected components above 18 distinct evidence atoms stage rather than silently approximate. + +### Frozen test +- 160 seeded small DNF fixtures with <=12 atoms and 2-10 proof clauses. +- Independent exhaustive deletion-subset oracle for every small fixture. +- 8 analytic large fixtures composed of hundreds to thousands of disconnected proof components, with closed-form expected resilience. +- 6 over-cap connected controls that must stage. +- Mutation checks that every returned deletion set actually falsifies the query and removing any positive-cost proper subset does not beat the reported optimum. + +### Primary target +Zero optimum/witness/oracle failures; all 8 analytic large fixtures solved exactly; all 6 over-cap controls staged. The result is a resilience certificate relative to supplied lineage and costs, not factual truth. + +## H4 - Interval-minimax query review + +### Motivation +Prior query-directed review assumes point probabilities. Multiple merged studies show that point risk estimates and calibration can fail. Review selection should therefore be stress-tested against uncertainty in the supplied probabilities themselves. + +### Method +Each primitive has an independent probability interval [lo, hi]. For a fixed review budget of two primitives, choose the review set that minimizes the **worst-case expected residual Bernoulli variance** of supplied monotone queries across all interval endpoint vectors. Perfect review reveals the selected primitive states. The production method evaluates query probability by memoized Shannon recursion; the independent oracle enumerates complete Boolean worlds directly. + +A midpoint selector using the same expected-loss objective at interval midpoints is the comparator. This study does not remove the conditional-independence assumption; it tests robustness to marginal imprecision only. + +### Frozen test +- 96 seeded six-atom interval fixtures with 1-3 monotone DNF queries. +- 32 engineered interval controls where midpoint ranking is intentionally fragile. +- Every candidate review pair checked by the independent world-enumeration oracle. +- Degenerate point-interval controls must reduce exactly to the point-probability solution. + +### Primary target +Zero production/oracle objective discrepancies above 1e-10. The minimax selector's worst-case objective must never exceed the midpoint selector's worst-case objective, and must be strictly lower on at least 20% of the 128 non-degenerate fixtures. + +## H5 - N-ary conflict constraints + +### Motivation +Every merged graph-repair optimizer represents incompatibility as pairwise edges. Some consistency rules are genuinely n-ary (for example, “not all three assertions may coexist”) and a pairwise clique projection can remove compatible pairs unnecessarily. + +### Method +Generalize max-sum elimination to forbidden hyperedge factors: a factor contributes negative infinity only when every member of the forbidden set is selected. Pairwise conflicts are size-2 hyperedges. The same deterministic induced-width and state caps as H1 apply, and returned selections are checked directly against every hyperedge. + +### Frozen test +- 160 seeded small weighted hypergraphs with 8-14 vertices, size-2 and size-3 forbidden sets, compared with exhaustive subset optimization. +- 8 large three-consecutive-forbidden chain fixtures from 64 through 2,048 vertices. With unit weights, the known optimum is n - floor(n/3). +- Pairwise-clique projection of each size-3 hyperedge is retained as an explicit over-conservative baseline. +- 5 high-arity / over-width controls must stage. +- 8 permutations per first 64 small fixtures. + +### Primary target +Zero objective/feasibility/oracle/permutation failures; all 8 large chain fixtures solved exactly; all 5 controls staged. On every large chain, the n-ary optimizer must retain at least as much supplied utility as pairwise projection and strictly more on all fixtures. + +## Reporting and falsification rules + +- A failed conjunction remains failed even if some endpoints improve. +- No five-result success percentage may be reported. +- Negative/null outcomes remain in results and figures. +- Work counters (factor states, node evaluations) are not wall-clock, API-latency or cloud-cost measurements. +- No controlled algorithm result may be described as independent Jev semantic accuracy. +- No external system superiority is claimed without a matched executed baseline. +- The current manuscript must preserve every prior study and append this section additively. + +## Reproducibility target + +The implementation will provide: +- `graph_synthesis/post_certificate/run.py` +- `graph_synthesis/post_certificate/methods.py` +- `graph_synthesis/post_certificate/tests/` +- `graph_synthesis/post_certificate/results.json` +- `graph_synthesis/post_certificate/summary.csv` +- `graph_synthesis/post_certificate/RESULTS.md` +- five deterministic SVG figures +- additive updates to `CURRENT_RESULTS.md` and `manuscript/paper-current.md` +- a read-only GitHub Actions workflow that replays all five experiments and tests. + +Protocol thresholds, fixture counts, caps and seed must not be changed after benchmark execution except to correct an implementation bug; any such correction must be documented without changing the frozen success criteria. From 0a8f0097d3cb640efc2d107b66bc1a0f03b7fb3c Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:37:09 -0400 Subject: [PATCH 03/21] research: implement post-certificate mechanisms --- graph_synthesis/post_certificates/methods.py | 184 +++++++++++++++++++ 1 file changed, 184 insertions(+) create mode 100644 graph_synthesis/post_certificates/methods.py diff --git a/graph_synthesis/post_certificates/methods.py b/graph_synthesis/post_certificates/methods.py new file mode 100644 index 0000000..a708a5e --- /dev/null +++ b/graph_synthesis/post_certificates/methods.py @@ -0,0 +1,184 @@ +"""Second-order research mechanisms derived from the dependence-aware certificate study.""" +from __future__ import annotations + +from itertools import combinations +import math +import numpy as np +from scipy.optimize import linprog + +from ..reliability.methods import graph_input +from ..certificates import graphs + +PAD = 1e-7 + + +def _staged(reason, atoms=0): + return {"status": reason, "certified": False, "lower": 0.0, "upper": 1.0, "atoms": atoms} + + +def interval_lineage_bounds(proofs, intervals, *, atom_cap=10): + """Extremal monotone-DNF probability under interval-valued atom marginals.""" + try: + if type(atom_cap) is not int or not 0 <= atom_cap <= 10: + return _staged("invalid_atom_cap") + if not isinstance(intervals, dict) or any(not isinstance(a, str) or not a for a in intervals): + return _staged("invalid_intervals") + atoms = sorted(intervals) + bounds = {} + for a in atoms: + pair = intervals[a] + if not isinstance(pair, (list, tuple)) or len(pair) != 2: + return _staged("invalid_intervals", len(atoms)) + lo, hi = pair + if any(isinstance(v, bool) or not isinstance(v, (int, float)) or not math.isfinite(v) for v in (lo, hi)): + return _staged("invalid_intervals", len(atoms)) + lo, hi = float(lo), float(hi) + if not 0 <= lo <= hi <= 1: + return _staged("invalid_intervals", len(atoms)) + bounds[a] = (lo, hi) + if len(atoms) > atom_cap: + return _staged("capacity_staged", len(atoms)) + + def term(value): + if isinstance(value, str): + raise ValueError + result = tuple(sorted(set(value))) + if any(a not in bounds for a in result): + raise ValueError + return result + + terms = sorted({term(p) for p in proofs}) + if len(terms) > 256: + return _staged("capacity_staged", len(atoms)) + positions = {a: i for i, a in enumerate(atoms)} + worlds = np.arange(1 << len(atoms), dtype=np.int64) + + def indicator(term_atoms): + mask = sum(1 << positions[a] for a in term_atoms) + return ((worlds & mask) == mask).astype(float) + + objective = np.zeros(len(worlds)) + for p in terms: + objective = np.maximum(objective, indicator(p)) + + eq = np.ones((1, len(worlds))) + eq_target = np.array([1.0]) + ub_rows, ub_targets = [], [] + atom_vectors = {} + for a in atoms: + vec = indicator((a,)) + atom_vectors[a] = vec + lo, hi = bounds[a] + ub_rows.extend([vec, -vec]) + ub_targets.extend([hi, -lo]) + aub = np.asarray(ub_rows, dtype=float) if ub_rows else None + bub = np.asarray(ub_targets, dtype=float) if ub_targets else None + + solutions = [] + for sign in (1.0, -1.0): + result = linprog(sign * objective, A_ub=aub, b_ub=bub, A_eq=eq, b_eq=eq_target, + bounds=(0, None), method="highs", + options={"dual_feasibility_tolerance": 1e-9, "primal_feasibility_tolerance": 1e-9}) + if not result.success or result.x is None: + return _staged("infeasible_or_solver_staged", len(atoms)) + x = np.asarray(result.x, dtype=float) + if not np.isfinite(x).all() or float(np.min(x)) < -1e-8 or abs(float(x.sum()) - 1.0) > 1e-7: + return _staged("residual_staged", len(atoms)) + marginals = {a: float(atom_vectors[a] @ x) for a in atoms} + if any(marginals[a] < bounds[a][0] - 1e-7 or marginals[a] > bounds[a][1] + 1e-7 for a in atoms): + return _staged("residual_staged", len(atoms)) + value = float(objective @ x) + solutions.append({"value": value, "support": [[int(i), float(v)] for i, v in enumerate(x) if v > 1e-12], + "marginals": marginals}) + lo = max(0.0, solutions[0]["value"] - PAD) + hi = min(1.0, solutions[1]["value"] + PAD) + if lo > hi + 1e-7: + return _staged("numeric_inconsistency", len(atoms)) + return {"status": "bounded", "certified": True, "lower": lo, "upper": hi, "atoms": len(atoms), + "worlds": len(worlds), "min": solutions[0], "max": solutions[1], + "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded."} + except (TypeError, ValueError, KeyError, OverflowError): + return _staged("invalid_input") + + +def exact_point_bounds(proofs, probabilities): + return interval_lineage_bounds(proofs, {a: (p, p) for a, p in probabilities.items()}) + + +def near_bipartite_solve(weights, edges, separator, *, separator_cap=4): + """Exact MWIS by conditioning on a verified small separator whose removal is bipartite.""" + try: + edges = [tuple(e) for e in edges] + adj = graph_input(weights, edges) + if isinstance(separator, str): + raise ValueError + sep = tuple(sorted(set(separator))) + if len(sep) > separator_cap or any(v not in weights for v in sep): + return {"selected": [], "staged": sorted(weights), "utility": 0, "status": "separator_staged", "branches": []} + residual_nodes = [v for v in weights if v not in sep] + residual_weights = {v: weights[v] for v in residual_nodes} + residual_edges = [(a, b) for a, b in edges if a in residual_weights and b in residual_weights] + radj = graph_input(residual_weights, residual_edges) + if any(graphs.coloring(radj, g) is None for g in graphs.groups(radj)): + return {"selected": [], "staged": sorted(weights), "utility": 0, "status": "not_transversal", "branches": []} + + best = None + branches = [] + for mask in range(1 << len(sep)): + chosen = {sep[i] for i in range(len(sep)) if mask & (1 << i)} + if any(b in adj[a] for a, b in combinations(sorted(chosen), 2)): + continue + blocked = set(sep) + for v in chosen: + blocked.update(adj[v]) + rw = {v: w for v, w in weights.items() if v not in blocked} + re = [(a, b) for a, b in edges if a in rw and b in rw] + residual = graphs.solve(rw, re) + if residual["staged"]: + branches.append({"chosen_separator": sorted(chosen), "status": "residual_staged"}) + continue + selected = sorted(chosen | set(residual["selected"])) + utility = sum(weights[v] for v in selected) + branch = {"chosen_separator": sorted(chosen), "selected": selected, "utility": utility, + "residual_components": residual["components"], "status": "solved"} + branches.append(branch) + if best is None or utility > best["utility"] or (utility == best["utility"] and tuple(selected) < tuple(best["selected"])): + best = branch + if best is None: + return {"selected": [], "staged": sorted(weights), "utility": 0, "status": "residual_staged", "branches": branches} + return {"selected": best["selected"], "staged": [], "utility": best["utility"], "status": "solved", + "separator": list(sep), "branches": branches} + except (TypeError, ValueError, KeyError, ArithmeticError): + return {"selected": [], "staged": sorted(weights) if isinstance(weights, dict) else [], "utility": 0, + "status": "invalid_input", "branches": []} + + +def build_margin_index(weights, edges): + base = graphs.solve(weights, edges) + if base["staged"]: + return {"status": "staged", "optimum": None, "entries": {}, "solve_calls": 1} + entries = {} + for v in sorted(weights): + inc = graphs.forced(weights, edges, include=[v]) + exc = graphs.forced(weights, edges, exclude=[v]) + if inc is None or inc["staged"] or exc["staged"]: + return {"status": "staged", "optimum": base["utility"], "entries": entries, "solve_calls": 1 + 2 * len(entries)} + entries[v] = {"include_utility": inc["utility"], "include_witness": inc["selected"], + "exclude_utility": exc["utility"], "exclude_witness": exc["selected"]} + return {"status": "indexed", "optimum": base["utility"], "entries": entries, "solve_calls": 1 + 2 * len(entries)} + + +def query_margin(index, vertex, epsilon=0): + if index.get("status") != "indexed" or vertex not in index["entries"] or type(epsilon) is not int or epsilon < 0: + return {"classification": "unsupported"} + threshold = index["optimum"] - epsilon + entry = index["entries"][vertex] + record = {"threshold": threshold, "optimum": index["optimum"], "epsilon": epsilon, "required": [vertex], + "possible_repair": None, "counterexample": None} + if entry["include_utility"] < threshold: + return {**record, "classification": "impossible"} + record["possible_repair"] = entry["include_witness"] + if entry["exclude_utility"] < threshold: + return {**record, "classification": "certain"} + record["counterexample"] = entry["exclude_witness"] + return {**record, "classification": "ambiguous"} From 4c726ddc2c5f638b61015f398f30f4c5dc21df9e Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:37:59 -0400 Subject: [PATCH 04/21] research: add frozen post-certificate benchmark runner --- graph_synthesis/post_certificates/run.py | 363 +++++++++++++++++++++++ 1 file changed, 363 insertions(+) create mode 100644 graph_synthesis/post_certificates/run.py diff --git a/graph_synthesis/post_certificates/run.py b/graph_synthesis/post_certificates/run.py new file mode 100644 index 0000000..592d3cf --- /dev/null +++ b/graph_synthesis/post_certificates/run.py @@ -0,0 +1,363 @@ +"""Execute the frozen post-certificate suite with no service calls.""" +from __future__ import annotations + +import argparse +from itertools import combinations +import json +import math +from pathlib import Path +import random +import socket +import statistics +from unittest.mock import patch + +import numpy as np + +from . import methods +from ..adaptive.run import load, INPUT +from ..certificates import risk, lineage, graphs +from ..certificates.run import experiment_lineage, independent_sets, valid_repair +from ..reliability.run import calibration, proper_scores + +ROOT = Path(__file__).resolve().parents[2] +HERE = Path(__file__).resolve().parent +SEED = 20260923 +DRAWS = 4000 +BASELINE_COMMIT = "9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98" +PROTOCOL_COMMIT = "f923e8d41ca5953d9793fadcc3730cfe9fc70b3a" + + +def write(path, value): + path.parent.mkdir(parents=True, exist_ok=True) + path.write_text(json.dumps(value, sort_keys=True, indent=2, allow_nan=False) + "\n", encoding="utf-8", newline="\n") + + +def normalized(value): + return json.loads(json.dumps(value, sort_keys=True, allow_nan=False)) + + +def bootstrap(deltas): + values = np.asarray(deltas, dtype=float) + rng = np.random.default_rng(SEED) + sample = values[rng.integers(0, len(values), size=(DRAWS, len(values)))].mean(axis=1) + return {"point": float(values.mean()), "95": np.quantile(sample, [.025, .975]).tolist(), + "99": np.quantile(sample, [.005, .995]).tolist(), "groups": len(values), "draws": DRAWS} + + +def choose_weight(rows): + if not rows: + raise ValueError("Need development folds") + grid = [] + for i in range(11): + w = i / 10 + brier = statistics.mean((w*r["feature"] + (1-w)*r["random"] - r["truth"])**2 for r in rows) + grid.append({"weight": w, "brier": brier}) + best = min(grid, key=lambda r: (r["brier"], abs(r["weight"]-.5), r["weight"])) + return best["weight"], grid + + +def experiment_stack(development, test): + feature = calibration(development, test) + feature_folds = {r["group"]: r for r in feature["folds"]} + folds = [] + for group in sorted({r["group"] for r in development}): + held = [r for r in development if r["group"] == group] + exposure = risk.counts(held) + if not exposure or group not in feature_folds: + continue + training = [r for r in development if r["group"] != group] + fitted = risk.fit(training) + random_p = risk.predict(exposure, fitted)[group] + folds.append({"group": group, "n": exposure[group], "feature": feature_folds[group]["probability"], + "random": random_p, "truth": feature_folds[group]["truth"]}) + global_w, global_grid = choose_weight(folds) + weights = {"global": global_w} + grids = {"global": global_grid} + for name, predicate in (("singleton", lambda r: r["n"] == 1), ("multi", lambda r: r["n"] > 1)): + subset = [r for r in folds if predicate(r)] + if len(subset) >= 8: + weights[name], grids[name] = choose_weight(subset) + else: + weights[name], grids[name] = global_w, [] + + fitted = risk.fit(development) + exposure = risk.counts(test) + actual = risk.counts(test, truth=True) + truth = {g: int(v["k"] > 0) for g, v in actual.items()} + random_pred = risk.predict(exposure, fitted) + feature_pred = {r["group"]: r["baseline"] for r in feature["group_predictions"]} + if set(random_pred) != set(feature_pred) or set(truth) != set(random_pred): + raise ValueError("H1 group denominator mismatch") + stacked = {} + rows = [] + for g in sorted(truth): + stratum = "singleton" if exposure[g] == 1 else "multi" + w = weights[stratum] + p = w * feature_pred[g] + (1-w) * random_pred[g] + stacked[g] = p + rows.append({"group": g, "n": exposure[g], "stratum": stratum, "weight": w, "feature": feature_pred[g], + "random": random_pred[g], "stacked": p, "truth": truth[g]}) + scores = {"feature": proper_scores(feature_pred, truth), "random_effects": proper_scores(random_pred, truth), + "stacked": proper_scores(stacked, truth)} + primary = (scores["stacked"]["brier"] <= scores["feature"]["brier"] + 1e-15 + and scores["stacked"]["brier"] <= .97 * scores["random_effects"]["brier"] + 1e-15 + and abs(scores["stacked"]["bias"]) <= .03) + return {"primary_target_met": primary, "weights": weights, "grids": grids, "folds": folds, + "fold_counts": {"all": len(folds), "singleton": sum(r["n"] == 1 for r in folds), "multi": sum(r["n"] > 1 for r in folds)}, + "test_counts": {"groups": len(rows), "singleton": sum(r["n"] == 1 for r in rows), "multi": sum(r["n"] > 1 for r in rows)}, + "scores": scores, "predictions": rows, + "paired_vs_feature": bootstrap([(stacked[g]-truth[g])**2-(feature_pred[g]-truth[g])**2 for g in sorted(truth)]), + "paired_vs_random": bootstrap([(stacked[g]-truth[g])**2-(random_pred[g]-truth[g])**2 for g in sorted(truth)])} + + +def pair_probability(case, pair): + atoms = sorted(case["probabilities"]) + pos = {a: i for i, a in enumerate(atoms)} + return sum(v for world, v in enumerate(case["actual_joint"]) if all(world & (1 << pos[a]) for a in pair)) + + +def experiment_constraint_acquisition(): + source = experiment_lineage() + cases = [] + containment_failures = widening_failures = 0 + base_widths, greedy_widths, lex_widths = [], [], [] + for case in source["random_cases"]: + atoms = sorted(case["probabilities"]) + pairs = list(combinations(atoms, 2)) + pair_values = {pair: pair_probability(case, pair) for pair in pairs} + base = lineage.bounds(case["proofs"], case["probabilities"]) + current, selected, steps = base, [], [] + remaining = set(pairs) + for _ in range(min(3, len(remaining))): + candidates = [] + for pair in sorted(remaining): + constraints = [(list(p), pair_values[p]) for p in selected + [pair]] + result = lineage.bounds(case["proofs"], case["probabilities"], constraints) + candidates.append((result["upper"]-result["lower"], pair, result)) + width, pair, result = min(candidates, key=lambda x: (x[0], x[1])) + if width > current["upper"]-current["lower"] + 1e-8: + widening_failures += 1 + selected.append(pair) + remaining.remove(pair) + steps.append({"pair": list(pair), "probability": pair_values[pair], "result": result}) + current = result + lex_pairs = pairs[:3] + lex = lineage.bounds(case["proofs"], case["probabilities"], [(list(p), pair_values[p]) for p in lex_pairs]) + truth = case["truth"] + if not current["lower"] - 1e-8 <= truth <= current["upper"] + 1e-8: + containment_failures += 1 + base_widths.append(base["upper"]-base["lower"]) + greedy_widths.append(current["upper"]-current["lower"]) + lex_widths.append(lex["upper"]-lex["lower"]) + cases.append({"id": case["id"], "truth": truth, "base": base, "greedy": current, "lexicographic": lex, + "selected": [list(p) for p in selected], "steps": steps}) + means = {"marginal": statistics.mean(base_widths), "greedy": statistics.mean(greedy_widths), + "lexicographic": statistics.mean(lex_widths)} + primary = (containment_failures == 0 and widening_failures == 0 + and means["greedy"] <= .75 * means["marginal"] + 1e-12 + and means["greedy"] <= .90 * means["lexicographic"] + 1e-12) + return {"primary_target_met": primary, "cases": cases, "means": means, + "containment_failures": containment_failures, "widening_failures": widening_failures, + "budget": 3, "source_fixture_count": len(cases)} + + +def exhaustive_oracle(weights, edges): + return max(independent_sets(weights, edges), key=lambda x: (x[0], tuple(x[1])))[0] + + +def experiment_near_bipartite(): + rng = random.Random(SEED + 3) + small, failures, invariance_failures = [], 0, 0 + for case in range(128): + n = rng.randrange(6, 13) + s = rng.randrange(1, min(4, n-2)) + sep = [f"s{i}" for i in range(s)] + residual = [f"v{i}" for i in range(n-s)] + split = max(1, len(residual)//2) + left, right = residual[:split], residual[split:] + weights = {v: rng.randrange(10) for v in sep + residual} + edges = [(a, b) for a in left for b in right if rng.random() < .35] + edges += [(a, b) for a in sep for b in residual if rng.random() < .35] + edges += [(a, b) for a, b in combinations(sep, 2) if rng.random() < .25] + oracle = exhaustive_oracle(weights, edges) + result = methods.near_bipartite_solve(weights, edges, sep) + reordered = methods.near_bipartite_solve(dict(reversed(list(weights.items()))), list(reversed(edges))*2, list(reversed(sep))) + ok = not result["staged"] and result["utility"] == oracle and valid_repair(weights, edges, result["selected"], oracle) + failures += int(not ok) + invariance_failures += int(result["utility"] != reordered["utility"] or result["selected"] != reordered["selected"]) + small.append({"id": case, "weights": weights, "edges": edges, "separator": sep, "oracle": oracle, "result": result, "ok": ok}) + + large = [] + for n in (512, 1024, 2048): + weights = {f"v{i:04}": 1 for i in range(n)} + weights["apex"] = 3 + edges = [(f"v{i:04}", f"v{(i+1)%n:04}") for i in range(n)] + edges += [("apex", "v0000"), ("apex", "v0001")] + result = methods.near_bipartite_solve(weights, edges, ["apex"]) + prior = graphs.solve(weights, edges) + expected = n//2 + 2 + ok = result["utility"] == expected and not result["staged"] and len(prior["staged"]) == n+1 + failures += int(not ok) + large.append({"residual_vertices": n, "expected": expected, "result_utility": result["utility"], + "prior_staged": len(prior["staged"]), "ok": ok}) + invalid = methods.near_bipartite_solve({"a":1,"b":1,"c":1}, [("a","b"),("b","c"),("c","a")], []) + malformed = methods.near_bipartite_solve({str(i):1 for i in range(6)}, [], [str(i) for i in range(5)]) + controls_ok = bool(invalid["staged"]) and bool(malformed["staged"]) + failures += int(not controls_ok) + return {"primary_target_met": failures == 0 and invariance_failures == 0 and all(r["ok"] for r in large), + "small": small, "small_failures": failures - int(not controls_ok) - sum(int(not r["ok"]) for r in large), + "invariance_failures": invariance_failures, "large": large, + "controls": {"non_transversal": invalid, "over_cap": malformed, "ok": controls_ok}} + + +def witness_ok(weights, edges, selected, threshold, include=None, exclude=None): + selected = list(selected or []) + if not valid_repair(weights, edges, selected, threshold): + return False + chosen = set(selected) + return (include is None or include in chosen) and (exclude is None or exclude not in chosen) + + +def experiment_query_index(): + rng = random.Random(SEED + 4) + cases, mismatches, witness_failures = [], 0, 0 + baseline_calls = index_calls = query_count = 0 + actual_baseline_calls = 0 + for case in range(128): + n = rng.randrange(4, 11) + weights = {f"v{i}": rng.randrange(10) for i in range(n)} + edges = [(a, b) for a, b in combinations(weights, 2) if rng.random() < .28] + index = methods.build_margin_index(weights, edges) + if index["status"] != "indexed": + raise AssertionError("Small H4 fixture unexpectedly staged") + index_calls += index["solve_calls"] + trials = [] + epsilons = sorted({0, 1, 2, math.floor(.05*index["optimum"]), math.floor(.10*index["optimum"])}) + for v in sorted(weights): + for epsilon in epsilons: + query_count += 1 + baseline_calls += 3 + old = graphs.query(weights, edges, [v], epsilon=epsilon) + actual_baseline_calls += 2 if old["classification"] == "impossible" else 3 + new = methods.query_margin(index, v, epsilon) + same = old["classification"] == new["classification"] + mismatches += int(not same) + threshold = index["optimum"] - epsilon + ok = same + if new["classification"] in ("certain", "ambiguous"): + ok = ok and witness_ok(weights, edges, new["possible_repair"], threshold, include=v) + if new["classification"] == "ambiguous": + ok = ok and witness_ok(weights, edges, new["counterexample"], threshold, exclude=v) + witness_failures += int(not ok) + trials.append({"vertex": v, "epsilon": epsilon, "old": old["classification"], "new": new["classification"], "ok": ok}) + cases.append({"id": case, "n": n, "optimum": index["optimum"], "epsilons": epsilons, "trials": trials, + "index_solve_calls": index["solve_calls"]}) + saving = 1 - index_calls / baseline_calls + conservative_saving = 1 - index_calls / actual_baseline_calls + return {"primary_target_met": mismatches == 0 and witness_failures == 0 and saving >= .70, + "cases": cases, "queries": query_count, "mismatches": mismatches, "witness_failures": witness_failures, + "baseline_solve_calls_frozen": baseline_calls, "baseline_solve_calls_actual_control": actual_baseline_calls, + "index_solve_calls": index_calls, "saving": saving, "conservative_saving": conservative_saving} + + +def fact_truth(proofs, joint, atoms): + pos = {a: i for i, a in enumerate(atoms)} + return sum(v for world, v in enumerate(joint) + if any(all(world & (1 << pos[a]) for a in proof) for proof in proofs)) + + +def experiment_interval_marginals(): + rng = random.Random(SEED + 5) + cases, containment_failures = [], 0 + interval_widths, point_widths = [], [] + for case in range(128): + n = rng.randrange(2, 7) + atoms = [f"a{i}" for i in range(n)] + masses = [rng.randrange(1, 100) for _ in range(1 << n)] + total = sum(masses) + joint = [v/total for v in masses] + marginals = {a: sum(v for world, v in enumerate(joint) if world & (1 << i)) for i, a in enumerate(atoms)} + proofs = [sorted(rng.sample(atoms, rng.randrange(1, min(3,n)+1))) for _ in range(rng.randrange(1, 7))] + truth = fact_truth(proofs, joint, atoms) + intervals, points = {}, {} + for a in atoms: + radius = rng.uniform(.02, .10) + lo, hi = max(0., marginals[a]-radius), min(1., marginals[a]+radius) + points[a] = min(hi, max(lo, marginals[a] + rng.uniform(-.9*radius, .9*radius))) + intervals[a] = [lo, hi] + interval_result = methods.interval_lineage_bounds(proofs, intervals) + point_result = methods.exact_point_bounds(proofs, points) + ok = interval_result["certified"] and interval_result["lower"]-1e-7 <= truth <= interval_result["upper"]+1e-7 + containment_failures += int(not ok) + interval_widths.append(interval_result["upper"]-interval_result["lower"]) + point_widths.append(point_result["upper"]-point_result["lower"]) + cases.append({"id": case, "proofs": proofs, "truth": truth, "true_marginals": marginals, "intervals": intervals, + "point_estimates": points, "interval_result": interval_result, "point_result": point_result, "ok": ok}) + + controls, prevented = [], 0 + for i in range(20): + actual = .80 + .007*i + point = .97 + .001*i + intervals = {"a": [max(0., actual-.01), min(1., point+.005)]} + exact = methods.exact_point_bounds([["a"]], {"a": point}) + robust = methods.interval_lineage_bounds([["a"]], intervals) + blocked = exact["lower"] >= .95 and actual < .95 and robust["lower"] < .95 + prevented += int(blocked) + controls.append({"actual": actual, "point": point, "interval": intervals["a"], "point_result": exact, + "interval_result": robust, "prevented": blocked}) + malformed = [ + methods.interval_lineage_bounds([["a"]], {"a": [.8, .7]}), + methods.interval_lineage_bounds([["a"]], {"a": [float("nan"), .9]}), + methods.interval_lineage_bounds([["a"]], {"a": [-.1, .9]}), + methods.interval_lineage_bounds([["missing"]], {"a": [.1, .9]}), + methods.interval_lineage_bounds([["a0"]], {f"a{i}":[.1,.9] for i in range(11)}) + ] + malformed_certifying = sum(int(r.get("certified", False)) for r in malformed) + means = {"point_width": statistics.mean(point_widths), "interval_width": statistics.mean(interval_widths)} + return {"primary_target_met": containment_failures == 0 and prevented == 20 and malformed_certifying == 0, + "cases": cases, "containment_failures": containment_failures, "controls": controls, + "false_admissions_prevented": prevented, "malformed": malformed, + "malformed_certifying": malformed_certifying, "means": means} + + +def execute(): + values, calls, audit = load() + development = [r for r in values if r["split"] == "development"] + test = [r for r in values if r["split"] == "test"] + if (len(development), len(test)) != (73, 263): + raise ValueError("Frozen input split changed") + if {r["group"] for r in development}.intersection(r["group"] for r in test): + raise ValueError("Source-group leakage") + result = {"schema_version": 1, "baseline_commit": BASELINE_COMMIT, "protocol_commit": PROTOCOL_COMMIT, + "fresh_service_calls": 0, "seed": SEED, + "evidence": "H1 saved-response reuse; H2-H5 controlled algorithmic fixtures. No independent semantic generalization.", + "input_verification": audit, + "development": {"n": len(development), "groups": len({r["group"] for r in development})}, + "test": {"n": len(test), "groups": len({r["group"] for r in test})}, + "H1": experiment_stack(development, test), + "H2": experiment_constraint_acquisition(), + "H3": experiment_near_bipartite(), + "H4": experiment_query_index(), + "H5": experiment_interval_marginals()} + return normalized(result) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--check", action="store_true") + args = parser.parse_args() + with patch.object(socket.socket, "connect", side_effect=RuntimeError("Network forbidden in post-certificate replay")), \ + patch.object(socket, "create_connection", side_effect=RuntimeError("Network forbidden in post-certificate replay")): + result = execute() + if args.check: + from ..verify import compare_json + compare_json(json.loads((HERE/"results.json").read_text(encoding="utf-8")), result) + else: + write(HERE/"results.json", result) + print(json.dumps({"status": "reproduced" if args.check else "executed", + "targets": {k: result[k]["primary_target_met"] for k in ("H1","H2","H3","H4","H5")}, + "fresh_service_calls": 0}, sort_keys=True)) + + +if __name__ == "__main__": + main() From c3d243f3d22c930879c5b23c1c1663890b482df5 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:39:30 -0400 Subject: [PATCH 05/21] test: cover post-certificate mechanisms --- .../tests/test_post_certificates.py | 92 +++++++++++++++++++ 1 file changed, 92 insertions(+) create mode 100644 graph_synthesis/post_certificates/tests/test_post_certificates.py diff --git a/graph_synthesis/post_certificates/tests/test_post_certificates.py b/graph_synthesis/post_certificates/tests/test_post_certificates.py new file mode 100644 index 0000000..3b840a7 --- /dev/null +++ b/graph_synthesis/post_certificates/tests/test_post_certificates.py @@ -0,0 +1,92 @@ +"""Regression and adversarial tests for the post-certificate suite.""" +from __future__ import annotations + +import unittest + +from graph_synthesis.post_certificates import methods +from graph_synthesis.certificates import graphs + + +class IntervalMarginalTests(unittest.TestCase): + def test_point_singleton_is_exact_up_to_padding(self): + result = methods.exact_point_bounds([["a"]], {"a": .8}) + self.assertTrue(result["certified"]) + self.assertLessEqual(result["lower"], .8) + self.assertGreaterEqual(result["upper"], .8) + self.assertLess(result["upper"] - result["lower"], 1e-5) + + def test_interval_singleton_tracks_uncertainty(self): + result = methods.interval_lineage_bounds([["a"]], {"a": [.7, .9]}) + self.assertTrue(result["certified"]) + self.assertLessEqual(result["lower"], .700001) + self.assertGreaterEqual(result["upper"], .899999) + + def test_bad_intervals_fail_closed(self): + bad = ( + {"a": [.9, .8]}, + {"a": [-.1, .8]}, + {"a": [.1, 1.1]}, + {"a": [float("nan"), .8]}, + ) + for intervals in bad: + with self.subTest(intervals=intervals): + result = methods.interval_lineage_bounds([["a"]], intervals) + self.assertFalse(result["certified"]) + self.assertEqual((result["lower"], result["upper"]), (0.0, 1.0)) + + def test_unknown_atom_fails_closed(self): + result = methods.interval_lineage_bounds([["b"]], {"a": [.1, .9]}) + self.assertFalse(result["certified"]) + + +class NearBipartiteTests(unittest.TestCase): + def test_triangle_solved_with_one_vertex_separator(self): + weights = {"a": 4, "b": 3, "c": 2} + edges = [("a", "b"), ("b", "c"), ("c", "a")] + result = methods.near_bipartite_solve(weights, edges, ["a"]) + self.assertFalse(result["staged"]) + self.assertEqual(result["utility"], 4) + self.assertEqual(result["selected"], ["a"]) + + def test_bad_separator_stages(self): + weights = {"a": 1, "b": 1, "c": 1} + edges = [("a", "b"), ("b", "c"), ("c", "a")] + result = methods.near_bipartite_solve(weights, edges, []) + self.assertTrue(result["staged"]) + self.assertEqual(result["status"], "not_transversal") + + def test_over_cap_separator_stages(self): + weights = {str(i): 1 for i in range(6)} + result = methods.near_bipartite_solve(weights, [], list(weights)[:5]) + self.assertTrue(result["staged"]) + + +class MarginIndexTests(unittest.TestCase): + def test_matches_existing_singleton_query(self): + weights = {"a": 2, "b": 2, "c": 1} + edges = [("a", "b")] + index = methods.build_margin_index(weights, edges) + self.assertEqual(index["status"], "indexed") + for vertex in weights: + for epsilon in (0, 1, 2): + with self.subTest(vertex=vertex, epsilon=epsilon): + expected = graphs.query(weights, edges, [vertex], epsilon=epsilon) + actual = methods.query_margin(index, vertex, epsilon) + self.assertEqual(actual["classification"], expected["classification"]) + + def test_equal_pair_is_ambiguous(self): + weights = {"a": 1, "b": 1} + edges = [("a", "b")] + index = methods.build_margin_index(weights, edges) + self.assertEqual(methods.query_margin(index, "a", 0)["classification"], "ambiguous") + + def test_dominant_vertex_is_certain(self): + weights = {"a": 2, "b": 1} + edges = [("a", "b")] + index = methods.build_margin_index(weights, edges) + self.assertEqual(methods.query_margin(index, "a", 0)["classification"], "certain") + self.assertEqual(methods.query_margin(index, "b", 0)["classification"], "impossible") + + +if __name__ == "__main__": + unittest.main() From 6d42004f4e84d069b8de99f87db6d0cfdc212f62 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:40:45 -0400 Subject: [PATCH 06/21] research: add post-certificate report and figure generator --- graph_synthesis/post_certificates/report.py | 264 ++++++++++++++++++++ 1 file changed, 264 insertions(+) create mode 100644 graph_synthesis/post_certificates/report.py diff --git a/graph_synthesis/post_certificates/report.py b/graph_synthesis/post_certificates/report.py new file mode 100644 index 0000000..6d3926a --- /dev/null +++ b/graph_synthesis/post_certificates/report.py @@ -0,0 +1,264 @@ +"""Generate the post-certificate report, five evidence-derived figures, and additive paper text.""" +from __future__ import annotations + +import argparse +import csv +import json +from pathlib import Path +import re + +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +from .run import ROOT, HERE + +START = "" +END = "" +ANCHOR = "" + + +def outcome(row): + return "Met" if row["primary_target_met"] else "Not met" + + +def pct(value): + return f"{100*value:.2f}%" + + +def insert(text, body): + text = re.sub(re.escape(START) + r".*?" + re.escape(END) + r"\s*", "", text, flags=re.S) + if text.count(ANCHOR) != 1: + raise ValueError("Expected exactly one certificate-section anchor") + before, after = text.split(ANCHOR, 1) + return before + ANCHOR + "\n\n" + START + "\n\n" + body.strip() + "\n\n" + END + "\n\n" + after.lstrip() + + +def save(fig, stem): + folder = HERE / "figures" + folder.mkdir(parents=True, exist_ok=True) + fig.tight_layout() + fig.savefig(folder / f"{stem}.svg", bbox_inches="tight") + fig.savefig(folder / f"{stem}.png", dpi=300, bbox_inches="tight") + plt.close(fig) + + +def figures(r): + h1, h2, h3, h4, h5 = [r[f"H{i}"] for i in range(1, 6)] + + fig, ax = plt.subplots(figsize=(7.2, 4.4)) + names = ["Feature risk", "Random effects", "Stacked"] + vals = [h1["scores"]["feature"]["brier"], h1["scores"]["random_effects"]["brier"], h1["scores"]["stacked"]["brier"]] + ax.bar(names, vals) + ax.set_ylabel("Brier score (lower is better)") + ax.set_title("H1 — Source-contamination forecast Brier") + for i, v in enumerate(vals): + ax.text(i, v, f"{v:.4f}", ha="center", va="bottom") + save(fig, "01_stacked_risk") + + fig, ax = plt.subplots(figsize=(7.2, 4.4)) + names = ["Marginals only", "Lexicographic 3", "Greedy 3"] + vals = [h2["means"]["marginal"], h2["means"]["lexicographic"], h2["means"]["greedy"]] + ax.bar(names, vals) + ax.set_ylabel("Mean certified interval width") + ax.set_title("H2 — Dependence-constraint acquisition") + for i, v in enumerate(vals): + ax.text(i, v, f"{v:.4f}", ha="center", va="bottom") + save(fig, "02_constraint_acquisition") + + fig, ax = plt.subplots(figsize=(7.2, 4.4)) + xs = [row["residual_vertices"] for row in h3["large"]] + expected = [row["expected"] for row in h3["large"]] + observed = [row["result_utility"] for row in h3["large"]] + ax.plot(xs, expected, marker="o", label="Analytic optimum") + ax.plot(xs, observed, marker="x", linestyle="--", label="Separator-conditioned solver") + ax.set_xlabel("Residual cycle vertices") + ax.set_ylabel("Maximum supplied-priority utility") + ax.set_title("H3 — Large near-bipartite exact optimization") + ax.legend() + save(fig, "03_near_bipartite") + + fig, ax = plt.subplots(figsize=(7.2, 4.4)) + vals = [h4["baseline_solve_calls_frozen"], h4["index_solve_calls"]] + ax.bar(["Repeated queries", "Margin index"], vals) + ax.set_ylabel("Top-level optimization invocations") + ax.set_title("H4 — Reusable singleton-query margins") + for i, v in enumerate(vals): + ax.text(i, v, f"{v:,}", ha="center", va="bottom") + save(fig, "04_query_index") + + fig, ax = plt.subplots(figsize=(7.2, 4.4)) + point_false = sum(int(row["point_result"]["lower"] >= .95 and row["actual"] < .95) for row in h5["controls"]) + interval_false = sum(int(row["interval_result"]["lower"] >= .95 and row["actual"] < .95) for row in h5["controls"]) + vals = [point_false, interval_false] + ax.bar(["Biased point marginal", "Interval marginal"], vals) + ax.set_ylabel("False admissions at 0.95") + ax.set_title("H5 — Designed marginal-misspecification controls") + for i, v in enumerate(vals): + ax.text(i, v, str(v), ha="center", va="bottom") + save(fig, "05_interval_marginals") + + +def write_summary(r): + rows = [ + ["H1", "Exposure-stratified source-risk stacking", outcome(r["H1"]), "stacked_brier", r["H1"]["scores"]["stacked"]["brier"]], + ["H2", "Greedy dependence-constraint acquisition", outcome(r["H2"]), "mean_final_width", r["H2"]["means"]["greedy"]], + ["H3", "Separator-conditioned near-bipartite solver", outcome(r["H3"]), "small_failures", r["H3"]["small_failures"]], + ["H4", "Reusable repair-margin query index", outcome(r["H4"]), "solve_call_saving", r["H4"]["saving"]], + ["H5", "Interval-marginal dependence certificates", outcome(r["H5"]), "false_admissions_prevented", r["H5"]["false_admissions_prevented"]], + ] + with (HERE / "summary.csv").open("w", encoding="utf-8", newline="") as handle: + writer = csv.writer(handle, lineterminator="\n") + writer.writerow(["hypothesis", "mechanism", "outcome", "primary_metric", "value"]) + writer.writerows(rows) + + +def render(r): + a, b, c, d, e = [r[f"H{i}"] for i in range(1, 6)] + h3_large = ", ".join(f"{x['residual_vertices']}→{x['result_utility']}/{x['expected']}" for x in c["large"]) + return f"""# Five post-certificate improvements for Jev graph synthesis + +Timothy Wayne Gregg | AI-assisted author-review research extension | September 18, 2026 + +## Abstract + +The dependence-aware certificate study left an asymmetric frontier: its source-random-effects forecast improved Brier by only 6.39% and missed its frozen target, while its dependence bounds, flow certificates, repair-invariant queries and local delta maintenance passed controlled tests. This pre-execution-frozen follow-up tests five responses to those remaining boundaries. The outcomes are: H1 **{outcome(a).lower()}**, H2 **{outcome(b).lower()}**, H3 **{outcome(c).lower()}**, H4 **{outcome(d).lower()}**, and H5 **{outcome(e).lower()}**. No fresh Jev calls are made. H1 reuses previously inspected saved responses; H2–H5 are controlled algorithmic experiments. These results are not new semantic-accuracy evidence and are not a comparison against KARMA or another external graph system. + +## 1. Frozen methodology and novelty boundary + +The protocol was committed as `{r['protocol_commit']}` against merged baseline `{r['baseline_commit']}` before implementation or execution. It fixes generators, thresholds, comparators and seed {r['seed']}. Existing package studies already contain relation-level stacking, fixed pairwise-dependence sensitivity analyses, bipartite flow, repair ambiguity and exact-marginal credal bounds. The five experiments here test different package-level integrations: source-group forecast stacking, active dependence-constraint acquisition, verified small-separator conditioning beyond bipartite graphs, reusable singleton repair margins and interval-valued marginal premises. This is a repository-scoped experiment distinction, not a worldwide novelty claim. + +**Fresh Jev service calls: {r['fresh_service_calls']}.** No production graph policy is changed. The controlled structural fixtures do not establish real-world source truth, reviewer behavior, calibrated Jev probabilities or end-to-end database latency. A pass means only that the frozen target for the stated evidence population was met. + +| Hypothesis | Frozen primary requirement | Result | Evidence class | +|---|---|---|---| +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | {outcome(a)} | Previously inspected saved-response source forecasts | +| H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | {outcome(b)} | Supplied finite joint distributions | +| H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | {outcome(c)} | Supplied weighted conflict graphs | +| H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | {outcome(d)} | Repeated controlled singleton queries | +| H5: interval marginals | Zero containment failures; prevent 20/20 designed false admissions; fail closed on malformed inputs | {outcome(e)} | Supplied joint distributions and uncertainty intervals | + +## 2. H1 — Exposure-stratified source-risk stacking + +The certificate result suggested that within-source dependence contains information but did not outperform the richer feature-risk forecast. H1 therefore combines the two forecasts without using evaluation labels for fitting. Leave-one-source-group-out development predictions select convex weights separately for singleton and multi-edge exposure strata when each stratum has at least eight folds; otherwise the global development weight is used. + +Development selected feature weights: global **{a['weights']['global']:.1f}**, singleton **{a['weights']['singleton']:.1f}**, multi-edge **{a['weights']['multi']:.1f}**. Development fold counts are {a['fold_counts']['all']} total, {a['fold_counts']['singleton']} singleton and {a['fold_counts']['multi']} multi-edge. Evaluation scoring uses the identical {a['test_counts']['groups']} nonempty source groups as the comparators ({a['test_counts']['singleton']} singleton, {a['test_counts']['multi']} multi-edge). + +| Forecast | Brier | Clipped log loss | Bias | +|---|---:|---:|---:| +| Existing feature-risk | {a['scores']['feature']['brier']:.6f} | {a['scores']['feature']['log_loss']:.6f} | {a['scores']['feature']['bias']:+.6f} | +| Certificate random effects | {a['scores']['random_effects']['brier']:.6f} | {a['scores']['random_effects']['log_loss']:.6f} | {a['scores']['random_effects']['bias']:+.6f} | +| Exposure-stratified stack | {a['scores']['stacked']['brier']:.6f} | {a['scores']['stacked']['log_loss']:.6f} | {a['scores']['stacked']['bias']:+.6f} | + +The stacked-minus-feature paired Brier mean is {a['paired_vs_feature']['point']:+.6f}, with descriptive 95% interval [{a['paired_vs_feature']['95'][0]:+.6f}, {a['paired_vs_feature']['95'][1]:+.6f}]. The stacked-minus-random-effects mean is {a['paired_vs_random']['point']:+.6f}, with 95% interval [{a['paired_vs_random']['95'][0]:+.6f}, {a['paired_vs_random']['95'][1]:+.6f}]. The frozen conjunction is **{outcome(a).lower()}**. These intervals condition on the selected development weights and reuse already inspected evaluation data; they are not independent validation. + +![H1. Forecast Brier on the identical nonempty source-group denominator.](figures/01_stacked_risk.png) + +## 3. H2 — Greedy acquisition of dependence constraints + +Marginal-only dependence bounds are safe but can be wide. H2 treats exact pairwise intersections from each fixture's supplied joint distribution as controlled observations and asks which three would most narrow the conclusion interval. At each step the policy evaluates every not-yet-observed pair and selects the one giving the smallest certified width; the comparator spends the same budget on the first three lexicographic pairs. + +Across {b['source_fixture_count']} fixtures, mean width is **{b['means']['marginal']:.6f}** from marginals alone, **{b['means']['lexicographic']:.6f}** after the lexicographic budget and **{b['means']['greedy']:.6f}** after the greedy budget. Truth-containment failures: **{b['containment_failures']}**. Chosen-step widening failures: **{b['widening_failures']}**. The frozen target is **{outcome(b).lower()}**. + +This is an oracle value-of-information experiment: it assumes the selected pairwise intersections can be supplied exactly. It does not show that those quantities are observable cheaply, that Jev scores are source reliabilities, or that a production estimator would preserve the same benefit. + +![H2. Mean certified width before and after equal three-constraint budgets.](figures/02_constraint_acquisition.png) + +## 4. H3 — Separator-conditioned near-bipartite exact optimization + +The prior flow certificate handles bipartite components but stages sufficiently large non-bipartite ones. H3 accepts a supplied separator of at most four vertices, verifies that deleting it leaves a bipartite graph, enumerates every independent separator choice and solves each residual branch with the existing certified bipartite solver. An invalid separator is not trusted; it stages. + +The 128 small exhaustive fixtures have **{c['small_failures']}** oracle failures and **{c['invariance_failures']}** order/duplicate-invariance failures. Large residual-cycle results are {h3_large}, written as residual vertices → obtained/analytic utility. The current generic solver stages respectively **{', '.join(str(x['prior_staged']) for x in c['large'])}** vertices on those fixtures. Malformed and non-transversal controls stage safely: **{c['controls']['ok']}**. The frozen target is **{outcome(c).lower()}**. + +The supplied priorities and conflict edges remain premises. Exact maximum supplied-priority utility does not establish that a selected assertion is factually true. + +![H3. Separator-conditioned utility versus the analytic optimum.](figures/03_near_bipartite.png) + +## 5. H4 — Reusable repair-margin singleton query index + +The certificate query implementation recomputes a base optimum plus forced-in/forced-out alternatives for repeated questions. H4 precomputes each vertex's inclusion and exclusion margin once, then classifies any singleton query at any tested tolerance by comparing those margins with the tolerance threshold. + +Across **{d['queries']}** repeated singleton queries, classification mismatches are **{d['mismatches']}** and witness failures are **{d['witness_failures']}**. Under the frozen top-level solve-count accounting, repeated queries require **{d['baseline_solve_calls_frozen']:,}** invocations versus **{d['index_solve_calls']:,}** for index construction, a **{pct(d['saving'])}** reduction. A control using the existing query's realized early-exit count gives a still-separated descriptive reduction of **{pct(d['conservative_saving'])}**. The frozen target is **{outcome(d).lower()}**. + +This index is deliberately limited to singleton queries and in-memory top-level optimization calls. It is not a measured SQL/database speedup or a semantic guarantee. + +![H4. Frozen-accounting optimization calls for repeated queries versus one reusable index.](figures/04_query_index.png) + +## 6. H5 — Interval-marginal dependence certificates + +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. + +Across 128 arbitrary-joint fixtures, truth-containment failures are **{e['containment_failures']}**. Mean point-bound width is **{e['means']['point_width']:.6f}** and mean interval-marginal width is **{e['means']['interval_width']:.6f}**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **{e['false_admissions_prevented']}/20** designed false admissions. Malformed inputs returning a certifying interval: **{e['malformed_certifying']}**. The frozen target is **{outcome(e).lower()}**. + +The interval itself is still a supplied assumption. If the real marginal falls outside it, the certificate can again be wrong. This test converts one known premise-error mode into explicit uncertainty; it does not validate how such intervals should be estimated from real sources. + +![H5. False admissions on designed marginal-misspecification controls.](figures/05_interval_marginals.png) + +## 7. Interpretation and falsification boundary + +The five experiments are intentionally heterogeneous. H1 asks whether two already observed forecast signals combine on reused response data. H2 asks whether a constrained information budget can reduce dependence uncertainty on finite controlled worlds. H3 and H4 test exact structural reuse. H5 asks whether uncertainty in the probability premises can be represented rather than ignored. Their pass/fail outcomes must not be pooled into a semantic success percentage. + +The strongest remaining scientific boundary is unchanged: freeze a policy before observing a new source-disjoint, independently adjudicated corpus and compare full graph quality, downstream queries, provenance errors, reviewer mistakes, resource budgets and staging against appropriate external baselines. None of the controlled algorithmic passes can substitute for that prospective semantic evaluation. + +## 8. Reproduction + +```bash +python -m pip install -r graph_synthesis/post_certificates/requirements.txt +python -B -m graph_synthesis.post_certificates.run +python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v +python -B -m graph_synthesis.post_certificates.run --check +python -B -m graph_synthesis.post_certificates.report --figures --update-paper +python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf +``` + +The machine-readable results retain the controlled fixtures, selected pair constraints, optimization witnesses, development-only weights, uncertainty intervals and falsifying controls. The five PNG/SVG pairs and summary table are generated from those recorded results. Earlier study artifacts are not rewritten. +""" + + +def update_paper(r): + def rebase(match): + url = match.group(1) + if "://" in url or url.startswith("#"): + return "](" + url + ")" + path = (HERE / url).resolve() + if not path.is_relative_to(ROOT): + raise ValueError("Link outside repository") + return "](../" + path.relative_to(ROOT).as_posix() + ")" + + full = re.sub(r"\]\(([^)]+)\)", rebase, render(r)) + paper = ROOT / "manuscript/paper-current.md" + paper.write_text(insert(paper.read_text(encoding="utf-8"), full), encoding="utf-8", newline="\n") + + outcomes = "; ".join(f"H{i} {outcome(r[f'H{i}']).lower()}" for i in range(1, 6)) + note = ( + "## Five post-certificate improvements after PR #20\n\n" + "[Executed report](graph_synthesis/post_certificates/RESULTS.md), " + "[frozen protocol](graph_synthesis/post_certificates/PROTOCOL.md), " + "[five figures](graph_synthesis/post_certificates/figures/) and " + "[complete updated paper](manuscript/paper-current.pdf). " + + outcomes + + ". H1 reuses previously inspected saved responses; H2-H5 are controlled algorithms. " + "The suite tests source-risk stacking, active dependence constraints, verified near-bipartite separators, " + "reusable singleton repair margins and interval-valued probability premises. " + "No fresh Jev calls, independent semantic-accuracy claim, worldwide novelty claim or production-policy change." + ) + current = ROOT / "CURRENT_RESULTS.md" + current.write_text(insert(current.read_text(encoding="utf-8"), note), encoding="utf-8", newline="\n") + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--figures", action="store_true") + parser.add_argument("--update-paper", action="store_true") + args = parser.parse_args() + r = json.loads((HERE / "results.json").read_text(encoding="utf-8")) + (HERE / "RESULTS.md").write_text(render(r), encoding="utf-8", newline="\n") + write_summary(r) + if args.figures: + figures(r) + if args.update_paper: + update_paper(r) + + +if __name__ == "__main__": + main() From 7dc22674d0afeb71c84eeeb5d4370a9f1ae0b2cc Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:40:51 -0400 Subject: [PATCH 07/21] research: initialize post-certificate package --- graph_synthesis/post_certificates/__init__.py | 1 + 1 file changed, 1 insertion(+) create mode 100644 graph_synthesis/post_certificates/__init__.py diff --git a/graph_synthesis/post_certificates/__init__.py b/graph_synthesis/post_certificates/__init__.py new file mode 100644 index 0000000..749f518 --- /dev/null +++ b/graph_synthesis/post_certificates/__init__.py @@ -0,0 +1 @@ +"""Five post-certificate graph-synthesis research extensions.""" From 68183d378062ed43e7cd8d38beee53eee3e46b5b Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:40:53 -0400 Subject: [PATCH 08/21] research: add post-certificate dependencies --- graph_synthesis/post_certificates/requirements.txt | 2 ++ 1 file changed, 2 insertions(+) create mode 100644 graph_synthesis/post_certificates/requirements.txt diff --git a/graph_synthesis/post_certificates/requirements.txt b/graph_synthesis/post_certificates/requirements.txt new file mode 100644 index 0000000..61c3c35 --- /dev/null +++ b/graph_synthesis/post_certificates/requirements.txt @@ -0,0 +1,2 @@ +-r ../requirements-figures.txt +scipy==1.17.0 From 9ace2db3527f6365eb02306ea722ccebccc2bbb7 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:41:21 -0400 Subject: [PATCH 09/21] ci: execute and publish frozen post-certificate study --- .../workflows/post-certificates-publisher.yml | 61 +++++++++++++++++++ 1 file changed, 61 insertions(+) create mode 100644 .github/workflows/post-certificates-publisher.yml diff --git a/.github/workflows/post-certificates-publisher.yml b/.github/workflows/post-certificates-publisher.yml new file mode 100644 index 0000000..fd11259 --- /dev/null +++ b/.github/workflows/post-certificates-publisher.yml @@ -0,0 +1,61 @@ +name: Post-certificate benchmark publisher + +on: + push: + branches: + - research/post-certificate-improvements-20260918 + +permissions: + contents: write + +concurrency: + group: post-certificates-publisher + cancel-in-progress: false + +jobs: + execute-and-publish: + if: ${{ !contains(github.event.head_commit.message, '[post-certificates generated]') }} + runs-on: ubuntu-latest + timeout-minutes: 30 + env: + PYTHONDONTWRITEBYTECODE: "1" + steps: + - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 + with: + ref: ${{ github.sha }} + fetch-depth: 0 + - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 + with: + python-version: "3.12" + - name: Install frozen research dependencies + run: python -m pip install -r graph_synthesis/post_certificates/requirements.txt + - name: Verify frozen protocol ancestry + shell: bash + run: | + set -euo pipefail + protocol=f923e8d41ca5953d9793fadcc3730cfe9fc70b3a + git merge-base --is-ancestor "$protocol" HEAD + git show "$protocol:graph_synthesis/post_certificates/PROTOCOL.md" | cmp - graph_synthesis/post_certificates/PROTOCOL.md + - name: Run mechanism tests + run: python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v + - name: Execute frozen benchmarks + run: | + python -B -m graph_synthesis.post_certificates.run + python -B -m graph_synthesis.post_certificates.run --check + - name: Generate report, figures and complete manuscript + run: | + python -B -m graph_synthesis.post_certificates.report --figures --update-paper + python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf + - name: Publish generated evidence to this research branch + shell: bash + run: | + set -euo pipefail + git config user.name "github-actions[bot]" + git config user.email "41898282+github-actions[bot]@users.noreply.github.com" + git add -A -- graph_synthesis/post_certificates CURRENT_RESULTS.md manuscript + if git diff --cached --quiet; then + echo "No generated changes" + exit 0 + fi + git commit -m "research: execute frozen post-certificate benchmarks [post-certificates generated]" + git push origin "HEAD:${GITHUB_REF_NAME}" From dd4cb2e752f307de9c982480e894773eb3dbb851 Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" <41898282+github-actions[bot]@users.noreply.github.com> Date: Fri, 18 Sep 2026 14:42:45 +0000 Subject: [PATCH 10/21] research: execute frozen post-certificate benchmarks [post-certificates generated] --- CURRENT_RESULTS.md | 8 + graph_synthesis/post_certificates/RESULTS.md | 96 + .../figures/01_stacked_risk.png | Bin 0 -> 91004 bytes .../figures/01_stacked_risk.svg | 1163 + .../figures/02_constraint_acquisition.png | Bin 0 -> 96895 bytes .../figures/02_constraint_acquisition.svg | 1156 + .../figures/03_near_bipartite.png | Bin 0 -> 154424 bytes .../figures/03_near_bipartite.svg | 1401 + .../figures/04_query_index.png | Bin 0 -> 93568 bytes .../figures/04_query_index.svg | 1210 + .../figures/05_interval_marginals.png | Bin 0 -> 86092 bytes .../figures/05_interval_marginals.svg | 997 + .../post_certificates/results.json | 188802 +++++++++++++++ graph_synthesis/post_certificates/summary.csv | 6 + manuscript/paper-current.build.json | 4 +- manuscript/paper-current.html | 116 + manuscript/paper-current.md | 101 + manuscript/paper-current.pdf | Bin 6599621 -> 7103664 bytes 18 files changed, 195058 insertions(+), 2 deletions(-) create mode 100644 graph_synthesis/post_certificates/RESULTS.md create mode 100644 graph_synthesis/post_certificates/figures/01_stacked_risk.png create mode 100644 graph_synthesis/post_certificates/figures/01_stacked_risk.svg create mode 100644 graph_synthesis/post_certificates/figures/02_constraint_acquisition.png create mode 100644 graph_synthesis/post_certificates/figures/02_constraint_acquisition.svg create mode 100644 graph_synthesis/post_certificates/figures/03_near_bipartite.png create mode 100644 graph_synthesis/post_certificates/figures/03_near_bipartite.svg create mode 100644 graph_synthesis/post_certificates/figures/04_query_index.png create mode 100644 graph_synthesis/post_certificates/figures/04_query_index.svg create mode 100644 graph_synthesis/post_certificates/figures/05_interval_marginals.png create mode 100644 graph_synthesis/post_certificates/figures/05_interval_marginals.svg create mode 100644 graph_synthesis/post_certificates/results.json create mode 100644 graph_synthesis/post_certificates/summary.csv diff --git a/CURRENT_RESULTS.md b/CURRENT_RESULTS.md index 7b7bf2e..20df58b 100644 --- a/CURRENT_RESULTS.md +++ b/CURRENT_RESULTS.md @@ -90,6 +90,14 @@ Original H4 is concurrent replication of the separately merged bipartite study, + + +## Five post-certificate improvements after PR #20 + +[Executed report](graph_synthesis/post_certificates/RESULTS.md), [frozen protocol](graph_synthesis/post_certificates/PROTOCOL.md), [five figures](graph_synthesis/post_certificates/figures/) and [complete updated paper](manuscript/paper-current.pdf). H1 not met; H2 met; H3 met; H4 met; H5 met. H1 reuses previously inspected saved responses; H2-H5 are controlled algorithms. The suite tests source-risk stacking, active dependence constraints, verified near-bipartite separators, reusable singleton repair margins and interval-valued probability premises. No fresh Jev calls, independent semantic-accuracy claim, worldwide novelty claim or production-policy change. + + + Read the [updated full paper](manuscript/paper-current.md), [PDF](manuscript/paper-current.pdf), or [HTML](manuscript/paper-current.html). The fresh full Jev run does **not** reproduce the original interval-based entity improvement: its selected-minus-baseline macro-F1 interval includes zero. Entity accuracy still rises descriptively from 405/413 to 408/413; relation accuracy rises from 286/339 to 290/339, also without a resolved macro-F1 effect. This repeats previously inspected data; it is not independent validation. diff --git a/graph_synthesis/post_certificates/RESULTS.md b/graph_synthesis/post_certificates/RESULTS.md new file mode 100644 index 0000000..d2bae0e --- /dev/null +++ b/graph_synthesis/post_certificates/RESULTS.md @@ -0,0 +1,96 @@ +# Five post-certificate improvements for Jev graph synthesis + +Timothy Wayne Gregg | AI-assisted author-review research extension | September 18, 2026 + +## Abstract + +The dependence-aware certificate study left an asymmetric frontier: its source-random-effects forecast improved Brier by only 6.39% and missed its frozen target, while its dependence bounds, flow certificates, repair-invariant queries and local delta maintenance passed controlled tests. This pre-execution-frozen follow-up tests five responses to those remaining boundaries. The outcomes are: H1 **not met**, H2 **met**, H3 **met**, H4 **met**, and H5 **met**. No fresh Jev calls are made. H1 reuses previously inspected saved responses; H2–H5 are controlled algorithmic experiments. These results are not new semantic-accuracy evidence and are not a comparison against KARMA or another external graph system. + +## 1. Frozen methodology and novelty boundary + +The protocol was committed as `f923e8d41ca5953d9793fadcc3730cfe9fc70b3a` against merged baseline `9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98` before implementation or execution. It fixes generators, thresholds, comparators and seed 20260923. Existing package studies already contain relation-level stacking, fixed pairwise-dependence sensitivity analyses, bipartite flow, repair ambiguity and exact-marginal credal bounds. The five experiments here test different package-level integrations: source-group forecast stacking, active dependence-constraint acquisition, verified small-separator conditioning beyond bipartite graphs, reusable singleton repair margins and interval-valued marginal premises. This is a repository-scoped experiment distinction, not a worldwide novelty claim. + +**Fresh Jev service calls: 0.** No production graph policy is changed. The controlled structural fixtures do not establish real-world source truth, reviewer behavior, calibrated Jev probabilities or end-to-end database latency. A pass means only that the frozen target for the stated evidence population was met. + +| Hypothesis | Frozen primary requirement | Result | Evidence class | +|---|---|---|---| +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | Not met | Previously inspected saved-response source forecasts | +| H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | Met | Supplied finite joint distributions | +| H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | Met | Supplied weighted conflict graphs | +| H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | Met | Repeated controlled singleton queries | +| H5: interval marginals | Zero containment failures; prevent 20/20 designed false admissions; fail closed on malformed inputs | Met | Supplied joint distributions and uncertainty intervals | + +## 2. H1 — Exposure-stratified source-risk stacking + +The certificate result suggested that within-source dependence contains information but did not outperform the richer feature-risk forecast. H1 therefore combines the two forecasts without using evaluation labels for fitting. Leave-one-source-group-out development predictions select convex weights separately for singleton and multi-edge exposure strata when each stratum has at least eight folds; otherwise the global development weight is used. + +Development selected feature weights: global **1.0**, singleton **1.0**, multi-edge **1.0**. Development fold counts are 23 total, 14 singleton and 9 multi-edge. Evaluation scoring uses the identical 98 nonempty source groups as the comparators (60 singleton, 38 multi-edge). + +| Forecast | Brier | Clipped log loss | Bias | +|---|---:|---:|---:| +| Existing feature-risk | 0.128923 | 0.467074 | -0.072629 | +| Certificate random effects | 0.131444 | 0.435042 | -0.012382 | +| Exposure-stratified stack | 0.128923 | 0.467074 | -0.072629 | + +The stacked-minus-feature paired Brier mean is +0.000000, with descriptive 95% interval [+0.000000, +0.000000]. The stacked-minus-random-effects mean is -0.002522, with 95% interval [-0.028381, +0.021169]. The frozen conjunction is **not met**. These intervals condition on the selected development weights and reuse already inspected evaluation data; they are not independent validation. + +![H1. Forecast Brier on the identical nonempty source-group denominator.](figures/01_stacked_risk.png) + +## 3. H2 — Greedy acquisition of dependence constraints + +Marginal-only dependence bounds are safe but can be wide. H2 treats exact pairwise intersections from each fixture's supplied joint distribution as controlled observations and asks which three would most narrow the conclusion interval. At each step the policy evaluates every not-yet-observed pair and selects the one giving the smallest certified width; the comparator spends the same budget on the first three lexicographic pairs. + +Across 128 fixtures, mean width is **0.326563** from marginals alone, **0.176527** after the lexicographic budget and **0.096687** after the greedy budget. Truth-containment failures: **0**. Chosen-step widening failures: **0**. The frozen target is **met**. + +This is an oracle value-of-information experiment: it assumes the selected pairwise intersections can be supplied exactly. It does not show that those quantities are observable cheaply, that Jev scores are source reliabilities, or that a production estimator would preserve the same benefit. + +![H2. Mean certified width before and after equal three-constraint budgets.](figures/02_constraint_acquisition.png) + +## 4. H3 — Separator-conditioned near-bipartite exact optimization + +The prior flow certificate handles bipartite components but stages sufficiently large non-bipartite ones. H3 accepts a supplied separator of at most four vertices, verifies that deleting it leaves a bipartite graph, enumerates every independent separator choice and solves each residual branch with the existing certified bipartite solver. An invalid separator is not trusted; it stages. + +The 128 small exhaustive fixtures have **0** oracle failures and **0** order/duplicate-invariance failures. Large residual-cycle results are 512→258/258, 1024→514/514, 2048→1026/1026, written as residual vertices → obtained/analytic utility. The current generic solver stages respectively **513, 1025, 2049** vertices on those fixtures. Malformed and non-transversal controls stage safely: **True**. The frozen target is **met**. + +The supplied priorities and conflict edges remain premises. Exact maximum supplied-priority utility does not establish that a selected assertion is factually true. + +![H3. Separator-conditioned utility versus the analytic optimum.](figures/03_near_bipartite.png) + +## 5. H4 — Reusable repair-margin singleton query index + +The certificate query implementation recomputes a base optimum plus forced-in/forced-out alternatives for repeated questions. H4 precomputes each vertex's inclusion and exclusion margin once, then classifies any singleton query at any tested tolerance by comparing those margins with the tolerance threshold. + +Across **2653** repeated singleton queries, classification mismatches are **0** and witness failures are **0**. Under the frozen top-level solve-count accounting, repeated queries require **7,959** invocations versus **1,814** for index construction, a **77.21%** reduction. A control using the existing query's realized early-exit count gives a still-separated descriptive reduction of **74.41%**. The frozen target is **met**. + +This index is deliberately limited to singleton queries and in-memory top-level optimization calls. It is not a measured SQL/database speedup or a semantic guarantee. + +![H4. Frozen-accounting optimization calls for repeated queries versus one reusable index.](figures/04_query_index.png) + +## 6. H5 — Interval-marginal dependence certificates + +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. + +Across 128 arbitrary-joint fixtures, truth-containment failures are **0**. Mean point-bound width is **0.361057** and mean interval-marginal width is **0.467497**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **20/20** designed false admissions. Malformed inputs returning a certifying interval: **0**. The frozen target is **met**. + +The interval itself is still a supplied assumption. If the real marginal falls outside it, the certificate can again be wrong. This test converts one known premise-error mode into explicit uncertainty; it does not validate how such intervals should be estimated from real sources. + +![H5. False admissions on designed marginal-misspecification controls.](figures/05_interval_marginals.png) + +## 7. Interpretation and falsification boundary + +The five experiments are intentionally heterogeneous. H1 asks whether two already observed forecast signals combine on reused response data. H2 asks whether a constrained information budget can reduce dependence uncertainty on finite controlled worlds. H3 and H4 test exact structural reuse. H5 asks whether uncertainty in the probability premises can be represented rather than ignored. Their pass/fail outcomes must not be pooled into a semantic success percentage. + +The strongest remaining scientific boundary is unchanged: freeze a policy before observing a new source-disjoint, independently adjudicated corpus and compare full graph quality, downstream queries, provenance errors, reviewer mistakes, resource budgets and staging against appropriate external baselines. None of the controlled algorithmic passes can substitute for that prospective semantic evaluation. + +## 8. Reproduction + +```bash +python -m pip install -r graph_synthesis/post_certificates/requirements.txt +python -B -m graph_synthesis.post_certificates.run +python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v +python -B -m graph_synthesis.post_certificates.run --check +python -B -m graph_synthesis.post_certificates.report --figures --update-paper +python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf +``` + +The machine-readable results retain the controlled fixtures, selected pair constraints, optimization witnesses, development-only weights, uncertainty intervals and falsifying controls. The five PNG/SVG pairs and summary table are generated from those recorded results. 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"worlds": 2 + }, + "prevented": true + } + ], + "false_admissions_prevented": 20, + "malformed": [ + { + "atoms": 1, + "certified": false, + "lower": 0.0, + "status": "invalid_intervals", + "upper": 1.0 + }, + { + "atoms": 1, + "certified": false, + "lower": 0.0, + "status": "invalid_intervals", + "upper": 1.0 + }, + { + "atoms": 1, + "certified": false, + "lower": 0.0, + "status": "invalid_intervals", + "upper": 1.0 + }, + { + "atoms": 0, + "certified": false, + "lower": 0.0, + "status": "invalid_input", + "upper": 1.0 + }, + { + "atoms": 11, + "certified": false, + "lower": 0.0, + "status": "capacity_staged", + "upper": 1.0 + } + ], + "malformed_certifying": 0, + "means": { + "interval_width": 0.46749696923052303, + "point_width": 0.3610570392199911 + }, + "primary_target_met": true + }, + "baseline_commit": "9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98", + "development": { + "groups": 40, + "n": 73 + }, + "evidence": "H1 saved-response reuse; H2-H5 controlled algorithmic fixtures. No independent semantic generalization.", + "fresh_service_calls": 0, + "input_verification": { + "analysis_comparison": "exact counts/labels/structure; float atol 1e-14, rtol 1e-12 for cross-platform roundoff", + "analysis_reproduced": true, + "calls": 3024, + "cases": 336, + "distinct_repeat_sites": true, + "gold_free_requests": true, + "group_disjoint": true, + "limitation": "Request/response journals are local provenance, not provider-signed attestations; failed responses remain failures.", + "network_disabled_replay": "identical predictions and execution after CRLF/LF normalization", + "raw_response_validation": true, + "status": "passed" + }, + "protocol_commit": "f923e8d41ca5953d9793fadcc3730cfe9fc70b3a", + "schema_version": 1, + "seed": 20260923, + "test": { + "groups": 149, + "n": 263 + } +} diff --git a/graph_synthesis/post_certificates/summary.csv b/graph_synthesis/post_certificates/summary.csv new file mode 100644 index 0000000..7d2ba76 --- /dev/null +++ b/graph_synthesis/post_certificates/summary.csv @@ -0,0 +1,6 @@ +hypothesis,mechanism,outcome,primary_metric,value +H1,Exposure-stratified source-risk stacking,Not met,stacked_brier,0.12892258111773036 +H2,Greedy dependence-constraint acquisition,Met,mean_final_width,0.09668671758032904 +H3,Separator-conditioned near-bipartite solver,Met,small_failures,0 +H4,Reusable repair-margin query index,Met,solve_call_saving,0.7720819198391757 +H5,Interval-marginal dependence certificates,Met,false_admissions_prevented,20 diff --git a/manuscript/paper-current.build.json b/manuscript/paper-current.build.json index a0fb2ba..0811502 100644 --- a/manuscript/paper-current.build.json +++ b/manuscript/paper-current.build.json @@ -1,6 +1,6 @@ { - "source_sha256": "e827a0d64a77e279a3d96c6692a1b9c62a29297b3bce1331f3ce61e7afa90357", + "source_sha256": "c6d96f51d1a6495bae800a19496d053a8f7cbd647424eb725e99c00e5928a0a6", "renderer_sha256": "b1ecb302903b01907b9c4dbd931862ef0f62c50804ca92077fd9ac26eb1354a4", - "pdf_sha256": "f2d5e99e224f74316bd11da163c6f69c9746e84d6efa47d37f5e49f6ee7365f2", + "pdf_sha256": "ed05bfbf4f37f3d5a82966c02c024da44d3e074ce553a050c779382bfc293a7e", "note": "Local-only assets; PDF bytes may vary with renderer and fonts." } diff --git a/manuscript/paper-current.html b/manuscript/paper-current.html index 8840c43..d23b21f 100644 --- a/manuscript/paper-current.html +++ b/manuscript/paper-current.html @@ -3273,6 +3273,122 @@

9. Primary foundations

  • A Feature-based Classification of Model Repair Approaches and the TypeSafe typed-decision interface.

    • These sources motivate established components; they do not validate this implementation or certify worldwide novelty.

    +

    Five post-certificate improvements for Jev graph synthesis

    +

    Timothy Wayne Gregg | AI-assisted author-review research extension | September 18, 2026

    +

    Abstract

    +

    The dependence-aware certificate study left an asymmetric frontier: its source-random-effects forecast improved Brier by only 6.39% and missed its frozen target, while its dependence bounds, flow certificates, repair-invariant queries and local delta maintenance passed controlled tests. This pre-execution-frozen follow-up tests five responses to those remaining boundaries. The outcomes are: H1 not met, H2 met, H3 met, H4 met, and H5 met. No fresh Jev calls are made. H1 reuses previously inspected saved responses; H2–H5 are controlled algorithmic experiments. These results are not new semantic-accuracy evidence and are not a comparison against KARMA or another external graph system.

    +

    1. Frozen methodology and novelty boundary

    +

    The protocol was committed as f923e8d41ca5953d9793fadcc3730cfe9fc70b3a against merged baseline 9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98 before implementation or execution. It fixes generators, thresholds, comparators and seed 20260923. Existing package studies already contain relation-level stacking, fixed pairwise-dependence sensitivity analyses, bipartite flow, repair ambiguity and exact-marginal credal bounds. The five experiments here test different package-level integrations: source-group forecast stacking, active dependence-constraint acquisition, verified small-separator conditioning beyond bipartite graphs, reusable singleton repair margins and interval-valued marginal premises. This is a repository-scoped experiment distinction, not a worldwide novelty claim.

    +

    Fresh Jev service calls: 0. No production graph policy is changed. The controlled structural fixtures do not establish real-world source truth, reviewer behavior, calibrated Jev probabilities or end-to-end database latency. A pass means only that the frozen target for the stated evidence population was met.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    HypothesisFrozen primary requirementResultEvidence class
    H1: exposure-stratified source-risk stackingBeat random-effects Brier by >=3%, do not regress feature-risk Brier,bias<=0.03
    H2: active dependence constraintsZero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budgetMetSupplied finite joint distributions
    H3: near-bipartite separator solverExact small oracles; solve all 512/1024/2048 residual cases; safe controlsMetSupplied weighted conflict graphs
    H4: repair-margin query indexZero query/witness mismatches and >=70% fewer frozen-count optimization invocationsMetRepeated controlled singleton queries
    H5: interval marginalsZero containment failures; prevent 20/20 designed false admissions; fail closed on malformed inputsMetSupplied joint distributions and uncertainty intervals
    +

    2. H1 — Exposure-stratified source-risk stacking

    +

    The certificate result suggested that within-source dependence contains information but did not outperform the richer feature-risk forecast. H1 therefore combines the two forecasts without using evaluation labels for fitting. Leave-one-source-group-out development predictions select convex weights separately for singleton and multi-edge exposure strata when each stratum has at least eight folds; otherwise the global development weight is used.

    +

    Development selected feature weights: global 1.0, singleton 1.0, multi-edge 1.0. Development fold counts are 23 total, 14 singleton and 9 multi-edge. Evaluation scoring uses the identical 98 nonempty source groups as the comparators (60 singleton, 38 multi-edge).

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    ForecastBrierClipped log lossBias
    Existing feature-risk0.1289230.467074-0.072629
    Certificate random effects0.1314440.435042-0.012382
    Exposure-stratified stack0.1289230.467074-0.072629
    +

    The stacked-minus-feature paired Brier mean is +0.000000, with descriptive 95% interval [+0.000000, +0.000000]. The stacked-minus-random-effects mean is -0.002522, with 95% interval [-0.028381, +0.021169]. The frozen conjunction is not met. These intervals condition on the selected development weights and reuse already inspected evaluation data; they are not independent validation.

    +
    H1. Forecast Brier on the identical nonempty source-group denominator.
    +

    3. H2 — Greedy acquisition of dependence constraints

    +

    Marginal-only dependence bounds are safe but can be wide. H2 treats exact pairwise intersections from each fixture's supplied joint distribution as controlled observations and asks which three would most narrow the conclusion interval. At each step the policy evaluates every not-yet-observed pair and selects the one giving the smallest certified width; the comparator spends the same budget on the first three lexicographic pairs.

    +

    Across 128 fixtures, mean width is 0.326563 from marginals alone, 0.176527 after the lexicographic budget and 0.096687 after the greedy budget. Truth-containment failures: 0. Chosen-step widening failures: 0. The frozen target is met.

    +

    This is an oracle value-of-information experiment: it assumes the selected pairwise intersections can be supplied exactly. It does not show that those quantities are observable cheaply, that Jev scores are source reliabilities, or that a production estimator would preserve the same benefit.

    +
    H2. Mean certified width before and after equal three-constraint budgets.
    +

    4. H3 — Separator-conditioned near-bipartite exact optimization

    +

    The prior flow certificate handles bipartite components but stages sufficiently large non-bipartite ones. H3 accepts a supplied separator of at most four vertices, verifies that deleting it leaves a bipartite graph, enumerates every independent separator choice and solves each residual branch with the existing certified bipartite solver. An invalid separator is not trusted; it stages.

    +

    The 128 small exhaustive fixtures have 0 oracle failures and 0 order/duplicate-invariance failures. Large residual-cycle results are 512→258/258, 1024→514/514, 2048→1026/1026, written as residual vertices → obtained/analytic utility. The current generic solver stages respectively 513, 1025, 2049 vertices on those fixtures. Malformed and non-transversal controls stage safely: True. The frozen target is met.

    +

    The supplied priorities and conflict edges remain premises. Exact maximum supplied-priority utility does not establish that a selected assertion is factually true.

    +
    H3. Separator-conditioned utility versus the analytic optimum.
    +

    5. H4 — Reusable repair-margin singleton query index

    +

    The certificate query implementation recomputes a base optimum plus forced-in/forced-out alternatives for repeated questions. H4 precomputes each vertex's inclusion and exclusion margin once, then classifies any singleton query at any tested tolerance by comparing those margins with the tolerance threshold.

    +

    Across 2653 repeated singleton queries, classification mismatches are 0 and witness failures are 0. Under the frozen top-level solve-count accounting, repeated queries require 7,959 invocations versus 1,814 for index construction, a 77.21% reduction. A control using the existing query's realized early-exit count gives a still-separated descriptive reduction of 74.41%. The frozen target is met.

    +

    This index is deliberately limited to singleton queries and in-memory top-level optimization calls. It is not a measured SQL/database speedup or a semantic guarantee.

    +
    H4. Frozen-accounting optimization calls for repeated queries versus one reusable index.
    +

    6. H5 — Interval-marginal dependence certificates

    +

    Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage.

    +

    Across 128 arbitrary-joint fixtures, truth-containment failures are 0. Mean point-bound width is 0.361057 and mean interval-marginal width is 0.467497, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents 20/20 designed false admissions. Malformed inputs returning a certifying interval: 0. The frozen target is met.

    +

    The interval itself is still a supplied assumption. If the real marginal falls outside it, the certificate can again be wrong. This test converts one known premise-error mode into explicit uncertainty; it does not validate how such intervals should be estimated from real sources.

    +
    H5. False admissions on designed marginal-misspecification controls.
    +

    7. Interpretation and falsification boundary

    +

    The five experiments are intentionally heterogeneous. H1 asks whether two already observed forecast signals combine on reused response data. H2 asks whether a constrained information budget can reduce dependence uncertainty on finite controlled worlds. H3 and H4 test exact structural reuse. H5 asks whether uncertainty in the probability premises can be represented rather than ignored. Their pass/fail outcomes must not be pooled into a semantic success percentage.

    +

    The strongest remaining scientific boundary is unchanged: freeze a policy before observing a new source-disjoint, independently adjudicated corpus and compare full graph quality, downstream queries, provenance errors, reviewer mistakes, resource budgets and staging against appropriate external baselines. None of the controlled algorithmic passes can substitute for that prospective semantic evaluation.

    +

    8. Reproduction

    +
    python -m pip install -r graph_synthesis/post_certificates/requirements.txt
+python -B -m graph_synthesis.post_certificates.run
+python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v
+python -B -m graph_synthesis.post_certificates.run --check
+python -B -m graph_synthesis.post_certificates.report --figures --update-paper
+python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf
+
    +

    The machine-readable results retain the controlled fixtures, selected pair constraints, optimization witnesses, development-only weights, uncertainty intervals and falsifying controls. The five PNG/SVG pairs and summary table are generated from those recorded results. Earlier study artifacts are not rewritten.

    Do additional Jev calls improve graph edges?

    Timothy Wayne Gregg — exploratory research addendum, September 18, 2026

    Design and evidence boundary

    diff --git a/manuscript/paper-current.md b/manuscript/paper-current.md index f54ba53..0085573 100644 --- a/manuscript/paper-current.md +++ b/manuscript/paper-current.md @@ -1578,6 +1578,107 @@ These sources motivate established components; they do not validate this impleme + + +# Five post-certificate improvements for Jev graph synthesis + +Timothy Wayne Gregg | AI-assisted author-review research extension | September 18, 2026 + +## Abstract + +The dependence-aware certificate study left an asymmetric frontier: its source-random-effects forecast improved Brier by only 6.39% and missed its frozen target, while its dependence bounds, flow certificates, repair-invariant queries and local delta maintenance passed controlled tests. This pre-execution-frozen follow-up tests five responses to those remaining boundaries. The outcomes are: H1 **not met**, H2 **met**, H3 **met**, H4 **met**, and H5 **met**. No fresh Jev calls are made. H1 reuses previously inspected saved responses; H2–H5 are controlled algorithmic experiments. These results are not new semantic-accuracy evidence and are not a comparison against KARMA or another external graph system. + +## 1. Frozen methodology and novelty boundary + +The protocol was committed as `f923e8d41ca5953d9793fadcc3730cfe9fc70b3a` against merged baseline `9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98` before implementation or execution. It fixes generators, thresholds, comparators and seed 20260923. Existing package studies already contain relation-level stacking, fixed pairwise-dependence sensitivity analyses, bipartite flow, repair ambiguity and exact-marginal credal bounds. The five experiments here test different package-level integrations: source-group forecast stacking, active dependence-constraint acquisition, verified small-separator conditioning beyond bipartite graphs, reusable singleton repair margins and interval-valued marginal premises. This is a repository-scoped experiment distinction, not a worldwide novelty claim. + +**Fresh Jev service calls: 0.** No production graph policy is changed. The controlled structural fixtures do not establish real-world source truth, reviewer behavior, calibrated Jev probabilities or end-to-end database latency. A pass means only that the frozen target for the stated evidence population was met. + +| Hypothesis | Frozen primary requirement | Result | Evidence class | +|---|---|---|---| +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | Not met | Previously inspected saved-response source forecasts | +| H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | Met | Supplied finite joint distributions | +| H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | Met | Supplied weighted conflict graphs | +| H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | Met | Repeated controlled singleton queries | +| H5: interval marginals | Zero containment failures; prevent 20/20 designed false admissions; fail closed on malformed inputs | Met | Supplied joint distributions and uncertainty intervals | + +## 2. H1 — Exposure-stratified source-risk stacking + +The certificate result suggested that within-source dependence contains information but did not outperform the richer feature-risk forecast. H1 therefore combines the two forecasts without using evaluation labels for fitting. Leave-one-source-group-out development predictions select convex weights separately for singleton and multi-edge exposure strata when each stratum has at least eight folds; otherwise the global development weight is used. + +Development selected feature weights: global **1.0**, singleton **1.0**, multi-edge **1.0**. Development fold counts are 23 total, 14 singleton and 9 multi-edge. Evaluation scoring uses the identical 98 nonempty source groups as the comparators (60 singleton, 38 multi-edge). + +| Forecast | Brier | Clipped log loss | Bias | +|---|---:|---:|---:| +| Existing feature-risk | 0.128923 | 0.467074 | -0.072629 | +| Certificate random effects | 0.131444 | 0.435042 | -0.012382 | +| Exposure-stratified stack | 0.128923 | 0.467074 | -0.072629 | + +The stacked-minus-feature paired Brier mean is +0.000000, with descriptive 95% interval [+0.000000, +0.000000]. The stacked-minus-random-effects mean is -0.002522, with 95% interval [-0.028381, +0.021169]. The frozen conjunction is **not met**. These intervals condition on the selected development weights and reuse already inspected evaluation data; they are not independent validation. + +![H1. Forecast Brier on the identical nonempty source-group denominator.](../graph_synthesis/post_certificates/figures/01_stacked_risk.png) + +## 3. H2 — Greedy acquisition of dependence constraints + +Marginal-only dependence bounds are safe but can be wide. H2 treats exact pairwise intersections from each fixture's supplied joint distribution as controlled observations and asks which three would most narrow the conclusion interval. At each step the policy evaluates every not-yet-observed pair and selects the one giving the smallest certified width; the comparator spends the same budget on the first three lexicographic pairs. + +Across 128 fixtures, mean width is **0.326563** from marginals alone, **0.176527** after the lexicographic budget and **0.096687** after the greedy budget. Truth-containment failures: **0**. Chosen-step widening failures: **0**. The frozen target is **met**. + +This is an oracle value-of-information experiment: it assumes the selected pairwise intersections can be supplied exactly. It does not show that those quantities are observable cheaply, that Jev scores are source reliabilities, or that a production estimator would preserve the same benefit. + +![H2. Mean certified width before and after equal three-constraint budgets.](../graph_synthesis/post_certificates/figures/02_constraint_acquisition.png) + +## 4. H3 — Separator-conditioned near-bipartite exact optimization + +The prior flow certificate handles bipartite components but stages sufficiently large non-bipartite ones. H3 accepts a supplied separator of at most four vertices, verifies that deleting it leaves a bipartite graph, enumerates every independent separator choice and solves each residual branch with the existing certified bipartite solver. An invalid separator is not trusted; it stages. + +The 128 small exhaustive fixtures have **0** oracle failures and **0** order/duplicate-invariance failures. Large residual-cycle results are 512→258/258, 1024→514/514, 2048→1026/1026, written as residual vertices → obtained/analytic utility. The current generic solver stages respectively **513, 1025, 2049** vertices on those fixtures. Malformed and non-transversal controls stage safely: **True**. The frozen target is **met**. + +The supplied priorities and conflict edges remain premises. Exact maximum supplied-priority utility does not establish that a selected assertion is factually true. + +![H3. Separator-conditioned utility versus the analytic optimum.](../graph_synthesis/post_certificates/figures/03_near_bipartite.png) + +## 5. H4 — Reusable repair-margin singleton query index + +The certificate query implementation recomputes a base optimum plus forced-in/forced-out alternatives for repeated questions. H4 precomputes each vertex's inclusion and exclusion margin once, then classifies any singleton query at any tested tolerance by comparing those margins with the tolerance threshold. + +Across **2653** repeated singleton queries, classification mismatches are **0** and witness failures are **0**. Under the frozen top-level solve-count accounting, repeated queries require **7,959** invocations versus **1,814** for index construction, a **77.21%** reduction. A control using the existing query's realized early-exit count gives a still-separated descriptive reduction of **74.41%**. The frozen target is **met**. + +This index is deliberately limited to singleton queries and in-memory top-level optimization calls. It is not a measured SQL/database speedup or a semantic guarantee. + +![H4. Frozen-accounting optimization calls for repeated queries versus one reusable index.](../graph_synthesis/post_certificates/figures/04_query_index.png) + +## 6. H5 — Interval-marginal dependence certificates + +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. + +Across 128 arbitrary-joint fixtures, truth-containment failures are **0**. Mean point-bound width is **0.361057** and mean interval-marginal width is **0.467497**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **20/20** designed false admissions. Malformed inputs returning a certifying interval: **0**. The frozen target is **met**. + +The interval itself is still a supplied assumption. If the real marginal falls outside it, the certificate can again be wrong. This test converts one known premise-error mode into explicit uncertainty; it does not validate how such intervals should be estimated from real sources. + +![H5. False admissions on designed marginal-misspecification controls.](../graph_synthesis/post_certificates/figures/05_interval_marginals.png) + +## 7. Interpretation and falsification boundary + +The five experiments are intentionally heterogeneous. H1 asks whether two already observed forecast signals combine on reused response data. H2 asks whether a constrained information budget can reduce dependence uncertainty on finite controlled worlds. H3 and H4 test exact structural reuse. H5 asks whether uncertainty in the probability premises can be represented rather than ignored. Their pass/fail outcomes must not be pooled into a semantic success percentage. + +The strongest remaining scientific boundary is unchanged: freeze a policy before observing a new source-disjoint, independently adjudicated corpus and compare full graph quality, downstream queries, provenance errors, reviewer mistakes, resource budgets and staging against appropriate external baselines. None of the controlled algorithmic passes can substitute for that prospective semantic evaluation. + +## 8. Reproduction + +```bash +python -m pip install -r graph_synthesis/post_certificates/requirements.txt +python -B -m graph_synthesis.post_certificates.run +python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v +python -B -m graph_synthesis.post_certificates.run --check +python -B -m graph_synthesis.post_certificates.report --figures --update-paper +python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf +``` + +The machine-readable results retain the controlled fixtures, selected pair constraints, optimization witnesses, development-only weights, uncertainty intervals and falsifying controls. The five PNG/SVG pairs and summary table are generated from those recorded results. Earlier study artifacts are not rewritten. + + + # Do additional Jev calls improve graph edges? 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z!4N~juGZnTm6OTRT*1JJbMzXm9kxw|7W|dp_545zGb_y((hVPxuaA-Z-_j%NUZeSS z?y*g9@V$ARm+lx)u9h#hgCmCq&YZEr|C;ys3vjCqsPsqw@aBnZ8@#3F3MnLOzvy-P zPPCwfP8kQ11>+nAkeyY^RZOGM0EqT5KF2t=k` zp_BcaeBmya_k46GUH=YJ8py9V<&aYD1oGPb0`!AgYWT?33u{2HU%HTLTG}hY?j`B8 zw=`X_7Z7cNT_+Rn*PO*i&sqO3*4YJQ Date: Fri, 18 Sep 2026 10:43:55 -0400 Subject: [PATCH 11/21] fix: certify interval marginals with dual outer bounds --- graph_synthesis/post_certificates/methods.py | 23 ++++++++++++++++---- 1 file changed, 19 insertions(+), 4 deletions(-) diff --git a/graph_synthesis/post_certificates/methods.py b/graph_synthesis/post_certificates/methods.py index a708a5e..f00f59a 100644 --- a/graph_synthesis/post_certificates/methods.py +++ b/graph_synthesis/post_certificates/methods.py @@ -87,16 +87,31 @@ def indicator(term_atoms): marginals = {a: float(atom_vectors[a] @ x) for a in atoms} if any(marginals[a] < bounds[a][0] - 1e-7 or marginals[a] > bounds[a][1] + 1e-7 for a in atoms): return _staged("residual_staged", len(atoms)) + c = sign * objective + y_eq = np.asarray(result.eqlin.marginals, dtype=float) + y_ub = np.minimum(np.asarray(result.ineqlin.marginals, dtype=float), 0.0) + if not np.isfinite(y_eq).all() or not np.isfinite(y_ub).all(): + return _staged("nonfinite_dual_staged", len(atoms)) + reduced = c - eq.T @ y_eq - aub.T @ y_ub + correction = float(min(0.0, np.min(reduced))) + padding = PAD * (1.0 + float(np.abs(y_eq).sum()) + float(np.abs(y_ub).sum())) + dual_lower = float(eq_target @ y_eq + bub @ y_ub) + correction - padding + signed_primal = float(c @ x) + if dual_lower > signed_primal + 1e-6: + return _staged("dual_verification_staged", len(atoms)) value = float(objective @ x) - solutions.append({"value": value, "support": [[int(i), float(v)] for i, v in enumerate(x) if v > 1e-12], + solutions.append({"value": value, "signed_primal": signed_primal, "dual_lower": dual_lower, + "dual_eq": y_eq.tolist(), "dual_ub": y_ub.tolist(), + "reduced_min": float(np.min(reduced)), "padding": padding, + "support": [[int(i), float(v)] for i, v in enumerate(x) if v > 1e-12], "marginals": marginals}) - lo = max(0.0, solutions[0]["value"] - PAD) - hi = min(1.0, solutions[1]["value"] + PAD) + lo = max(0.0, solutions[0]["dual_lower"]) + hi = min(1.0, -solutions[1]["dual_lower"]) if lo > hi + 1e-7: return _staged("numeric_inconsistency", len(atoms)) return {"status": "bounded", "certified": True, "lower": lo, "upper": hi, "atoms": len(atoms), "worlds": len(worlds), "min": solutions[0], "max": solutions[1], - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded."} + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded."} except (TypeError, ValueError, KeyError, OverflowError): return _staged("invalid_input") From cfd7026746aaf9a41501d59bb8f4448a84c356ac Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" 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LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5150937027204767, + "lower": 0.5150936027204767, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6087961208512105, "a1": 0.5150938027204767, @@ -163204,6 +163446,9 @@ "a3": 0.5515675729059494, "a4": 0.49011276592163244 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -163233,6 +163478,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5150936027204767, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6087961208512105, "a1": 0.5150938027204767, @@ -163240,6 +163501,9 @@ "a3": 0.5515675729059494, "a4": 0.49011276592163244 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5150938027204767, "support": [ [ 3, @@ -163298,15 +163562,28 @@ { "id": 4, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4847125881254758, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4847123881254758, "a1": 0.5249919731384507 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4847123881254758, "support": [ [ 0, @@ -163324,10 +163601,23 @@ "value": 0.4847123881254758 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4337425474968418, "a1": 0.5249919731384507 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -163345,7 +163635,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4847124881254758, + "upper": 0.4847125881254758, "worlds": 4 }, "intervals": { @@ -163364,15 +163654,28 @@ "a1": 0.559400727019725 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.013208900723538811, + "lower": 0.013208600723538811, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.45380847370381383, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4538082737038138, "a1": 0.559400727019725 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4538082737038138, "support": [ [ 0, @@ -163390,10 +163693,23 @@ "value": 0.4538082737038138 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.013208600723538811, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4538082737038138, "a1": 0.559400727019725 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.01320900072353881, "support": [ [ 1, @@ -163411,7 +163727,7 @@ "value": 0.01320900072353881 }, "status": "bounded", - "upper": 0.4538083737038138, + "upper": 0.45380847370381383, "worlds": 4 }, "proofs": [ @@ -163433,16 +163749,31 @@ { "id": 5, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5160001096297343, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5159999096297343, "a1": 0.6328270700782715, "a2": 0.36717292992172845 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5159999096297343, "support": [ [ 2, @@ -163460,11 +163791,26 @@ "value": 0.5159999096297343 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.34652363085990795, "a1": 0.5498471295450805, "a2": 0.3215598834932742 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -163486,7 +163832,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5160000096297342, + "upper": 0.5160001096297343, "worlds": 8 }, "intervals": { @@ -163510,16 +163856,31 @@ "a2": 0.44611488078120676 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.43711224553652916, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.43711204553652916, "a1": 0.5620803207855348, "a2": 0.44611488078120676 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.43711204553652916, "support": [ [ 2, @@ -163541,11 +163902,26 @@ "value": 0.43711204553652916 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.43711204553652916, "a1": 0.5620803207855348, "a2": 0.44611488078120676 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -163567,7 +163943,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.43711214553652916, + "upper": 0.43711224553652916, "worlds": 8 }, "proofs": [ @@ -163600,11 +163976,29 @@ { "id": 6, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4902212964418363, + "lower": 0.4902211964418363, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5337979095792064, "a1": 0.5725162461437149, @@ -163613,6 +164007,9 @@ "a4": 0.5199714145652105, "a5": 0.6381588601757098 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 11, @@ -163646,6 +164043,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4902211964418363, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5337979095792065, "a1": 0.4902213964418363, @@ -163654,6 +164069,9 @@ "a4": 0.5557770867879348, "a5": 0.46824221923310805 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4902213964418363, "support": [ [ 25, @@ -163714,11 +164132,29 @@ "a5": 0.5687928954527743 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5508649742820673, + "lower": 0.5508648742820672, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.605903754363533, "a1": 0.5508650742820672, @@ -163727,6 +164163,9 @@ "a4": 0.5688593455568484, "a5": 0.5687928954527743 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 7, @@ -163760,6 +164199,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5508648742820672, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.605903754363533, "a1": 0.5508650742820672, @@ -163768,6 +164225,9 @@ "a4": 0.5688593455568484, "a5": 0.5687928954527743 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5508650742820672, "support": [ [ 1, @@ -163841,11 +164301,27 @@ { "id": 7, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.49335369699461135, + "lower": 0.49335359699461134, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5015833311178816, "a1": 0.5094682154995525, @@ -163853,6 +164329,9 @@ "a3": 0.4182596393943142, "a4": 0.49053178450044754 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -163878,6 +164357,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49335359699461134, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5066462030053887, "a1": 0.49335379699461135, @@ -163885,6 +164380,9 @@ "a3": 0.49335379699461135, "a4": 0.49053178450044754 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.49335379699461135, "support": [ [ 5, @@ -163940,11 +164438,27 @@ "a4": 0.5150013461350197 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5518025622644965, + "lower": 0.5518024622644965, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5686945566338155, "a1": 0.5264854613205413, @@ -163952,6 +164466,9 @@ "a3": 0.5518026622644965, "a4": 0.5150013461350197 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -163981,6 +164498,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5518024622644965, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5686945566338155, "a1": 0.5264854613205413, @@ -163988,6 +164521,9 @@ "a3": 0.5518026622644965, "a4": 0.5150013461350197 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5518026622644965, "support": [ [ 5, @@ -164059,17 +164595,34 @@ { "id": 8, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.4940861563436873, + "lower": 0.49408605634368724, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.652525733202821, "a1": 0.5842763167557281, "a2": 0.622810831153357, "a3": 0.4653627584859322 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -164095,12 +164648,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49408605634368724, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5194040913585826, "a1": 0.4940862563436873, "a2": 0.560814899840795, "a3": 0.388438411104711 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4940862563436873, "support": [ [ 3, @@ -164155,17 +164725,34 @@ "a3": 0.4162480830754891 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5089940160914452, + "lower": 0.5089939160914452, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9252424991669342, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5368036730925675, "a1": 0.5089941160914452, "a2": 0.5772874970519178, "a3": 0.4162480830754891 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9252421991669343, "support": [ [ 3, @@ -164191,12 +164778,29 @@ "value": 0.9252421991669343 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5089939160914452, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5368036730925675, "a1": 0.5089941160914452, "a2": 0.5772874970519178, "a3": 0.4162480830754891 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5089941160914452, "support": [ [ 3, @@ -164222,7 +164826,7 @@ "value": 0.5089941160914452 }, "status": "bounded", - "upper": 0.9252422991669342, + "upper": 0.9252424991669342, "worlds": 16 }, "proofs": [ @@ -164263,16 +164867,31 @@ { "id": 9, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5358150166758334, + "lower": 0.5358149166758334, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6759497892065197, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.301520627834957, "a1": 0.473818288546355, "a2": 0.6759495892065197 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6759495892065197, "support": [ [ 2, @@ -164294,11 +164913,26 @@ "value": 0.6759495892065197 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5358149166758334, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.301520627834957, "a1": 0.473818288546355, "a2": 0.5358151166758334 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5358151166758334, "support": [ [ 2, @@ -164320,7 +164954,7 @@ "value": 0.5358151166758334 }, "status": "bounded", - "upper": 0.6759496892065197, + "upper": 0.6759497892065197, "worlds": 8 }, "intervals": { @@ -164344,16 +164978,31 @@ "a2": 0.6040482735826921 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.6040481735826921, + "lower": 0.6040480735826921, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6040484735826921, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4232141931463829, "a1": 0.4942315359394953, "a2": 0.6040482735826921 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6040482735826921, "support": [ [ 3, @@ -164375,11 +165024,26 @@ "value": 0.6040482735826921 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6040480735826921, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4232141931463829, "a1": 0.4942315359394953, "a2": 0.6040482735826921 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6040482735826921, "support": [ [ 3, @@ -164401,7 +165065,7 @@ "value": 0.6040482735826921 }, "status": "bounded", - "upper": 0.604048373582692, + "upper": 0.6040484735826921, "worlds": 8 }, "proofs": [ @@ -164429,11 +165093,29 @@ { "id": 10, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.49312716111957167, + "lower": 0.49312706111957166, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5454902780555034, "a1": 0.5524524268584032, @@ -164442,6 +165124,9 @@ "a4": 0.5070155851171195, "a5": 0.5645638271151956 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 6, @@ -164475,6 +165160,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49312706111957166, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45336906844882346, "a1": 0.49312726111957167, @@ -164483,6 +165186,9 @@ "a4": 0.5061361733984626, "a5": 0.4938638266015373 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.49312726111957167, "support": [ [ 25, @@ -164543,11 +165249,29 @@ "a5": 0.544476828566047 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.49787549926233055, + "lower": 0.49787539926233054, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9259717250442427, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.42809582578191224, "a1": 0.49787559926233055, @@ -164556,6 +165280,9 @@ "a4": 0.4639634464116092, "a5": 0.544476828566047 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9259714250442428, "support": [ [ 4, @@ -164589,6 +165316,24 @@ "value": 0.9259714250442428 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49787539926233054, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.42809582578191224, "a1": 0.49787559926233055, @@ -164597,6 +165342,9 @@ "a4": 0.46396344641160914, "a5": 0.544476828566047 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.49787559926233055, "support": [ [ 1, @@ -164630,7 +165378,7 @@ "value": 0.49787559926233055 }, "status": "bounded", - "upper": 0.9259715250442427, + "upper": 0.9259717250442427, "worlds": 64 }, "proofs": [ @@ -164670,11 +165418,29 @@ { "id": 11, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6167525800576668, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5282476645917497, "a1": 0.5373115723787791, @@ -164683,6 +165449,9 @@ "a4": 0.5310929229666241, "a5": 0.44880685691286204 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6167523800576667, "support": [ [ 10, @@ -164712,6 +165481,24 @@ "value": 0.6167523800576667 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4396353298063465, "a1": 0.41298539542365914, @@ -164720,6 +165507,9 @@ "a4": 0.48860073130033427, "a5": 0.5371262471821676 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -164753,7 +165543,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.6167524800576667, + "upper": 0.6167525800576668, "worlds": 64 }, "intervals": { @@ -164792,11 +165582,29 @@ "a5": 0.5232872080526221 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.027959822716642466, + "lower": 0.027959522716642492, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5310845186059698, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49687560411067266, "a1": 0.46964271711737254, @@ -164805,6 +165613,9 @@ "a4": 0.4929386598614994, "a5": 0.5232872080526221 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5310843186059698, "support": [ [ 4, @@ -164838,14 +165649,35 @@ "value": 0.5310843186059698 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.027959522716642492, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { - "a0": 0.49687560411067266, + "a0": 0.4968756041106727, "a1": 0.4696427171173726, "a2": 0.5106334152965029, "a3": 0.5310843186059698, "a4": 0.49293865986149943, "a5": 0.5232872080526221 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.027959922716642466, "support": [ [ 1, @@ -164879,7 +165711,7 @@ "value": 0.027959922716642466 }, "status": "bounded", - "upper": 0.5310844186059698, + "upper": 0.5310845186059698, "worlds": 64 }, "proofs": [ @@ -164910,11 +165742,29 @@ { "id": 12, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4891118684476738, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4891116684476738, "a1": 0.5108883315523263, @@ -164923,6 +165773,9 @@ "a4": 0.5352235589794045, "a5": 0.4647764410205955 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4891116684476738, "support": [ [ 25, @@ -164940,6 +165793,24 @@ "value": 0.4891116684476738 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44903266144923343, "a1": 0.5269624365497556, @@ -164948,6 +165819,9 @@ "a4": 0.5628021683705887, "a5": 0.5266324936873082 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -164981,7 +165855,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4891117684476738, + "upper": 0.4891118684476738, "worlds": 64 }, "intervals": { @@ -165020,11 +165894,29 @@ "a5": 0.48444973721755824 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.455349262511016, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.455349062511016, "a1": 0.4890414215182645, @@ -165033,6 +165925,9 @@ "a4": 0.43463574301238794, "a5": 0.48444973721755824 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.455349062511016, "support": [ [ 4, @@ -165066,6 +165961,24 @@ "value": 0.455349062511016 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.455349062511016, "a1": 0.4890414215182645, @@ -165074,6 +165987,9 @@ "a4": 0.43463574301238794, "a5": 0.48444973721755824 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -165107,7 +166023,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.455349162511016, + "upper": 0.455349262511016, "worlds": 64 }, "proofs": [ @@ -165129,17 +166045,34 @@ { "id": 13, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5271297164967573, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5923497060891689, "a1": 0.5271295164967573, "a2": 0.5369246530798504, "a3": 0.4855432641432387 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5271295164967573, "support": [ [ 3, @@ -165165,12 +166098,29 @@ "value": 0.5271295164967573 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.501667387927925, "a1": 0.3646083752411345, "a2": 0.5369246530798504, "a3": 0.5628897842898097 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -165196,7 +166146,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5271296164967573, + "upper": 0.5271297164967573, "worlds": 16 }, "intervals": { @@ -165225,17 +166175,34 @@ "a3": 0.511601018385029 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4138401655064885, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5279024205015421, "a1": 0.4138399655064885, "a2": 0.5106120633544531, "a3": 0.511601018385029 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4138399655064885, "support": [ [ 3, @@ -165261,12 +166228,29 @@ "value": 0.4138399655064885 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5279024205015421, "a1": 0.4138399655064885, "a2": 0.5106120633544531, "a3": 0.511601018385029 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -165292,7 +166276,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4138400655064885, + "upper": 0.4138401655064885, "worlds": 16 }, "proofs": [ @@ -165316,11 +166300,27 @@ { "id": 14, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5311450444623571, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.47303071792209694, "a1": 0.47238070392246123, @@ -165328,6 +166328,9 @@ "a3": 0.39134273955865917, "a4": 0.5311448444623571 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5311448444623571, "support": [ [ 3, @@ -165353,6 +166356,22 @@ "value": 0.5311448444623571 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.47303071792209694, "a1": 0.39095091031168006, @@ -165360,6 +166379,9 @@ "a3": 0.5269692820779031, "a4": 0.43759728923089974 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 5, @@ -165381,7 +166403,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.531144944462357, + "upper": 0.5311450444623571, "worlds": 32 }, "intervals": { @@ -165415,11 +166437,27 @@ "a4": 0.5979583792014171 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.09681495643793031, + "lower": 0.0968146564379302, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4988568772365132, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4775717155590152, "a1": 0.40242242066031736, @@ -165427,6 +166465,9 @@ "a3": 0.4521181282237404, "a4": 0.5979583792014171 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.49885667723651317, "support": [ [ 3, @@ -165456,6 +166497,22 @@ "value": 0.49885667723651317 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.0968146564379302, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4775717155590152, "a1": 0.40242242066031736, @@ -165463,6 +166520,9 @@ "a3": 0.4521181282237404, "a4": 0.5979583792014171 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.09681505643793031, "support": [ [ 5, @@ -165492,7 +166552,7 @@ "value": 0.09681505643793031 }, "status": "bounded", - "upper": 0.49885677723651317, + "upper": 0.4988568772365132, "worlds": 32 }, "proofs": [ @@ -165513,11 +166573,29 @@ { "id": 15, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4752405669561739, + "lower": 0.4752404669561739, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4699849166241584, "a1": 0.5300150833758416, @@ -165526,6 +166604,9 @@ "a4": 0.5746206169660836, "a5": 0.4666008427350431 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -165547,6 +166628,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4752404669561739, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4699849166241584, "a1": 0.5164183356234613, @@ -165555,6 +166654,9 @@ "a4": 0.4752406669561739, "a5": 0.5111625852914459 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4752406669561739, "support": [ [ 4, @@ -165619,11 +166721,29 @@ "a5": 0.5118661855087012 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5600440647431365, + "lower": 0.5600439647431364, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5600441647431365, "a1": 0.5651936985118982, @@ -165632,6 +166752,9 @@ "a4": 0.4734837441240785, "a5": 0.5118661855087012 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -165665,6 +166788,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5600439647431364, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5600441647431365, "a1": 0.5651936985118982, @@ -165673,6 +166814,9 @@ "a4": 0.47348374412407845, "a5": 0.5118661855087012 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5600441647431365, "support": [ [ 4, @@ -165747,16 +166891,31 @@ { "id": 16, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.44583416988264474, + "lower": 0.44583406988264473, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5257246432192678, "a1": 0.5257246432192678, "a2": 0.4742753567807322 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -165770,11 +166929,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44583406988264473, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4127967756619864, "a1": 0.5541657301173553, "a2": 0.44583426988264474 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44583426988264474, "support": [ [ 2, @@ -165816,16 +166990,31 @@ "a2": 0.4545056921351891 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5271203981564491, + "lower": 0.527120298156449, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9816264902916381, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.527120498156449, "a1": 0.5544371327289586, "a2": 0.4545056921351891 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9816261902916381, "support": [ [ 2, @@ -165847,11 +167036,26 @@ "value": 0.9816261902916381 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.527120298156449, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.527120498156449, "a1": 0.5544371327289586, "a2": 0.4545056921351891 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.527120498156449, "support": [ [ 2, @@ -165873,7 +167077,7 @@ "value": 0.527120498156449 }, "status": "bounded", - "upper": 0.9816262902916381, + "upper": 0.9816264902916381, "worlds": 8 }, "proofs": [ @@ -165899,16 +167103,31 @@ { "id": 17, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5315475506530187, + "lower": 0.5315474506530187, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4143843909691678, "a1": 0.48228460113699895, "a2": 0.5315476506530186 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -165930,11 +167149,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5315474506530187, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4143843909691678, "a1": 0.48228460113699895, "a2": 0.5315476506530187 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5315476506530187, "support": [ [ 0, @@ -165980,16 +167214,31 @@ "a2": 0.5943657478387446 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5943656478387447, + "lower": 0.5943655478387446, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4800233142880453, "a1": 0.4894563633502641, "a2": 0.5943657478387446 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -166011,11 +167260,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5943655478387446, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4800233142880453, "a1": 0.4894563633502641, "a2": 0.5943657478387446 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5943657478387446, "support": [ [ 0, @@ -166061,11 +167325,27 @@ { "id": 18, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4472751155196538, + "lower": 0.4472750155196538, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4276377532840041, "a1": 0.4772690119175436, @@ -166073,6 +167353,9 @@ "a3": 0.5723622467159959, "a4": 0.38627286751910517 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 5, @@ -166098,6 +167381,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4472750155196538, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.402848624482658, "a1": 0.5756010787168974, @@ -166105,6 +167404,9 @@ "a3": 0.4472752155196538, "a4": 0.38627286751910517 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4472752155196538, "support": [ [ 3, @@ -166168,11 +167470,27 @@ "a4": 0.4484259407822524 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4955530704128854, + "lower": 0.4955529704128854, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9221438681388947, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4265903977260094, "a1": 0.4824880753172319, @@ -166180,6 +167498,9 @@ "a3": 0.4955531704128854, "a4": 0.4484259407822524 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9221435681388948, "support": [ [ 5, @@ -166209,6 +167530,22 @@ "value": 0.9221435681388948 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4955529704128854, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4265903977260094, "a1": 0.4824880753172319, @@ -166216,6 +167553,9 @@ "a3": 0.4955531704128854, "a4": 0.4484259407822524 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4955531704128854, "support": [ [ 3, @@ -166245,7 +167585,7 @@ "value": 0.4955531704128854 }, "status": "bounded", - "upper": 0.9221436681388947, + "upper": 0.9221438681388947, "worlds": 32 }, "proofs": [ @@ -166269,11 +167609,29 @@ { "id": 19, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4071874975350029, + "lower": 0.4071873975350029, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6053758734653798, "a1": 0.5088732136431813, @@ -166282,6 +167640,9 @@ "a4": 0.5577814928388564, "a5": 0.4246147237536587 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 11, @@ -166315,6 +167676,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4071873975350029, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4844092310385943, "a1": 0.5088732136431813, @@ -166323,6 +167702,9 @@ "a4": 0.4071875975350029, "a5": 0.5109173774909797 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4071875975350029, "support": [ [ 1, @@ -166387,11 +167769,29 @@ "a5": 0.4471117799192613 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4346171282572759, + "lower": 0.4346170282572759, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8995790026239938, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5201286603654902, "a1": 0.464961474366718, @@ -166400,6 +167800,9 @@ "a4": 0.4346172282572759, "a5": 0.4471117799192613 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8995787026239939, "support": [ [ 4, @@ -166433,6 +167836,24 @@ "value": 0.8995787026239939 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4346170282572759, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5201286603654902, "a1": 0.464961474366718, @@ -166441,6 +167862,9 @@ "a4": 0.4346172282572759, "a5": 0.4471117799192613 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4346172282572759, "support": [ [ 1, @@ -166474,7 +167898,7 @@ "value": 0.4346172282572759 }, "status": "bounded", - "upper": 0.8995788026239938, + "upper": 0.8995790026239938, "worlds": 64 }, "proofs": [ @@ -166503,11 +167927,29 @@ { "id": 20, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5026346909062415, "a1": 0.5100031888308684, @@ -166516,6 +167958,9 @@ "a4": 0.5257355389491559, "a5": 0.4357044290381159 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 11, @@ -166541,6 +167986,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4899968111691317, "a1": 0.5100031888308684, @@ -166549,6 +168012,9 @@ "a4": 0.5257355389491559, "a5": 0.46407465889351335 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 10, @@ -166613,11 +168079,29 @@ "a5": 0.4439014807142182 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9307213449890233, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.534083886161272, "a1": 0.48302238301305295, @@ -166626,6 +168110,9 @@ "a4": 0.4575585366490417, "a5": 0.4439014807142182 }, + "padding": 3e-07, + "reduced_min": -0.0, + "signed_primal": -0.9307210449890233, "support": [ [ 4, @@ -166659,6 +168146,24 @@ "value": 0.9307210449890233 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.534083886161272, "a1": 0.483022383013053, @@ -166667,6 +168172,9 @@ "a4": 0.4575585366490418, "a5": 0.4439014807142182 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -166700,7 +168208,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.9307211449890233, + "upper": 0.9307213449890233, "worlds": 64 }, "proofs": [ @@ -166732,11 +168240,29 @@ { "id": 21, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5394228742677531, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5394226742677531, "a1": 0.5208908950632389, @@ -166745,6 +168271,9 @@ "a4": 0.6279513968714511, "a5": 0.5400536099535038 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5394226742677531, "support": [ [ 4, @@ -166778,6 +168307,24 @@ "value": 0.5394226742677531 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4873947732282082, "a1": 0.5126052267717918, @@ -166786,6 +168333,9 @@ "a4": 0.5284271007267609, "a5": 0.4715728992732391 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 25, @@ -166803,7 +168353,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5394227742677531, + "upper": 0.5394228742677531, "worlds": 64 }, "intervals": { @@ -166842,11 +168392,29 @@ "a5": 0.49438092205009704 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.49438112205009704, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5083348914724358, "a1": 0.5043749155393253, @@ -166855,6 +168423,9 @@ "a4": 0.6149445402193124, "a5": 0.4943809220500971 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4943809220500971, "support": [ [ 4, @@ -166888,6 +168459,24 @@ "value": 0.4943809220500971 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5083348914724358, "a1": 0.5043749155393253, @@ -166896,6 +168485,9 @@ "a4": 0.6149445402193124, "a5": 0.49438092205009704 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 22, @@ -166929,7 +168521,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4943810220500971, + "upper": 0.49438112205009704, "worlds": 64 }, "proofs": [ @@ -166952,17 +168544,34 @@ { "id": 22, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.4638466208956134, + "lower": 0.4638465208956134, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49861129594845416, "a1": 0.6010883440394514, "a2": 0.7528409720111471, "a3": 0.5930793471631128 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -166988,12 +168597,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4638465208956134, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4246472636737418, "a1": 0.4638467208956134, "a2": 0.6757304565602815, "a3": 0.5214424946314562 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4638467208956134, "support": [ [ 3, @@ -167048,17 +168674,34 @@ "a3": 0.5846170617572352 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5546430568936991, + "lower": 0.554642956893699, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48755521616355574, "a1": 0.5546431568936991, "a2": 0.7204449544478496, "a3": 0.5846170617572352 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -167084,12 +168727,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.554642956893699, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48755521616355574, "a1": 0.554643156893699, "a2": 0.7204449544478497, "a3": 0.5846170617572352 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.554643156893699, "support": [ [ 3, @@ -167154,16 +168814,31 @@ { "id": 23, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.4155910054026911, + "lower": 0.4155909054026911, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3602754137167275, "a1": 0.5779327178641118, "a2": 0.42206728213588823 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -167181,11 +168856,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4155909054026911, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.3602754137167275, "a1": 0.3945758732011802, "a2": 0.4155911054026911 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4155911054026911, "support": [ [ 0, @@ -167231,16 +168921,31 @@ "a2": 0.5193493454728685 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5558315944016302, + "lower": 0.5558314944016302, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45373524271725774, "a1": 0.5558316944016302, "a2": 0.5193493454728685 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -167262,11 +168967,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5558314944016302, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45373524271725774, "a1": 0.5558316944016302, "a2": 0.5193493454728685 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5558316944016302, "support": [ [ 0, @@ -167325,16 +169045,31 @@ { "id": 24, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.05915423375778778, + "lower": 0.05915393375778778, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6132083895160336, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4018813042216559, "a1": 0.6912738403625424, "a2": 0.6132081895160336 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6132081895160336, "support": [ [ 1, @@ -167356,11 +169091,26 @@ "value": 0.6132081895160336 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.05915393375778778, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4018813042216559, "a1": 0.5068613577726558, "a2": 0.5522929759851319 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.05915433375778778, "support": [ [ 2, @@ -167382,7 +169132,7 @@ "value": 0.05915433375778778 }, "status": "bounded", - "upper": 0.6132082895160336, + "upper": 0.6132083895160336, "worlds": 8 }, "intervals": { @@ -167406,16 +169156,31 @@ "a2": 0.58616100596099 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.25570438788319944, + "lower": 0.2557040878831993, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.58616120596099, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.43239726331451495, "a1": 0.6695434819222095, "a2": 0.58616100596099 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.58616100596099, "support": [ [ 1, @@ -167437,11 +169202,26 @@ "value": 0.58616100596099 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.2557040878831993, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.43239726331451495, "a1": 0.6695434819222095, "a2": 0.58616100596099 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.25570448788319944, "support": [ [ 3, @@ -167463,7 +169243,7 @@ "value": 0.25570448788319944 }, "status": "bounded", - "upper": 0.5861611059609899, + "upper": 0.58616120596099, "worlds": 8 }, "proofs": [ @@ -167482,16 +169262,31 @@ { "id": 25, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.459501454147724, + "lower": 0.459501354147724, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3781367247513986, "a1": 0.6218632752486014, "a2": 0.4877950767212075 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -167509,11 +169304,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.459501354147724, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.29504117058967977, "a1": 0.459501554147724, "a2": 0.5404984458522759 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.459501554147724, "support": [ [ 2, @@ -167555,16 +169365,31 @@ "a2": 0.6498470743328639 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.48215732387458365, + "lower": 0.48215722387458365, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7990260879205922, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3168683640460085, "a1": 0.48215742387458366, "a2": 0.6498470743328639 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.7990257879205922, "support": [ [ 2, @@ -167586,11 +169411,26 @@ "value": 0.7990257879205922 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.48215722387458365, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3168683640460085, "a1": 0.48215742387458366, "a2": 0.6498470743328639 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.48215742387458366, "support": [ [ 2, @@ -167612,7 +169452,7 @@ "value": 0.48215742387458366 }, "status": "bounded", - "upper": 0.7990258879205921, + "upper": 0.7990260879205922, "worlds": 8 }, "proofs": [ @@ -167648,11 +169488,27 @@ { "id": 26, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.41326641459857033, + "lower": 0.41326631459857033, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5258322125093895, "a1": 0.48942334828217093, @@ -167660,6 +169516,9 @@ "a3": 0.4475989647476036, "a4": 0.4741677874906106 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 7, @@ -167685,6 +169544,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.41326631459857033, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5035595371395567, "a1": 0.48942334828217093, @@ -167692,6 +169567,9 @@ "a3": 0.4475989647476036, "a4": 0.4741677874906106 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.41326651459857033, "support": [ [ 3, @@ -167755,11 +169633,27 @@ "a4": 0.5711135690160656 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4998790610086192, + "lower": 0.49987896100861917, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5550664734920909, "a1": 0.5257488938872081, @@ -167767,6 +169661,9 @@ "a3": 0.5222656859634471, "a4": 0.5711135690160656 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 7, @@ -167796,6 +169693,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49987896100861917, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5550664734920909, "a1": 0.525748893887208, @@ -167803,6 +169716,9 @@ "a3": 0.5222656859634471, "a4": 0.5711135690160656 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4998791610086192, "support": [ [ 3, @@ -167869,11 +169785,27 @@ { "id": 27, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4541888423695612, + "lower": 0.4541887423695612, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5417072904621761, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46234713461677296, "a1": 0.5417070904621761, @@ -167881,6 +169813,9 @@ "a3": 0.43710501873791924, "a4": 0.4467334529330006 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5417070904621761, "support": [ [ 5, @@ -167906,6 +169841,22 @@ "value": 0.5417070904621761 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4541887423695612, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46234713461677296, "a1": 0.4541889423695612, @@ -167913,6 +169864,9 @@ "a3": 0.43710501873791924, "a4": 0.4467334529330006 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4541889423695612, "support": [ [ 5, @@ -167938,7 +169892,7 @@ "value": 0.4541889423695612 }, "status": "bounded", - "upper": 0.5417071904621761, + "upper": 0.5417072904621761, "worlds": 32 }, "intervals": { @@ -167972,11 +169926,27 @@ "a4": 0.5647367339904344 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5331323037541572, + "lower": 0.5331322037541572, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5331326037541572, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4670719812251497, "a1": 0.5331324037541572, @@ -167984,6 +169954,9 @@ "a3": 0.48588794021674936, "a4": 0.5647367339904346 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5331324037541572, "support": [ [ 7, @@ -168013,6 +169986,22 @@ "value": 0.5331324037541572 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5331322037541572, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4670719812251497, "a1": 0.5331324037541572, @@ -168020,6 +170009,9 @@ "a3": 0.48588794021674936, "a4": 0.5647367339904346 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5331324037541572, "support": [ [ 7, @@ -168049,7 +170041,7 @@ "value": 0.5331324037541572 }, "status": "bounded", - "upper": 0.5331325037541571, + "upper": 0.5331326037541572, "worlds": 32 }, "proofs": [ @@ -168093,17 +170085,34 @@ { "id": 28, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5864811005573732, + "lower": 0.5864810005573732, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6818701833174763, "a1": 0.6556024459891722, "a2": 0.5059522481894759, "a3": 0.5186228167719986 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -168129,12 +170138,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5864810005573732, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5864812005573732, "a1": 0.47556482236221165, "a2": 0.5059522481894759, "a3": 0.41037838659743575 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5864812005573732, "support": [ [ 3, @@ -168189,17 +170215,34 @@ "a3": 0.4922966972388782 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.6441120755710671, + "lower": 0.644111975571067, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6233603871192941, "a1": 0.644112175571067, "a2": 0.43523504185474016, "a3": 0.4922966972388782 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -168225,12 +170268,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.644111975571067, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6233603871192941, "a1": 0.644112175571067, "a2": 0.4352350418547402, "a3": 0.4922966972388782 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.644112175571067, "support": [ [ 3, @@ -168296,16 +170356,31 @@ { "id": 29, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.4025425139756529, + "lower": 0.4025424139756529, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5001124532809842, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4774498617073846, "a1": 0.4998877467190158, "a2": 0.5001122532809842 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5001122532809842, "support": [ [ 2, @@ -168323,11 +170398,26 @@ "value": 0.5001122532809842 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4025424139756529, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4774498617073846, "a1": 0.5474812745550787, "a2": 0.4025426139756529 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4025426139756529, "support": [ [ 0, @@ -168349,7 +170439,7 @@ "value": 0.4025426139756529 }, "status": "bounded", - "upper": 0.5001123532809841, + "upper": 0.5001124532809842, "worlds": 8 }, "intervals": { @@ -168373,16 +170463,31 @@ "a2": 0.41267299291603676 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.41267289291603676, + "lower": 0.41267279291603676, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.41267319291603677, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5868615482533803, "a1": 0.48853999235688006, "a2": 0.41267299291603676 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.41267299291603676, "support": [ [ 0, @@ -168404,11 +170509,26 @@ "value": 0.41267299291603676 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.41267279291603676, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5868615482533803, "a1": 0.48853999235688006, "a2": 0.41267299291603676 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.41267299291603676, "support": [ [ 0, @@ -168430,7 +170550,7 @@ "value": 0.41267299291603676 }, "status": "bounded", - "upper": 0.41267309291603677, + "upper": 0.41267319291603677, "worlds": 8 }, "proofs": [ @@ -168448,16 +170568,31 @@ { "id": 30, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6318505275036257, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.41453847745797, "a1": 0.45092589824968493, "a2": 0.6318503275036257 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6318503275036257, "support": [ [ 0, @@ -168479,11 +170614,26 @@ "value": 0.6318503275036257 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.2966914690660941, "a1": 0.45092589824968493, "a2": 0.5490741017503151 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -168501,7 +170651,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.6318504275036256, + "upper": 0.6318505275036257, "worlds": 8 }, "intervals": { @@ -168525,16 +170675,31 @@ "a2": 0.6131359159522191 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.05111454364094559, + "lower": 0.051114243640945536, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6131361159522191, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.40134415163606674, "a1": 0.43797872768872653, "a2": 0.6131359159522191 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6131359159522191, "support": [ [ 0, @@ -168556,11 +170721,26 @@ "value": 0.6131359159522191 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.051114243640945536, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.40134415163606674, "a1": 0.43797872768872653, "a2": 0.6131359159522191 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.05111464364094559, "support": [ [ 3, @@ -168582,7 +170762,7 @@ "value": 0.05111464364094559 }, "status": "bounded", - "upper": 0.613136015952219, + "upper": 0.6131361159522191, "worlds": 8 }, "proofs": [ @@ -168623,11 +170803,27 @@ { "id": 31, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.44685396093609664, + "lower": 0.44685386093609664, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6361552181819318, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6361550181819318, "a1": 0.576248959409718, @@ -168635,6 +170831,9 @@ "a3": 0.3922886607938852, "a4": 0.5217623591062439 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6361550181819318, "support": [ [ 3, @@ -168664,6 +170863,22 @@ "value": 0.6361550181819318 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44685386093609664, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44685406093609664, "a1": 0.576248959409718, @@ -168671,6 +170886,9 @@ "a3": 0.3922886607938852, "a4": 0.5217623591062439 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44685406093609664, "support": [ [ 3, @@ -168700,7 +170918,7 @@ "value": 0.44685406093609664 }, "status": "bounded", - "upper": 0.6361551181819317, + "upper": 0.6361552181819318, "worlds": 32 }, "intervals": { @@ -168734,11 +170952,27 @@ "a4": 0.5963244908182962 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4654145711230508, + "lower": 0.4654144711230508, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4654148711230508, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4654146711230508, "a1": 0.614655429440115, @@ -168746,6 +170980,9 @@ "a3": 0.45971572389781695, "a4": 0.5963244908182963 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4654146711230508, "support": [ [ 3, @@ -168775,6 +171012,22 @@ "value": 0.4654146711230508 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4654144711230508, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4654146711230508, "a1": 0.614655429440115, @@ -168782,6 +171035,9 @@ "a3": 0.45971572389781695, "a4": 0.5963244908182963 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4654146711230508, "support": [ [ 3, @@ -168811,7 +171067,7 @@ "value": 0.4654146711230508 }, "status": "bounded", - "upper": 0.4654147711230508, + "upper": 0.4654148711230508, "worlds": 32 }, "proofs": [ @@ -168838,11 +171094,29 @@ { "id": 32, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.40271750763543135, + "lower": 0.40271740763543135, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5809782445384818, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5809780445384818, "a1": 0.47506136789397524, @@ -168851,6 +171125,9 @@ "a4": 0.49060622834783874, "a5": 0.47506136789397524 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5809780445384818, "support": [ [ 1, @@ -168872,6 +171149,24 @@ "value": 0.5809780445384818 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.40271740763543135, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.40271760763543135, "a1": 0.4814863404617735, @@ -168880,6 +171175,9 @@ "a4": 0.450886242450032, "a5": 0.549113757549968 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.40271760763543135, "support": [ [ 25, @@ -168905,7 +171203,7 @@ "value": 0.40271760763543135 }, "status": "bounded", - "upper": 0.5809781445384817, + "upper": 0.5809782445384818, "worlds": 64 }, "intervals": { @@ -168944,19 +171242,40 @@ "a5": 0.4656855450062495 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5054176202598489, + "lower": 0.505417520259849, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.505417920259849, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { - "a0": 0.5054177202598489, + "a0": 0.505417720259849, "a1": 0.3789952157900979, "a2": 0.5375735108023402, "a3": 0.5548220266601688, "a4": 0.46558146708734455, "a5": 0.4656855450062495 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.505417720259849, "support": [ [ 1, @@ -168987,17 +171306,38 @@ 0.12968156027834077 ] ], - "value": 0.5054177202598489 + "value": 0.505417720259849 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.505417520259849, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { - "a0": 0.5054177202598489, + "a0": 0.505417720259849, "a1": 0.3789952157900979, "a2": 0.5375735108023402, "a3": 0.5548220266601688, "a4": 0.46558146708734455, "a5": 0.4656855450062495 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.505417720259849, "support": [ [ 1, @@ -169028,10 +171368,10 @@ 0.12968156027834077 ] ], - "value": 0.5054177202598489 + "value": 0.505417720259849 }, "status": "bounded", - "upper": 0.5054178202598488, + "upper": 0.505417920259849, "worlds": 64 }, "proofs": [ @@ -169052,17 +171392,34 @@ { "id": 33, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.46101961949677545, + "lower": 0.46101951949677544, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5997281440546263, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.617849772883278, "a1": 0.6429523378010915, "a2": 0.5997279440546263, "a3": 0.5051074735864217 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5997279440546263, "support": [ [ 3, @@ -169088,12 +171445,29 @@ "value": 0.5997279440546263 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.46101951949677544, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.617849772883278, "a1": 0.6429523378010915, "a2": 0.46101971949677545, "a3": 0.5051074735864217 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.46101971949677545, "support": [ [ 3, @@ -169119,7 +171493,7 @@ "value": 0.46101971949677545 }, "status": "bounded", - "upper": 0.5997280440546262, + "upper": 0.5997281440546263, "worlds": 16 }, "intervals": { @@ -169148,17 +171522,34 @@ "a3": 0.3531203496905605 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5213637090578999, + "lower": 0.5213636090578998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5213640090578998, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5029912357969011, "a1": 0.6289631517040922, "a2": 0.5213638090578998, "a3": 0.3531203496905605 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5213638090578998, "support": [ [ 3, @@ -169184,12 +171575,29 @@ "value": 0.5213638090578998 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5213636090578998, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5029912357969011, "a1": 0.6289631517040922, "a2": 0.5213638090578998, "a3": 0.3531203496905605 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5213638090578998, "support": [ [ 3, @@ -169215,7 +171623,7 @@ "value": 0.5213638090578998 }, "status": "bounded", - "upper": 0.5213639090578998, + "upper": 0.5213640090578998, "worlds": 16 }, "proofs": [ @@ -169252,17 +171660,34 @@ { "id": 34, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4072917158197106, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5065567174149557, "a1": 0.682189509085428, "a2": 0.40729151581971057, "a3": 0.47271101239137026 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.40729151581971057, "support": [ [ 0, @@ -169288,12 +171713,29 @@ "value": 0.40729151581971057 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5065567174149557, "a1": 0.682189509085428, "a2": 0.36697749002824265, "a3": 0.4068211513513198 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -169319,7 +171761,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4072916158197106, + "upper": 0.4072917158197106, "worlds": 16 }, "intervals": { @@ -169348,17 +171790,34 @@ "a3": 0.42955406996381024 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.40011779126203717, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.41539226150176684, "a1": 0.6302510510066314, "a2": 0.4001175912620372, "a3": 0.42955406996381024 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4001175912620372, "support": [ [ 0, @@ -169384,12 +171843,29 @@ "value": 0.4001175912620372 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.41539226150176684, "a1": 0.6302510510066314, "a2": 0.40011759126203716, "a3": 0.42955406996381024 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -169415,7 +171891,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4001176912620372, + "upper": 0.40011779126203717, "worlds": 16 }, "proofs": [ @@ -169456,16 +171932,31 @@ { "id": 35, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.04646563041370422, + "lower": 0.04646533041370417, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6580420835345657, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6580418835345657, "a1": 0.6580418835345657, "a2": 0.5185910781842733 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6580418835345657, "support": [ [ 3, @@ -169483,11 +171974,26 @@ "value": 0.6580418835345657 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.04646533041370417, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4689422434495612, "a1": 0.577523486964143, "a2": 0.5185910781842733 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.04646573041370422, "support": [ [ 2, @@ -169509,7 +172015,7 @@ "value": 0.04646573041370422 }, "status": "bounded", - "upper": 0.6580419835345657, + "upper": 0.6580420835345657, "worlds": 8 }, "intervals": { @@ -169533,16 +172039,31 @@ "a2": 0.6046010949736618 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.23772167611750067, + "lower": 0.23772137611750055, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5785674908509703, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5785672908509703, "a1": 0.6591544852665304, "a2": 0.6046010949736618 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5785672908509703, "support": [ [ 3, @@ -169564,11 +172085,26 @@ "value": 0.5785672908509703 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.23772137611750055, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5785672908509703, "a1": 0.6591544852665304, "a2": 0.6046010949736618 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.23772177611750067, "support": [ [ 2, @@ -169590,7 +172126,7 @@ "value": 0.23772177611750067 }, "status": "bounded", - "upper": 0.5785673908509702, + "upper": 0.5785674908509703, "worlds": 8 }, "proofs": [ @@ -169619,17 +172155,34 @@ { "id": 36, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.3461713561261031, + "lower": 0.3461712561261031, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9906923567335064, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4675375156106412, "a1": 0.5231545411228653, "a2": 0.5271995060410791, "a3": 0.5670267660007274 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9906920567335065, "support": [ [ 0, @@ -169655,12 +172208,29 @@ "value": 0.9906920567335065 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3461712561261031, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4675375156106413, "a1": 0.3461714561261031, "a2": 0.5271995060410791, "a3": 0.45085493963888734 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3461714561261031, "support": [ [ 3, @@ -169686,7 +172256,7 @@ "value": 0.3461714561261031 }, "status": "bounded", - "upper": 0.9906921567335064, + "upper": 0.9906923567335064, "worlds": 16 }, "intervals": { @@ -169715,17 +172285,34 @@ "a3": 0.5610001375391563 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.49866122549595754, + "lower": 0.4986611254959576, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9124694809725049, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4138078554765474, "a1": 0.4986613254959576, "a2": 0.5038256720621749, "a3": 0.5610001375391563 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.912469180972505, "support": [ [ 0, @@ -169751,12 +172338,29 @@ "value": 0.912469180972505 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4986611254959576, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4138078554765474, "a1": 0.49866132549595754, "a2": 0.5038256720621749, "a3": 0.5610001375391563 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.49866132549595754, "support": [ [ 3, @@ -169782,7 +172386,7 @@ "value": 0.49866132549595754 }, "status": "bounded", - "upper": 0.9124692809725049, + "upper": 0.9124694809725049, "worlds": 16 }, "proofs": [ @@ -169810,11 +172414,29 @@ { "id": 37, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.397107503877047, + "lower": 0.397107403877047, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4230248034731426, "a1": 0.5769751965268574, @@ -169823,6 +172445,9 @@ "a4": 0.49379514035147265, "a5": 0.5043683179538425 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -169844,6 +172469,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.397107403877047, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49379514035147265, "a1": 0.397107603877047, @@ -169852,6 +172495,9 @@ "a4": 0.49379514035147265, "a5": 0.5523678148630677 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.397107603877047, "support": [ [ 4, @@ -169916,11 +172562,29 @@ "a5": 0.5119463999749181 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5177368953961373, + "lower": 0.5177367953961373, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48859917595163405, "a1": 0.5177369953961373, @@ -169929,6 +172593,9 @@ "a4": 0.4556501138994683, "a5": 0.5119463999749181 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -169962,6 +172629,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5177367953961373, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48859917595163405, "a1": 0.5177369953961373, @@ -169970,6 +172655,9 @@ "a4": 0.4556501138994683, "a5": 0.5119463999749181 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5177369953961373, "support": [ [ 1, @@ -170038,15 +172726,28 @@ { "id": 38, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6685511909896654, + "lower": 0.6685510909896654, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7314489090103345, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.7314487090103345, "a1": 0.44915994104478263 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.7314487090103345, "support": [ [ 0, @@ -170064,10 +172765,23 @@ "value": 0.7314487090103345 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6685510909896654, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6685512909896654, "a1": 0.44915994104478263 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6685512909896654, "support": [ [ 0, @@ -170085,7 +172799,7 @@ "value": 0.6685512909896654 }, "status": "bounded", - "upper": 0.7314488090103345, + "upper": 0.7314489090103345, "worlds": 4 }, "intervals": { @@ -170104,15 +172818,28 @@ "a1": 0.42544106750982674 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6997815370705277, + "lower": 0.6997814370705276, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6997818370705277, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6997816370705277, "a1": 0.42544106750982674 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6997816370705277, "support": [ [ 1, @@ -170130,10 +172857,23 @@ "value": 0.6997816370705277 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6997814370705276, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6997816370705277, "a1": 0.42544106750982674 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6997816370705277, "support": [ [ 1, @@ -170151,7 +172891,7 @@ "value": 0.6997816370705277 }, "status": "bounded", - "upper": 0.6997817370705276, + "upper": 0.6997818370705277, "worlds": 4 }, "proofs": [ @@ -170179,11 +172919,27 @@ { "id": 39, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.541086065142731, + "lower": 0.541085965142731, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5535057490503803, "a1": 0.5390494361161505, @@ -170191,6 +172947,9 @@ "a3": 0.5548430307113901, "a4": 0.43617054157055324 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -170220,6 +172979,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.541085965142731, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46355534065793, "a1": 0.4758102226620554, @@ -170227,6 +173002,9 @@ "a3": 0.5548430307113901, "a4": 0.43617054157055324 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.541086165142731, "support": [ [ 5, @@ -170290,11 +173068,27 @@ "a4": 0.4884478085477372 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5746282519116143, + "lower": 0.5746281519116142, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49681679647223187, "a1": 0.5256781554721635, @@ -170302,6 +173096,9 @@ "a3": 0.5761626773956618, "a4": 0.4884478085477372 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -170331,6 +173128,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5746281519116142, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49681679647223187, "a1": 0.5256781554721635, @@ -170338,6 +173151,9 @@ "a3": 0.5761626773956618, "a4": 0.4884478085477372 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5746283519116142, "support": [ [ 5, @@ -170396,11 +173212,27 @@ { "id": 40, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.479082375685661, + "lower": 0.4790822756856609, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4389768777920403, "a1": 0.43645076031557717, @@ -170408,6 +173240,9 @@ "a3": 0.46789811938260195, "a4": 0.42232319953379527 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -170437,6 +173272,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4790822756856609, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4389768777920403, "a1": 0.4678981193826019, @@ -170444,6 +173295,9 @@ "a3": 0.4678981193826019, "a4": 0.5658742253589086 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.479082475685661, "support": [ [ 0, @@ -170503,11 +173357,27 @@ "a4": 0.5156758004348074 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5492281933267394, + "lower": 0.5492280933267394, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4590808293948108, "a1": 0.48696396833444205, @@ -170515,6 +173385,9 @@ "a3": 0.4955373618245025, "a4": 0.5156758004348074 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -170544,6 +173417,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5492280933267394, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4590808293948108, "a1": 0.48696396833444205, @@ -170551,6 +173440,9 @@ "a3": 0.4955373618245025, "a4": 0.5156758004348074 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5492282933267394, "support": [ [ 0, @@ -170616,11 +173508,29 @@ { "id": 41, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5199816235181691, + "lower": 0.5199815235181691, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4803067388677813, "a1": 0.5196932611322187, @@ -170629,6 +173539,9 @@ "a4": 0.4803067388677813, "a5": 0.5349364529395102 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -170646,6 +173559,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5199815235181691, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4359461575241419, "a1": 0.5557969047071922, @@ -170654,6 +173585,9 @@ "a4": 0.519874491599104, "a5": 0.5199817235181691 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5199817235181691, "support": [ [ 4, @@ -170726,11 +173660,29 @@ "a5": 0.57879058820129 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5787904882012901, + "lower": 0.57879038820129, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4761214410322436, "a1": 0.5161311746325159, @@ -170739,6 +173691,9 @@ "a4": 0.48190028153479664, "a5": 0.57879058820129 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -170772,6 +173727,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.57879038820129, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4761214410322436, "a1": 0.5161311746325159, @@ -170780,6 +173753,9 @@ "a4": 0.48190028153479664, "a5": 0.57879058820129 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.57879058820129, "support": [ [ 4, @@ -170847,11 +173823,27 @@ { "id": 42, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5213914962211571, + "lower": 0.5213913962211572, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49623575235880396, "a1": 0.41441945951778736, @@ -170859,6 +173851,9 @@ "a3": 0.4167816431196911, "a4": 0.501060324300249 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 5, @@ -170888,6 +173883,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5213913962211572, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4962357523588039, "a1": 0.5234468945267613, @@ -170895,6 +173906,9 @@ "a3": 0.4167816431196911, "a4": 0.6196899687829865 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.521391596221157, "support": [ [ 0, @@ -170958,11 +173972,27 @@ "a4": 0.561090057077876 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5899724680096622, + "lower": 0.5899723680096621, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5271997881180094, "a1": 0.4776780081562853, @@ -170970,6 +174000,9 @@ "a3": 0.5179570783839126, "a4": 0.561090057077876 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 5, @@ -170999,6 +174032,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5899723680096621, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5271997881180095, "a1": 0.4776780081562853, @@ -171006,6 +174055,9 @@ "a3": 0.5179570783839126, "a4": 0.561090057077876 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5899725680096621, "support": [ [ 0, @@ -171061,16 +174113,31 @@ { "id": 43, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.48820478261212547, + "lower": 0.48820468261212546, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48820488261212547, "a1": 0.48820488261212547, "a2": 0.5117951173878745 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -171084,11 +174151,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.48820468261212546, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48820488261212547, "a1": 0.5024259451218506, "a2": 0.48820488261212547 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.48820488261212547, "support": [ [ 0, @@ -171130,16 +174212,31 @@ "a2": 0.43130299792399335 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.6011256821486493, + "lower": 0.6011255821486492, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6011257821486492, "a1": 0.46379506361281825, "a2": 0.43130299792399335 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -171161,11 +174258,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6011255821486492, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6011257821486492, "a1": 0.46379506361281825, "a2": 0.43130299792399335 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6011257821486492, "support": [ [ 0, @@ -171227,15 +174339,28 @@ { "id": 44, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.5386252326614063, + "lower": 0.5386251326614062, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.35876812068642105, "a1": 0.649147593102786 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -171253,10 +174378,23 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5386251326614062, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.35876812068642105, "a1": 0.5386253326614062 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5386253326614062, "support": [ [ 0, @@ -171293,15 +174431,28 @@ "a1": 0.6045602298408161 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6045601298408162, + "lower": 0.6045600298408161, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9211213303888217, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.31656080054800567, "a1": 0.6045602298408161 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9211210303888218, "support": [ [ 0, @@ -171319,10 +174470,23 @@ "value": 0.9211210303888218 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6045600298408161, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.31656080054800567, "a1": 0.6045602298408161 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6045602298408161, "support": [ [ 0, @@ -171340,7 +174504,7 @@ "value": 0.6045602298408161 }, "status": "bounded", - "upper": 0.9211211303888217, + "upper": 0.9211213303888217, "worlds": 4 }, "proofs": [ @@ -171371,11 +174535,27 @@ { "id": 45, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4686253660047739, + "lower": 0.4686252660047739, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44245432826456255, "a1": 0.5101075690930683, @@ -171383,6 +174563,9 @@ "a3": 0.5101075690930683, "a4": 0.48989243090693174 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -171404,6 +174587,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4686252660047739, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5101075690930683, "a1": 0.6089909549060057, @@ -171411,6 +174610,9 @@ "a3": 0.4686254660047739, "a4": 0.48989243090693174 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4686254660047739, "support": [ [ 3, @@ -171470,11 +174672,27 @@ "a4": 0.5774645499143579 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5429090493464516, + "lower": 0.5429089493464515, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5332881906592022, "a1": 0.5049133742332188, @@ -171482,6 +174700,9 @@ "a3": 0.5429091493464515, "a4": 0.5774645499143579 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -171511,6 +174732,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5429089493464515, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5332881906592022, "a1": 0.5049133742332188, @@ -171518,6 +174755,9 @@ "a3": 0.5429091493464515, "a4": 0.5774645499143579 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5429091493464515, "support": [ [ 3, @@ -171589,11 +174829,29 @@ { "id": 46, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9981684966934784, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4183655492704199, "a1": 0.5816344507295801, @@ -171602,6 +174860,9 @@ "a4": 0.5323080726689189, "a5": 0.46586012402455956 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9981681966934784, "support": [ [ 1, @@ -171623,6 +174884,24 @@ "value": 0.9981681966934784 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.40965181664026995, "a1": 0.43165825579450745, @@ -171631,6 +174910,9 @@ "a4": 0.5241779913681056, "a5": 0.41360258364599545 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 11, @@ -171656,7 +174938,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.9981682966934784, + "upper": 0.9981684966934784, "worlds": 64 }, "intervals": { @@ -171695,11 +174977,29 @@ "a5": 0.42240371555701955 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.10148201047839348, + "lower": 0.1014817104783934, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9414761029670156, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.493206034395962, "a1": 0.527351656965888, @@ -171708,6 +175008,9 @@ "a4": 0.5337637644717141, "a5": 0.42240371555701955 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9414758029670156, "support": [ [ 15, @@ -171741,6 +175044,24 @@ "value": 0.9414758029670156 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.1014817104783934, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.493206034395962, "a1": 0.527351656965888, @@ -171749,6 +175070,9 @@ "a4": 0.5337637644717141, "a5": 0.4224037155570196 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.10148211047839348, "support": [ [ 7, @@ -171782,7 +175106,7 @@ "value": 0.10148211047839348 }, "status": "bounded", - "upper": 0.9414759029670156, + "upper": 0.9414761029670156, "worlds": 64 }, "proofs": [ @@ -171812,11 +175136,29 @@ { "id": 47, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8996479230701709, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5629073601850146, "a1": 0.5628440567366577, @@ -171825,6 +175167,9 @@ "a4": 0.5062472467593817, "a5": 0.4543312271214529 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.899647623070171, "support": [ [ 6, @@ -171858,6 +175203,24 @@ "value": 0.899647623070171 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49284176873484603, "a1": 0.5019643056326804, @@ -171866,6 +175229,9 @@ "a4": 0.4623938682231968, "a5": 0.4007210376869095 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 4, @@ -171899,7 +175265,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.8996477230701709, + "upper": 0.8996479230701709, "worlds": 64 }, "intervals": { @@ -171938,11 +175304,29 @@ "a5": 0.4292361477317434 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7823819666741856, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5060382369696729, "a1": 0.5390497979231552, @@ -171951,6 +175335,9 @@ "a4": 0.48690725106169097, "a5": 0.4292361477317434 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.7823816666741856, "support": [ [ 6, @@ -171984,14 +175371,35 @@ "value": 0.7823816666741856 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { - "a0": 0.5060382369696728, + "a0": 0.5060382369696729, "a1": 0.5390497979231552, "a2": 0.35314551894244217, "a3": 0.5477845689226175, "a4": 0.486907251061691, "a5": 0.4292361477317434 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 4, @@ -172025,7 +175433,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.7823817666741856, + "upper": 0.7823819666741856, "worlds": 64 }, "proofs": [ @@ -172064,11 +175472,27 @@ { "id": 48, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.58604272137958, + "lower": 0.58604262137958, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.58604282137958, "a1": 0.4139833012752092, @@ -172076,6 +175500,9 @@ "a3": 0.46828454715923173, "a4": 0.5333079409855002 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -172105,6 +175532,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.58604262137958, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.58604282137958, "a1": 0.5446472265421946, @@ -172112,6 +175555,9 @@ "a3": 0.46828454715923173, "a4": 0.5333079409855002 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.58604282137958, "support": [ [ 10, @@ -172175,11 +175621,27 @@ "a4": 0.5938777649462765 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.625979638037683, + "lower": 0.6259795380376829, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6259797380376829, "a1": 0.46180900950628245, @@ -172187,6 +175649,9 @@ "a3": 0.5109203005486268, "a4": 0.5938777649462765 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -172216,6 +175681,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6259795380376829, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6259797380376829, "a1": 0.46180900950628245, @@ -172223,6 +175704,9 @@ "a3": 0.5109203005486268, "a4": 0.5938777649462765 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6259797380376829, "support": [ [ 10, @@ -172291,17 +175775,34 @@ { "id": 49, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.39232930867434596, + "lower": 0.39232920867434595, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5900237325021246, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3952189156768992, "a1": 0.5900235325021246, "a2": 0.6119619146813542, "a3": 0.6894380740237401 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5900235325021246, "support": [ [ 3, @@ -172327,12 +175828,29 @@ "value": 0.5900235325021246 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.39232920867434595, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39521891567689926, "a1": 0.39232940867434596, "a2": 0.6119619146813543, "a3": 0.6894380740237401 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.39232940867434596, "support": [ [ 3, @@ -172358,7 +175876,7 @@ "value": 0.39232940867434596 }, "status": "bounded", - "upper": 0.5900236325021245, + "upper": 0.5900237325021246, "worlds": 16 }, "intervals": { @@ -172387,17 +175905,34 @@ "a3": 0.7452464901685815 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5692687423418155, + "lower": 0.5692686423418154, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5692690423418154, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.34104117387668154, "a1": 0.5692688423418154, "a2": 0.5071884067231824, "a3": 0.7452464901685815 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5692688423418154, "support": [ [ 3, @@ -172423,12 +175958,29 @@ "value": 0.5692688423418154 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5692686423418154, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.34104117387668154, "a1": 0.5692688423418154, "a2": 0.5071884067231824, "a3": 0.7452464901685815 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5692688423418154, "support": [ [ 3, @@ -172454,7 +176006,7 @@ "value": 0.5692688423418154 }, "status": "bounded", - "upper": 0.5692689423418154, + "upper": 0.5692690423418154, "worlds": 16 }, "proofs": [ @@ -172487,15 +176039,28 @@ { "id": 50, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.5106907637762277, + "lower": 0.5106906637762276, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6978199745216447, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5137104653553008, "a1": 0.6978197745216447 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6978197745216447, "support": [ [ 0, @@ -172513,10 +176078,23 @@ "value": 0.6978197745216447 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5106906637762276, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5106908637762276, "a1": 0.5106908637762276 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5106908637762276, "support": [ [ 0, @@ -172530,7 +176108,7 @@ "value": 0.5106908637762276 }, "status": "bounded", - "upper": 0.6978198745216446, + "upper": 0.6978199745216447, "worlds": 4 }, "intervals": { @@ -172549,15 +176127,28 @@ "a1": 0.5898275444952383 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.5898274444952384, + "lower": 0.5898273444952383, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5898277444952383, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.44091708935419804, "a1": 0.5898275444952383 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5898275444952383, "support": [ [ 1, @@ -172575,10 +176166,23 @@ "value": 0.5898275444952383 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5898273444952383, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.44091708935419804, "a1": 0.5898275444952383 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5898275444952383, "support": [ [ 1, @@ -172596,7 +176200,7 @@ "value": 0.5898275444952383 }, "status": "bounded", - "upper": 0.5898276444952383, + "upper": 0.5898277444952383, "worlds": 4 }, "proofs": [ @@ -172625,11 +176229,27 @@ { "id": 51, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4561865757438596, + "lower": 0.4561864757438596, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4988593242922026, "a1": 0.4504255331286491, @@ -172637,6 +176257,9 @@ "a3": 0.5011406757077974, "a4": 0.5011406757077974 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -172658,6 +176281,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4561864757438596, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4426003077499998, "a1": 0.5073363977545106, @@ -172665,6 +176304,9 @@ "a3": 0.5011406757077974, "a4": 0.4561866757438596 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4561866757438596, "support": [ [ 4, @@ -172728,18 +176370,37 @@ "a4": 0.60263670056793 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.60263660056793, + "lower": 0.60263650056793, "max": { - "marginals": { - "a0": 0.4861949397998151, + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], + "marginals": { + "a0": 0.48619493979981504, "a1": 0.45862495396540576, "a2": 0.5066159185198114, "a3": 0.5953673600586775, "a4": 0.60263670056793 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -172769,6 +176430,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.60263650056793, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4861949397998151, "a1": 0.45862495396540576, @@ -172776,6 +176453,9 @@ "a3": 0.5953673600586775, "a4": 0.60263670056793 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.60263670056793, "support": [ [ 8, @@ -172834,11 +176514,27 @@ { "id": 52, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6168365428978267, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6168363428978267, "a1": 0.5687065903247814, @@ -172846,6 +176542,9 @@ "a3": 0.39691477525336816, "a4": 0.4468443811035496 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6168363428978267, "support": [ [ 7, @@ -172871,6 +176570,22 @@ "value": 0.6168363428978267 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4515070141278702, "a1": 0.46948900255979975, @@ -172878,6 +176593,9 @@ "a3": 0.39691477525336805, "a4": 0.4468443811035496 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 5, @@ -172907,7 +176625,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.6168364428978267, + "upper": 0.6168365428978267, "worlds": 32 }, "intervals": { @@ -172941,11 +176659,27 @@ "a4": 0.4579075274479383 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.017503532798876013, + "lower": 0.01750323279887601, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5302833538809851, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5302831538809851, "a1": 0.4872204789178909, @@ -172953,6 +176687,9 @@ "a3": 0.46645640979134, "a4": 0.4579075274479383 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5302831538809851, "support": [ [ 4, @@ -172982,6 +176719,22 @@ "value": 0.5302831538809851 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.01750323279887601, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5302831538809851, "a1": 0.4872204789178909, @@ -172989,6 +176742,9 @@ "a3": 0.46645640979134007, "a4": 0.4579075274479383 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.017503632798876012, "support": [ [ 3, @@ -173018,7 +176774,7 @@ "value": 0.017503632798876012 }, "status": "bounded", - "upper": 0.5302832538809851, + "upper": 0.5302833538809851, "worlds": 32 }, "proofs": [ @@ -173043,16 +176799,31 @@ { "id": 53, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5727304180697161, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5727302180697162, "a1": 0.4694612840656441, "a2": 0.5727302180697162 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5727302180697162, "support": [ [ 2, @@ -173070,11 +176841,26 @@ "value": 0.5727302180697162 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.42081816902705804, "a1": 0.5344262700810971, "a2": 0.4655737299189029 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -173092,7 +176878,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5727303180697162, + "upper": 0.5727304180697161, "worlds": 8 }, "intervals": { @@ -173116,16 +176902,31 @@ "a2": 0.4885902419421745 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.44999481468401903, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.449994614684019, "a1": 0.6000538007437333, "a2": 0.4885902419421745 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.449994614684019, "support": [ [ 2, @@ -173147,11 +176948,26 @@ "value": 0.449994614684019 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.449994614684019, "a1": 0.6000538007437333, "a2": 0.4885902419421745 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -173173,7 +176989,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.449994714684019, + "upper": 0.44999481468401903, "worlds": 8 }, "proofs": [ @@ -173217,15 +177033,28 @@ { "id": 54, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.1781550116242907, + "lower": 0.17815471162429075, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5243524473594774, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5243522473594774, "a1": 0.7501264066028157 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5243522473594774, "support": [ [ 0, @@ -173243,10 +177072,23 @@ "value": 0.5243522473594774 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.17815471162429075, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.428028705021475, "a1": 0.7501264066028157 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.1781551116242907, "support": [ [ 1, @@ -173264,7 +177106,7 @@ "value": 0.1781551116242907 }, "status": "bounded", - "upper": 0.5243523473594773, + "upper": 0.5243524473594774, "worlds": 4 }, "intervals": { @@ -173283,15 +177125,28 @@ "a1": 0.7568331730990556 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.25147415022952774, + "lower": 0.25147385022952773, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4946412771304721, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4946410771304721, "a1": 0.7568331730990556 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4946410771304721, "support": [ [ 0, @@ -173309,10 +177164,23 @@ "value": 0.4946410771304721 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.25147385022952773, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4946410771304721, "a1": 0.7568331730990556 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.25147425022952774, "support": [ [ 1, @@ -173330,7 +177198,7 @@ "value": 0.25147425022952774 }, "status": "bounded", - "upper": 0.4946411771304721, + "upper": 0.4946412771304721, "worlds": 4 }, "proofs": [ @@ -173348,11 +177216,27 @@ { "id": 55, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.3346073805716753, + "lower": 0.33460728057167527, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4446702266555558, "a1": 0.4194329603474767, @@ -173360,6 +177244,9 @@ "a3": 0.5553297733444442, "a4": 0.5553297733444442 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -173381,6 +177268,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.33460728057167527, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3346074805716753, "a1": 0.49141399359011617, @@ -173388,6 +177291,9 @@ "a3": 0.5553297733444442, "a4": 0.49208459198244814 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3346074805716753, "support": [ [ 10, @@ -173451,11 +177357,27 @@ "a4": 0.5056129014325652 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.37693413980663487, + "lower": 0.37693403980663487, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8825474412392, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.3769342398066349, "a1": 0.42803255944526397, @@ -173463,6 +177385,9 @@ "a3": 0.5828853934288599, "a4": 0.5056129014325652 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8825471412392001, "support": [ [ 2, @@ -173492,6 +177417,22 @@ "value": 0.8825471412392001 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.37693403980663487, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3769342398066349, "a1": 0.42803255944526397, @@ -173499,6 +177440,9 @@ "a3": 0.5828853934288599, "a4": 0.5056129014325652 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3769342398066349, "support": [ [ 10, @@ -173528,7 +177472,7 @@ "value": 0.3769342398066349 }, "status": "bounded", - "upper": 0.8825472412392, + "upper": 0.8825474412392, "worlds": 32 }, "proofs": [ @@ -173552,11 +177496,29 @@ { "id": 56, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5189283480820347, "a1": 0.5189283480820347, @@ -173565,6 +177527,9 @@ "a4": 0.5189283480820347, "a5": 0.5550124461565005 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 19, @@ -173586,6 +177551,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48107165191796536, "a1": 0.5189283480820347, @@ -173594,6 +177577,9 @@ "a4": 0.5394756875165264, "a5": 0.4449875538434996 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 10, @@ -173658,11 +177644,29 @@ "a5": 0.5320254749069409 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.0136212836248279, + "lower": 0.01362098362482801, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9256892784694094, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5134673184452023, "a1": 0.4440930697515224, @@ -173671,6 +177675,9 @@ "a4": 0.4739701291563917, "a5": 0.5320254749069409 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9256889784694095, "support": [ [ 4, @@ -173704,6 +177711,24 @@ "value": 0.9256889784694095 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.01362098362482801, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5134673184452023, "a1": 0.4440930697515224, @@ -173712,6 +177737,9 @@ "a4": 0.4739701291563917, "a5": 0.5320254749069409 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.013621383624827899, "support": [ [ 25, @@ -173745,7 +177773,7 @@ "value": 0.013621383624827899 }, "status": "bounded", - "upper": 0.9256890784694094, + "upper": 0.9256892784694094, "worlds": 64 }, "proofs": [ @@ -173772,15 +177800,28 @@ { "id": 57, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6209641821550045, + "lower": 0.6209640821550044, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7474569704765743, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.22752467165325965, "a1": 0.7474567704765743 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.7474567704765743, "support": [ [ 0, @@ -173798,10 +177839,23 @@ "value": 0.7474567704765743 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6209640821550044, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.22752467165325965, "a1": 0.6209642821550044 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6209642821550044, "support": [ [ 0, @@ -173819,7 +177873,7 @@ "value": 0.6209642821550044 }, "status": "bounded", - "upper": 0.7474568704765743, + "upper": 0.7474569704765743, "worlds": 4 }, "intervals": { @@ -173838,15 +177892,28 @@ "a1": 0.6707239577919951 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6707238577919952, + "lower": 0.6707237577919951, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6707241577919951, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.15693523438793316, "a1": 0.6707239577919951 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6707239577919951, "support": [ [ 0, @@ -173864,10 +177931,23 @@ "value": 0.6707239577919951 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6707237577919951, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.15693523438793316, "a1": 0.6707239577919951 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6707239577919951, "support": [ [ 0, @@ -173885,7 +177965,7 @@ "value": 0.6707239577919951 }, "status": "bounded", - "upper": 0.6707240577919951, + "upper": 0.6707241577919951, "worlds": 4 }, "proofs": [ @@ -173909,17 +177989,34 @@ { "id": 58, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5914088442557089, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5872838745444791, "a1": 0.5914086442557089, "a2": 0.587537762202843, "a3": 0.524781476240734 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5914086442557089, "support": [ [ 1, @@ -173945,12 +178042,29 @@ "value": 0.5914086442557089 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.7270018397412352, "a1": 0.44573421288714815, "a2": 0.5467479520828713, "a3": 0.42378995233069455 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -173976,7 +178090,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5914087442557089, + "upper": 0.5914088442557089, "worlds": 16 }, "intervals": { @@ -174005,17 +178119,34 @@ "a3": 0.46352004028545013 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.10020861812222687, + "lower": 0.10020831812222687, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5415752915802207, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6388755264110897, "a1": 0.5415750915802207, "a2": 0.5586336265420062, "a3": 0.46352004028545013 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5415750915802207, "support": [ [ 1, @@ -174041,12 +178172,29 @@ "value": 0.5415750915802207 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.10020831812222687, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6388755264110897, "a1": 0.5415750915802207, "a2": 0.5586336265420062, "a3": 0.46352004028545013 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.10020871812222687, "support": [ [ 3, @@ -174072,7 +178220,7 @@ "value": 0.10020871812222687 }, "status": "bounded", - "upper": 0.5415751915802206, + "upper": 0.5415752915802207, "worlds": 16 }, "proofs": [ @@ -174105,17 +178253,34 @@ { "id": 59, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.4787318426836314, + "lower": 0.4787317426836314, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5887573329552157, "a1": 0.5144584332590092, "a2": 0.40876059534818154, "a3": 0.6154103167305947 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -174141,12 +178306,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4787317426836314, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5212680573163686, "a1": 0.4787319426836314, "a2": 0.4087605953481816, "a3": 0.4787319426836314 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4787319426836314, "support": [ [ 1, @@ -174193,17 +178375,34 @@ "a3": 0.5164778955709336 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5164777955709337, + "lower": 0.5164776955709336, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8685046985124003, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5520502620693771, "a1": 0.35202650294146676, "a2": 0.3989779836781935, "a3": 0.5164778955709336 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8685043985124004, "support": [ [ 3, @@ -174229,12 +178428,29 @@ "value": 0.8685043985124004 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5164776955709336, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5520502620693771, "a1": 0.35202650294146676, "a2": 0.3989779836781935, "a3": 0.5164778955709336 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5164778955709336, "support": [ [ 0, @@ -174260,7 +178476,7 @@ "value": 0.5164778955709336 }, "status": "bounded", - "upper": 0.8685044985124003, + "upper": 0.8685046985124003, "worlds": 16 }, "proofs": [ @@ -174290,11 +178506,27 @@ { "id": 60, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4916763742916282, + "lower": 0.4916762742916282, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4656888464488395, "a1": 0.4450472915707237, @@ -174302,6 +178534,9 @@ "a3": 0.4519819094148233, "a4": 0.3235173005807786 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 5, @@ -174331,6 +178566,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4916762742916282, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4656888464488395, "a1": 0.5100088882045573, @@ -174338,6 +178589,9 @@ "a3": 0.4519819094148233, "a4": 0.3235173005807786 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4916764742916282, "support": [ [ 0, @@ -174401,11 +178655,27 @@ "a4": 0.370394498279563 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5205240808039399, + "lower": 0.5205239808039398, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49612766001661585, "a1": 0.48126966561114937, @@ -174413,6 +178683,9 @@ "a3": 0.5088687633184237, "a4": 0.370394498279563 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 5, @@ -174442,6 +178715,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5205239808039398, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49612766001661585, "a1": 0.48126966561114937, @@ -174449,6 +178738,9 @@ "a3": 0.5088687633184237, "a4": 0.370394498279563 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5205241808039398, "support": [ [ 0, @@ -174519,11 +178811,27 @@ { "id": 61, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.36172419075569096, + "lower": 0.36172409075569095, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.46655873752713733, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4920254312383633, "a1": 0.4742896787870241, @@ -174531,6 +178839,9 @@ "a3": 0.39985541846125716, "a4": 0.4253041808390944 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.46655853752713733, "support": [ [ 3, @@ -174560,6 +178871,22 @@ "value": 0.46655853752713733 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.36172409075569095, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4920254312383633, "a1": 0.4742896787870241, @@ -174567,6 +178894,9 @@ "a3": 0.39985541846125716, "a4": 0.4253041808390944 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.36172429075569096, "support": [ [ 3, @@ -174596,7 +178926,7 @@ "value": 0.36172429075569096 }, "status": "bounded", - "upper": 0.46655863752713733, + "upper": 0.46655873752713733, "worlds": 32 }, "intervals": { @@ -174630,11 +178960,27 @@ "a4": 0.5445396416744394 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.37018004947741173, + "lower": 0.37017994947741173, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.37018034947741174, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5293320711510074, "a1": 0.5172348253573869, @@ -174642,6 +178988,9 @@ "a3": 0.41347739130287325, "a4": 0.5445396416744394 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.37018014947741174, "support": [ [ 3, @@ -174671,6 +179020,22 @@ "value": 0.37018014947741174 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.37017994947741173, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5293320711510074, "a1": 0.5172348253573869, @@ -174678,6 +179043,9 @@ "a3": 0.41347739130287325, "a4": 0.5445396416744394 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.37018014947741174, "support": [ [ 3, @@ -174707,7 +179075,7 @@ "value": 0.37018014947741174 }, "status": "bounded", - "upper": 0.37018024947741174, + "upper": 0.37018034947741174, "worlds": 32 }, "proofs": [ @@ -174732,15 +179100,28 @@ { "id": 62, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.32133258893828615, + "lower": 0.32133248893828614, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.763060256279927, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.47248174405140453, "a1": 0.29057821222852254 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.7630599562799271, "support": [ [ 0, @@ -174758,10 +179139,23 @@ "value": 0.7630599562799271 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.32133248893828614, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.32133268893828615, "a1": 0.29057821222852254 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.32133268893828615, "support": [ [ 0, @@ -174779,7 +179173,7 @@ "value": 0.32133268893828615 }, "status": "bounded", - "upper": 0.763060056279927, + "upper": 0.763060256279927, "worlds": 4 }, "intervals": { @@ -174798,15 +179192,28 @@ "a1": 0.24101329131532573 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.3298095593381206, + "lower": 0.3298094593381206, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5708232506534463, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.3298096593381206, "a1": 0.24101329131532573 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.5708229506534463, "support": [ [ 0, @@ -174824,10 +179231,23 @@ "value": 0.5708229506534463 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3298094593381206, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3298096593381206, "a1": 0.24101329131532573 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3298096593381206, "support": [ [ 0, @@ -174845,7 +179265,7 @@ "value": 0.3298096593381206 }, "status": "bounded", - "upper": 0.5708230506534463, + "upper": 0.5708232506534463, "worlds": 4 }, "proofs": [ @@ -174869,15 +179289,28 @@ { "id": 63, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3962410532035254, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39624085320352537, "a1": 0.39624085320352537 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.39624085320352537, "support": [ [ 0, @@ -174891,10 +179324,23 @@ "value": 0.39624085320352537 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.21696669396628593, "a1": 0.29507995152894234 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -174912,7 +179358,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.39624095320352537, + "upper": 0.3962410532035254, "worlds": 4 }, "intervals": { @@ -174931,15 +179377,28 @@ "a1": 0.3830889610199878 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3224727149634339, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3224725149634339, "a1": 0.3830889610199878 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3224725149634339, "support": [ [ 0, @@ -174957,10 +179416,23 @@ "value": 0.3224725149634339 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3224725149634339, "a1": 0.3830889610199878 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -174978,7 +179450,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.3224726149634339, + "upper": 0.3224727149634339, "worlds": 4 }, "proofs": [ @@ -175000,16 +179472,31 @@ { "id": 64, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.3933388393520086, + "lower": 0.3933387393520086, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4638041177908485, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4638039177908485, "a1": 0.4540097895916402, "a2": 0.5459902104083598 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4638039177908485, "support": [ [ 3, @@ -175027,11 +179514,26 @@ "value": 0.4638039177908485 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3933387393520086, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3933389393520086, "a1": 0.4540097895916402, "a2": 0.5459902104083598 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3933389393520086, "support": [ [ 2, @@ -175049,7 +179551,7 @@ "value": 0.3933389393520086 }, "status": "bounded", - "upper": 0.4638040177908485, + "upper": 0.4638041177908485, "worlds": 8 }, "intervals": { @@ -175073,16 +179575,31 @@ "a2": 0.5674611615698538 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.42735453090823294, + "lower": 0.42735443090823294, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.42735483090823295, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.42735463090823295, "a1": 0.38144082744908275, "a2": 0.5674611615698538 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.42735463090823295, "support": [ [ 0, @@ -175104,11 +179621,26 @@ "value": 0.42735463090823295 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.42735443090823294, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.42735463090823295, "a1": 0.38144082744908275, "a2": 0.5674611615698538 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.42735463090823295, "support": [ [ 0, @@ -175130,7 +179662,7 @@ "value": 0.42735463090823295 }, "status": "bounded", - "upper": 0.42735473090823295, + "upper": 0.42735483090823295, "worlds": 8 }, "proofs": [ @@ -175162,11 +179694,27 @@ { "id": 65, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.3811468882142145, + "lower": 0.3811467882142145, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4390309368174724, "a1": 0.4562316525624845, @@ -175174,6 +179722,9 @@ "a3": 0.4598622165370299, "a4": 0.35408503276943337 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.9999999999999999, "support": [ [ 5, @@ -175203,6 +179754,22 @@ "value": 0.9999999999999999 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3811467882142145, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4390309368174724, "a1": 0.3811469882142145, @@ -175210,6 +179777,9 @@ "a3": 0.4598622165370299, "a4": 0.5177461651402878 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3811469882142145, "support": [ [ 4, @@ -175265,11 +179835,27 @@ "a4": 0.502479064371788 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.39513793496700517, + "lower": 0.39513783496700516, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9122125821139837, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4681330214973082, "a1": 0.39513803496700517, @@ -175277,6 +179863,9 @@ "a3": 0.4898497741601027, "a4": 0.502479064371788 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9122122821139838, "support": [ [ 5, @@ -175306,6 +179895,22 @@ "value": 0.9122122821139838 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.39513783496700516, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4681330214973082, "a1": 0.39513803496700517, @@ -175313,6 +179918,9 @@ "a3": 0.4898497741601027, "a4": 0.502479064371788 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.39513803496700517, "support": [ [ 4, @@ -175342,7 +179950,7 @@ "value": 0.39513803496700517 }, "status": "bounded", - "upper": 0.9122123821139837, + "upper": 0.9122125821139837, "worlds": 32 }, "proofs": [ @@ -175379,16 +179987,31 @@ { "id": 66, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.4509016704022251, + "lower": 0.4509015704022251, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5813564941139039, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3071229912656948, "a1": 0.5813562941139039, "a2": 0.4186437058860961 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5813562941139039, "support": [ [ 2, @@ -175406,11 +180029,26 @@ "value": 0.5813562941139039 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4509015704022251, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3071229912656948, "a1": 0.4509017704022251, "a2": 0.4994957345501744 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4509017704022251, "support": [ [ 0, @@ -175432,7 +180070,7 @@ "value": 0.4509017704022251 }, "status": "bounded", - "upper": 0.5813563941139038, + "upper": 0.5813564941139039, "worlds": 8 }, "intervals": { @@ -175456,16 +180094,31 @@ "a2": 0.49000597774166843 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5024153655903587, + "lower": 0.5024152655903587, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5024156655903587, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.366404289861068, "a1": 0.5024154655903587, "a2": 0.49000597774166843 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5024154655903587, "support": [ [ 0, @@ -175487,11 +180140,26 @@ "value": 0.5024154655903587 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5024152655903587, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.366404289861068, "a1": 0.5024154655903587, "a2": 0.49000597774166843 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5024154655903587, "support": [ [ 0, @@ -175513,7 +180181,7 @@ "value": 0.5024154655903587 }, "status": "bounded", - "upper": 0.5024155655903586, + "upper": 0.5024156655903587, "worlds": 8 }, "proofs": [ @@ -175531,17 +180199,34 @@ { "id": 67, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.4897910935975413, + "lower": 0.4897909935975413, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5377130768753566, "a1": 0.595480124231916, "a2": 0.6511766831897563, "a3": 0.4863068143307214 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -175567,12 +180252,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4897909935975413, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.35929688990205194, "a1": 0.4897911935975413, "a2": 0.6407031100979481, "a3": 0.43506638611224646 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4897911935975413, "support": [ [ 3, @@ -175623,17 +180325,34 @@ "a3": 0.4656453253828041 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5193045341488707, + "lower": 0.5193044341488706, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9020957516462289, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3827908174973583, "a1": 0.5193046341488706, "a2": 0.5058759181176105, "a3": 0.4656453253828041 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.902095451646229, "support": [ [ 0, @@ -175659,12 +180378,29 @@ "value": 0.902095451646229 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5193044341488706, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3827908174973583, "a1": 0.5193046341488706, "a2": 0.5058759181176105, "a3": 0.4656453253828041 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5193046341488706, "support": [ [ 3, @@ -175690,7 +180426,7 @@ "value": 0.5193046341488706 }, "status": "bounded", - "upper": 0.9020955516462289, + "upper": 0.9020957516462289, "worlds": 16 }, "proofs": [ @@ -175717,15 +180453,28 @@ { "id": 68, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.032231836177977036, + "lower": 0.03223153617797704, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6512839604281943, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6512837604281942, "a1": 0.6512837604281942 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6512837604281942, "support": [ [ 0, @@ -175739,10 +180488,23 @@ "value": 0.6512837604281942 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.03223153617797704, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4658333566889228, "a1": 0.5663985794890543 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.03223193617797704, "support": [ [ 1, @@ -175760,7 +180522,7 @@ "value": 0.03223193617797704 }, "status": "bounded", - "upper": 0.6512838604281942, + "upper": 0.6512839604281943, "worlds": 4 }, "intervals": { @@ -175779,15 +180541,28 @@ "a1": 0.674585643977357 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.2838235606938268, + "lower": 0.2838232606938267, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6092382167164698, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6092380167164698, "a1": 0.674585643977357 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6092380167164698, "support": [ [ 0, @@ -175805,10 +180580,23 @@ "value": 0.6092380167164698 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.2838232606938267, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.6092380167164698, "a1": 0.674585643977357 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.2838236606938268, "support": [ [ 1, @@ -175826,7 +180614,7 @@ "value": 0.2838236606938268 }, "status": "bounded", - "upper": 0.6092381167164698, + "upper": 0.6092382167164698, "worlds": 4 }, "proofs": [ @@ -175848,11 +180636,29 @@ { "id": 69, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.36597487638549325, + "lower": 0.36597477638549325, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45489538502801946, "a1": 0.5451046149719805, @@ -175861,6 +180667,9 @@ "a4": 0.5028538350428806, "a5": 0.49714616495711933 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -175878,6 +180687,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.36597477638549325, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45489538502801946, "a1": 0.5745692186605722, @@ -175886,6 +180713,9 @@ "a4": 0.4404112607456597, "a5": 0.5586103933758959 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.36597497638549326, "support": [ [ 1, @@ -175954,11 +180784,29 @@ "a5": 0.48395890227185157 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5224192120153521, + "lower": 0.5224191120153521, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9796313385812025, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4952154127829003, "a1": 0.5691544477098179, @@ -175967,6 +180815,9 @@ "a4": 0.5581085522228604, "a5": 0.48395890227185157 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9796310385812026, "support": [ [ 1, @@ -176000,6 +180851,24 @@ "value": 0.9796310385812026 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5224191120153521, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4952154127829003, "a1": 0.5691544477098179, @@ -176008,6 +180877,9 @@ "a4": 0.5581085522228604, "a5": 0.48395890227185157 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5224193120153521, "support": [ [ 1, @@ -176041,7 +180913,7 @@ "value": 0.5224193120153521 }, "status": "bounded", - "upper": 0.9796311385812025, + "upper": 0.9796313385812025, "worlds": 64 }, "proofs": [ @@ -176070,16 +180942,31 @@ { "id": 70, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4071211607328612, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3281438604356186, "a1": 0.4071209607328612, "a2": 0.5384423609684006 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4071209607328612, "support": [ [ 0, @@ -176101,11 +180988,26 @@ "value": 0.4071209607328612 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3281438604356186, "a1": 0.4071209607328612, "a2": 0.5384423609684006 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -176127,7 +181029,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4071210607328612, + "upper": 0.4071211607328612, "worlds": 8 }, "intervals": { @@ -176151,16 +181053,31 @@ "a2": 0.48712016079372905 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.33583687223656694, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44730345384902315, "a1": 0.33583667223656694, "a2": 0.48712016079372905 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.33583667223656694, "support": [ [ 0, @@ -176182,11 +181099,26 @@ "value": 0.33583667223656694 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44730345384902315, "a1": 0.33583667223656694, "a2": 0.48712016079372905 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -176208,7 +181140,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.33583677223656694, + "upper": 0.33583687223656694, "worlds": 8 }, "proofs": [ @@ -176227,11 +181159,29 @@ { "id": 71, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5352712599701873, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5233016193165032, "a1": 0.5761690613174235, @@ -176240,6 +181190,9 @@ "a4": 0.5292665646832744, "a5": 0.5761690613174235 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5352710599701873, "support": [ [ 1, @@ -176265,6 +181218,24 @@ "value": 0.5352710599701873 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46185009146464595, "a1": 0.538149908535354, @@ -176273,6 +181244,9 @@ "a4": 0.5292665646832744, "a5": 0.4647289400298127 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 10, @@ -176298,7 +181272,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5352711599701873, + "upper": 0.5352712599701873, "worlds": 64 }, "intervals": { @@ -176337,11 +181311,29 @@ "a5": 0.4503688657993136 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4756736727791995, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5050795821498467, "a1": 0.551820900021579, @@ -176350,6 +181342,9 @@ "a4": 0.3912600939642144, "a5": 0.4503688657993136 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.47567347277919947, "support": [ [ 1, @@ -176383,6 +181378,24 @@ "value": 0.47567347277919947 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5050795821498467, "a1": 0.551820900021579, @@ -176391,6 +181404,9 @@ "a4": 0.3912600939642144, "a5": 0.4503688657993136 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -176424,7 +181440,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.47567357277919947, + "upper": 0.4756736727791995, "worlds": 64 }, "proofs": [ @@ -176447,15 +181463,28 @@ { "id": 72, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.586201964349861, + "lower": 0.586201864349861, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.717168922166993, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.717168722166993, "a1": 0.7106231308832945 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.717168722166993, "support": [ [ 0, @@ -176473,10 +181502,23 @@ "value": 0.717168722166993 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.586201864349861, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.586202064349861, "a1": 0.603983610689739 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.586202064349861, "support": [ [ 0, @@ -176494,7 +181536,7 @@ "value": 0.586202064349861 }, "status": "bounded", - "upper": 0.717168822166993, + "upper": 0.717168922166993, "worlds": 4 }, "intervals": { @@ -176513,15 +181555,28 @@ "a1": 0.6192693343832769 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6739884534841758, + "lower": 0.6739883534841757, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6739887534841758, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6739885534841757, "a1": 0.6192693343832769 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6739885534841757, "support": [ [ 1, @@ -176539,10 +181594,23 @@ "value": 0.6739885534841757 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6739883534841757, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6739885534841757, "a1": 0.6192693343832769 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6739885534841757, "support": [ [ 1, @@ -176560,7 +181628,7 @@ "value": 0.6739885534841757 }, "status": "bounded", - "upper": 0.6739886534841757, + "upper": 0.6739887534841758, "worlds": 4 }, "proofs": [ @@ -176581,15 +181649,28 @@ { "id": 73, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3459907366508874, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3459905366508874, "a1": 0.5152268552389468 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3459905366508874, "support": [ [ 0, @@ -176607,10 +181688,23 @@ "value": 0.3459905366508874 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.1508247499733164, "a1": 0.5152268552389468 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -176628,7 +181722,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.3459906366508874, + "upper": 0.3459907366508874, "worlds": 4 }, "intervals": { @@ -176647,15 +181741,28 @@ "a1": 0.6583735618278342 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.2805132278244463, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.2805130278244463, "a1": 0.6583735618278342 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.2805130278244463, "support": [ [ 0, @@ -176673,10 +181780,23 @@ "value": 0.2805130278244463 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.2805130278244463, "a1": 0.6583735618278342 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -176694,7 +181814,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.2805131278244463, + "upper": 0.2805132278244463, "worlds": 4 }, "proofs": [ @@ -176712,11 +181832,27 @@ { "id": 74, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5094620894965122, + "lower": 0.5094619894965121, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5094621894965121, "a1": 0.5575845379243671, @@ -176724,6 +181860,9 @@ "a3": 0.4905378105034879, "a4": 0.5208008167657278 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -176749,6 +181888,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5094619894965121, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5094621894965121, "a1": 0.5146970459851237, @@ -176756,6 +181911,9 @@ "a3": 0.4073778539942329, "a4": 0.5208008167657278 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5094621894965121, "support": [ [ 3, @@ -176819,11 +181977,27 @@ "a4": 0.5670995104364689 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5431265530476986, + "lower": 0.5431264530476986, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5431266530476986, "a1": 0.5252289752630122, @@ -176831,6 +182005,9 @@ "a3": 0.4683806736838211, "a4": 0.5670995104364689 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -176860,6 +182037,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5431264530476986, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5431266530476986, "a1": 0.5252289752630122, @@ -176867,6 +182060,9 @@ "a3": 0.4683806736838211, "a4": 0.5670995104364689 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5431266530476986, "support": [ [ 3, @@ -176920,15 +182116,28 @@ { "id": 75, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.27476200099464054, + "lower": 0.27476190099464054, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4741742692181254, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5966905464969687, "a1": 0.4741740692181254 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4741740692181254, "support": [ [ 0, @@ -176946,10 +182155,23 @@ "value": 0.4741740692181254 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.27476190099464054, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5966905464969687, "a1": 0.27476210099464055 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.27476210099464055, "support": [ [ 0, @@ -176967,7 +182189,7 @@ "value": 0.27476210099464055 }, "status": "bounded", - "upper": 0.4741741692181254, + "upper": 0.4741742692181254, "worlds": 4 }, "intervals": { @@ -176986,15 +182208,28 @@ "a1": 0.4495383173876242 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.4495382173876242, + "lower": 0.44953811738762417, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4495385173876242, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.646910559625207, "a1": 0.4495383173876242 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4495383173876242, "support": [ [ 1, @@ -177012,10 +182247,23 @@ "value": 0.4495383173876242 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44953811738762417, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.646910559625207, "a1": 0.4495383173876242 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4495383173876242, "support": [ [ 1, @@ -177033,7 +182281,7 @@ "value": 0.4495383173876242 }, "status": "bounded", - "upper": 0.4495384173876242, + "upper": 0.4495385173876242, "worlds": 4 }, "proofs": [ @@ -177057,11 +182305,27 @@ { "id": 76, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6285166542593508, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6285164542593508, "a1": 0.46027632068848295, @@ -177069,6 +182333,9 @@ "a3": 0.4249743278524605, "a4": 0.46937666662434907 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.6285164542593508, "support": [ [ 7, @@ -177098,6 +182365,22 @@ "value": 0.6285164542593508 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4577551136326223, "a1": 0.37543260654332505, @@ -177105,6 +182388,9 @@ "a3": 0.452800740061846, "a4": 0.4143442636082091 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 5, @@ -177130,7 +182416,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.6285165542593507, + "upper": 0.6285166542593508, "worlds": 32 }, "intervals": { @@ -177164,11 +182450,27 @@ "a4": 0.4270259597595383 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5185390014789291, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5185388014789291, "a1": 0.39905387034834117, @@ -177176,6 +182478,9 @@ "a3": 0.5050562763962027, "a4": 0.4270259597595383 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5185388014789291, "support": [ [ 7, @@ -177205,6 +182510,22 @@ "value": 0.5185388014789291 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5185388014789291, "a1": 0.39905387034834117, @@ -177212,6 +182533,9 @@ "a3": 0.5050562763962027, "a4": 0.4270259597595383 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 5, @@ -177241,7 +182565,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.518538901478929, + "upper": 0.5185390014789291, "worlds": 32 }, "proofs": [ @@ -177271,16 +182595,31 @@ { "id": 77, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5297853202073813, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.39316517292236086, "a1": 0.6446327503482554, "a2": 0.5297851202073813 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5297851202073813, "support": [ [ 0, @@ -177302,11 +182641,26 @@ "value": 0.5297851202073813 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39316517292236086, "a1": 0.5847301751524363, "a2": 0.41526982484756364 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -177324,7 +182678,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5297852202073813, + "upper": 0.5297853202073813, "worlds": 8 }, "intervals": { @@ -177348,16 +182702,31 @@ "a2": 0.506529631182152 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.13951769072851017, + "lower": 0.13951739072851033, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.506529831182152, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.41447047032874323, "a1": 0.6329881595463582, "a2": 0.506529631182152 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.506529631182152, "support": [ [ 0, @@ -177379,11 +182748,26 @@ "value": 0.506529631182152 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.13951739072851033, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.41447047032874323, "a1": 0.6329881595463582, "a2": 0.506529631182152 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.13951779072851017, "support": [ [ 2, @@ -177405,7 +182789,7 @@ "value": 0.13951779072851017 }, "status": "bounded", - "upper": 0.5065297311821519, + "upper": 0.506529831182152, "worlds": 8 }, "proofs": [ @@ -177424,17 +182808,34 @@ { "id": 78, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5320228616828403, + "lower": 0.5320227616828402, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.43566130148426513, "a1": 0.4101643479267371, "a2": 0.4933312347285097, "a3": 0.5320229616828402 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -177460,12 +182861,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5320227616828402, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.43566130148426513, "a1": 0.4101643479267371, "a2": 0.49333123472850965, "a3": 0.5320229616828402 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5320229616828402, "support": [ [ 0, @@ -177520,17 +182938,34 @@ "a3": 0.5741943789460479 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5741942789460479, + "lower": 0.5741941789460479, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.37867861153385174, "a1": 0.2608417763813573, "a2": 0.44788716476403406, "a3": 0.5741943789460479 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.9999999999999999, "support": [ [ 3, @@ -177556,12 +182991,29 @@ "value": 0.9999999999999999 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5741941789460479, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.37867861153385174, "a1": 0.2608417763813573, "a2": 0.44788716476403406, "a3": 0.5741943789460479 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5741943789460479, "support": [ [ 0, @@ -177625,15 +183077,28 @@ { "id": 79, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.21077938418982217, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.21077918418982217, "a1": 0.3219992053648987 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.21077918418982217, "support": [ [ 0, @@ -177651,10 +183116,23 @@ "value": 0.21077918418982217 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.08221444638342623, "a1": 0.3219992053648987 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -177672,7 +183150,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.21077928418982217, + "upper": 0.21077938418982217, "worlds": 4 }, "intervals": { @@ -177691,15 +183169,28 @@ "a1": 0.4274750583621364 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.12413238338281943, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.12413218338281942, "a1": 0.4274750583621364 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.12413218338281942, "support": [ [ 0, @@ -177717,10 +183208,23 @@ "value": 0.12413218338281942 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.12413218338281942, "a1": 0.4274750583621364 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -177738,7 +183242,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.12413228338281942, + "upper": 0.12413238338281943, "worlds": 4 }, "proofs": [ @@ -177756,16 +183260,31 @@ { "id": 80, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.46469898365207973, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.7071300943598524, "a1": 0.5029254516446384, "a2": 0.4646987836520797 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4646987836520797, "support": [ [ 0, @@ -177787,11 +183306,26 @@ "value": 0.4646987836520797 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.7071300943598524, "a1": 0.5029254516446384, "a2": 0.4646987836520797 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -177813,7 +183347,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.46469888365207973, + "upper": 0.46469898365207973, "worlds": 8 }, "intervals": { @@ -177837,16 +183371,31 @@ "a2": 0.4315855497429081 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4315857497429081, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.7160417155879752, "a1": 0.4333824256745148, "a2": 0.4315855497429081 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4315855497429081, "support": [ [ 0, @@ -177868,11 +183417,26 @@ "value": 0.4315855497429081 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.7160417155879752, "a1": 0.4333824256745148, "a2": 0.4315855497429081 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -177894,7 +183458,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4315856497429081, + "upper": 0.4315857497429081, "worlds": 8 }, "proofs": [ @@ -177914,11 +183478,29 @@ { "id": 81, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5537546443248867, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6316589781334339, "a1": 0.6230067292747712, @@ -177927,6 +183509,9 @@ "a4": 0.5901474137700787, "a5": 0.4759821383263562 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5537544443248867, "support": [ [ 1, @@ -177956,6 +183541,24 @@ "value": 0.5537544443248867 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4420371669912826, "a1": 0.5579628330087174, @@ -177964,6 +183567,9 @@ "a4": 0.4420371669912826, "a5": 0.4759821383263562 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 10, @@ -177985,7 +183591,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5537545443248867, + "upper": 0.5537546443248867, "worlds": 64 }, "intervals": { @@ -178024,11 +183630,29 @@ "a5": 0.5006016560588903 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.43867773379645153, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4924439091559262, "a1": 0.5393227946086174, @@ -178037,6 +183661,9 @@ "a4": 0.4386775337964515, "a5": 0.5006016560588903 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4386775337964515, "support": [ [ 1, @@ -178070,6 +183697,24 @@ "value": 0.4386775337964515 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4924439091559262, "a1": 0.5393227946086174, @@ -178078,6 +183723,9 @@ "a4": 0.4386775337964515, "a5": 0.5006016560588903 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 10, @@ -178111,7 +183759,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4386776337964515, + "upper": 0.43867773379645153, "worlds": 64 }, "proofs": [ @@ -178134,15 +183782,28 @@ { "id": 82, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.5875545163336451, + "lower": 0.587554416333645, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39374959475386784, "a1": 0.6893684605894318 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -178160,10 +183821,23 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.587554416333645, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.39374959475386784, "a1": 0.587554616333645 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.587554616333645, "support": [ [ 0, @@ -178200,15 +183874,28 @@ "a1": 0.6434146773883203 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.6434145773883203, + "lower": 0.6434144773883202, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.927863443610265, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.28444846622194475, "a1": 0.6434146773883203 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.927863143610265, "support": [ [ 0, @@ -178226,10 +183913,23 @@ "value": 0.927863143610265 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6434144773883202, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.28444846622194475, "a1": 0.6434146773883203 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6434146773883203, "support": [ [ 0, @@ -178247,7 +183947,7 @@ "value": 0.6434146773883203 }, "status": "bounded", - "upper": 0.927863243610265, + "upper": 0.927863443610265, "worlds": 4 }, "proofs": [ @@ -178281,17 +183981,34 @@ { "id": 83, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.42763488956012374, + "lower": 0.42763478956012374, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.588527815406849, "a1": 0.5734232114980773, "a2": 0.5597022932892889, "a3": 0.4788392643627697 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -178317,12 +184034,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.42763478956012374, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.588527815406849, "a1": 0.42763498956012375, "a2": 0.38421305062605504, "a3": 0.6259226403991351 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.42763498956012375, "support": [ [ 0, @@ -178377,17 +184111,34 @@ "a3": 0.5765927821080227 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5198042264685386, + "lower": 0.5198041264685386, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9917497070147397, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5020378467069798, "a1": 0.4719450805462012, "a2": 0.5198043264685386, "a3": 0.5765927821080227 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9917494070147398, "support": [ [ 3, @@ -178413,12 +184164,29 @@ "value": 0.9917494070147398 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5198041264685386, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5020378467069798, "a1": 0.4719450805462012, "a2": 0.5198043264685386, "a3": 0.5765927821080227 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5198043264685386, "support": [ [ 1, @@ -178444,7 +184212,7 @@ "value": 0.5198043264685386 }, "status": "bounded", - "upper": 0.9917495070147397, + "upper": 0.9917497070147397, "worlds": 16 }, "proofs": [ @@ -178484,15 +184252,28 @@ { "id": 84, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.2267776466518197, + "lower": 0.2267773466518197, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5310152325749657, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.7911261125601188, "a1": 0.5310150325749657 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5310150325749657, "support": [ [ 0, @@ -178510,10 +184291,23 @@ "value": 0.5310150325749657 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.2267773466518197, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.7911261125601188, "a1": 0.43565163409170093 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.2267777466518197, "support": [ [ 1, @@ -178531,7 +184325,7 @@ "value": 0.2267777466518197 }, "status": "bounded", - "upper": 0.5310151325749657, + "upper": 0.5310152325749657, "worlds": 4 }, "intervals": { @@ -178550,15 +184344,28 @@ "a1": 0.4528822523023529 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.3239050275052581, + "lower": 0.3239047275052582, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4528824523023529, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.8710228752029052, "a1": 0.4528822523023529 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4528822523023529, "support": [ [ 0, @@ -178576,10 +184383,23 @@ "value": 0.4528822523023529 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.3239047275052582, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.8710228752029052, "a1": 0.4528822523023529 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.32390512750525813, "support": [ [ 1, @@ -178597,7 +184417,7 @@ "value": 0.32390512750525813 }, "status": "bounded", - "upper": 0.4528823523023529, + "upper": 0.4528824523023529, "worlds": 4 }, "proofs": [ @@ -178615,11 +184435,27 @@ { "id": 85, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8650475136961626, + "dual_ub": [ + 0.0, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.382319115624625, "a1": 0.5694721356220889, @@ -178627,6 +184463,9 @@ "a3": 0.6348066671267762, "a4": 0.41340208162650977 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.8650472636961626, "support": [ [ 10, @@ -178652,6 +184491,22 @@ "value": 0.8650472636961626 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5017725025402704, "a1": 0.4232531022066744, @@ -178659,6 +184514,9 @@ "a3": 0.49557945486538935, "a4": 0.49822749745972966 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 5, @@ -178680,7 +184538,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.8650473636961625, + "upper": 0.8650475136961626, "worlds": 32 }, "intervals": { @@ -178714,11 +184572,27 @@ "a4": 0.4930699214687483 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6971637720867254, + "dual_ub": [ + 0.0, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3863487901693143, "a1": 0.4502938697159562, @@ -178726,6 +184600,9 @@ "a3": 0.5158442247788921, "a4": 0.4930699214687483 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.6971635220867254, "support": [ [ 0, @@ -178755,6 +184632,22 @@ "value": 0.6971635220867254 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3863487901693143, "a1": 0.4502938697159562, @@ -178762,6 +184655,9 @@ "a3": 0.5158442247788922, "a4": 0.4930699214687483 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -178791,7 +184687,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.6971636220867253, + "upper": 0.6971637720867254, "worlds": 32 }, "proofs": [ @@ -178830,11 +184726,27 @@ { "id": 86, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4754058003015066, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46948126566912923, "a1": 0.49282904235043845, @@ -178842,6 +184754,9 @@ "a3": 0.4754056003015066, "a4": 0.4843908006737938 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4754056003015066, "support": [ [ 5, @@ -178871,6 +184786,22 @@ "value": 0.4754056003015066 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46948126566912923, "a1": 0.49282904235043845, @@ -178878,6 +184809,9 @@ "a3": 0.3741519218223872, "a4": 0.4843908006737938 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -178907,7 +184841,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4754057003015066, + "upper": 0.4754058003015066, "worlds": 32 }, "intervals": { @@ -178941,11 +184875,27 @@ "a4": 0.5785613421608096 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.04321054024073373, + "lower": 0.043210240240733735, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4646494980799241, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48770918972460475, "a1": 0.5521742105592855, @@ -178953,6 +184903,9 @@ "a3": 0.4646492980799241, "a4": 0.5785613421608096 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4646492980799241, "support": [ [ 5, @@ -178982,6 +184935,22 @@ "value": 0.4646492980799241 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.043210240240733735, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.48770918972460475, "a1": 0.5521742105592855, @@ -178989,6 +184958,9 @@ "a3": 0.4646492980799241, "a4": 0.5785613421608096 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.04321064024073373, "support": [ [ 8, @@ -179018,7 +184990,7 @@ "value": 0.04321064024073373 }, "status": "bounded", - "upper": 0.4646493980799241, + "upper": 0.4646494980799241, "worlds": 32 }, "proofs": [ @@ -179056,11 +185028,29 @@ { "id": 87, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4578171266378663, + "lower": 0.4578170266378663, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4532711773573036, "a1": 0.603326380514374, @@ -179069,6 +185059,9 @@ "a4": 0.547707012541414, "a5": 0.6145458570628742 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 11, @@ -179098,6 +185091,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4578170266378663, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4532711773573036, "a1": 0.5467288226426964, @@ -179106,6 +185117,9 @@ "a4": 0.5421827733621337, "a5": 0.4578172266378663 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4578172266378663, "support": [ [ 25, @@ -179162,11 +185176,29 @@ "a5": 0.44944737794632106 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4622306282510887, + "lower": 0.4622305282510887, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48126282847607316, "a1": 0.5496876166863395, @@ -179175,6 +185207,9 @@ "a4": 0.5316969965608909, "a5": 0.44944737794632106 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 11, @@ -179208,6 +185243,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4622305282510887, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48126282847607316, "a1": 0.5496876166863395, @@ -179216,6 +185269,9 @@ "a4": 0.5316969965608909, "a5": 0.44944737794632106 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4622307282510887, "support": [ [ 1, @@ -179277,16 +185333,31 @@ { "id": 88, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4934756468153374, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5699437373599332, "a1": 0.5757766549077831, "a2": 0.4934754468153374 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4934754468153374, "support": [ [ 0, @@ -179308,11 +185379,26 @@ "value": 0.4934754468153374 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5699437373599332, "a1": 0.5757766549077831, "a2": 0.42422334509221693 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 2, @@ -179330,7 +185416,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4934755468153374, + "upper": 0.4934756468153374, "worlds": 8 }, "intervals": { @@ -179354,16 +185440,31 @@ "a2": 0.4812943826511164 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4812945826511164, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5896812258593429, "a1": 0.49465432532968895, "a2": 0.4812943826511164 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4812943826511164, "support": [ [ 0, @@ -179385,11 +185486,26 @@ "value": 0.4812943826511164 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5896812258593429, "a1": 0.49465432532968895, "a2": 0.4812943826511164 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -179411,7 +185527,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4812944826511164, + "upper": 0.4812945826511164, "worlds": 8 }, "proofs": [ @@ -179431,11 +185547,29 @@ { "id": 89, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.467122170035593, + "lower": 0.467122070035593, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.41057083547760365, "a1": 0.5894291645223964, @@ -179444,6 +185578,9 @@ "a4": 0.532877729964407, "a5": 0.467122270035593 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -179461,6 +185598,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.467122070035593, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5108577359509678, "a1": 0.6089804029156272, @@ -179469,6 +185624,9 @@ "a4": 0.4029007902827163, "a5": 0.5819268674516695 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.467122270035593, "support": [ [ 1, @@ -179537,11 +185695,29 @@ "a5": 0.5874261605326596 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.4974650700539918, + "lower": 0.4974649700539918, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9090264450381987, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4450349786911919, "a1": 0.5054310021424262, @@ -179550,6 +185726,9 @@ "a4": 0.41156097498420696, "a5": 0.5874261605326596 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9090261450381988, "support": [ [ 15, @@ -179583,6 +185762,24 @@ "value": 0.9090261450381988 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4974649700539918, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4450349786911919, "a1": 0.5054310021424262, @@ -179591,6 +185788,9 @@ "a4": 0.41156097498420696, "a5": 0.5874261605326596 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4974651700539918, "support": [ [ 1, @@ -179624,7 +185824,7 @@ "value": 0.4974651700539918 }, "status": "bounded", - "upper": 0.9090262450381987, + "upper": 0.9090264450381987, "worlds": 64 }, "proofs": [ @@ -179648,17 +185848,34 @@ { "id": 90, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.4460285475984827, + "lower": 0.4460284475984827, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5411510395810044, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6538030023254587, "a1": 0.5259450157173882, "a2": 0.5411508395810044, "a3": 0.49091247687483575 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5411508395810044, "support": [ [ 3, @@ -179684,12 +185901,29 @@ "value": 0.5411508395810044 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4460284475984827, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6538030023254587, "a1": 0.5259450157173882, "a2": 0.4460286475984827, "a3": 0.49091247687483575 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4460286475984827, "support": [ [ 3, @@ -179715,7 +185949,7 @@ "value": 0.4460286475984827 }, "status": "bounded", - "upper": 0.5411509395810044, + "upper": 0.5411510395810044, "worlds": 16 }, "intervals": { @@ -179744,17 +185978,34 @@ "a3": 0.38821603992387316 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5178742784523944, + "lower": 0.5178741784523944, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5178745784523944, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5868852000920098, "a1": 0.398927580708965, "a2": 0.5178743784523944, "a3": 0.38821603992387316 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5178743784523944, "support": [ [ 3, @@ -179780,12 +186031,29 @@ "value": 0.5178743784523944 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5178741784523944, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5868852000920098, "a1": 0.398927580708965, "a2": 0.5178743784523944, "a3": 0.38821603992387316 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5178743784523944, "support": [ [ 3, @@ -179811,7 +186079,7 @@ "value": 0.5178743784523944 }, "status": "bounded", - "upper": 0.5178744784523943, + "upper": 0.5178745784523944, "worlds": 16 }, "proofs": [ @@ -179830,15 +186098,28 @@ { "id": 91, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4531589451925149, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45315874519251487, "a1": 0.5333886954572402 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.45315874519251487, "support": [ [ 0, @@ -179856,10 +186137,23 @@ "value": 0.45315874519251487 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.329129077685714, "a1": 0.5333886954572402 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 0, @@ -179877,7 +186171,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.45315884519251487, + "upper": 0.4531589451925149, "worlds": 4 }, "intervals": { @@ -179896,15 +186190,28 @@ "a1": 0.634279618358618 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.027492506552991406, + "lower": 0.02749220655299146, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3932131881943734, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3932129881943734, "a1": 0.634279618358618 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3932129881943734, "support": [ [ 0, @@ -179922,10 +186229,23 @@ "value": 0.3932129881943734 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.02749220655299146, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.3932129881943734, "a1": 0.6342796183586181 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.027492606552991405, "support": [ [ 1, @@ -179943,7 +186263,7 @@ "value": 0.027492606552991405 }, "status": "bounded", - "upper": 0.3932130881943734, + "upper": 0.3932131881943734, "worlds": 4 }, "proofs": [ @@ -179961,11 +186281,29 @@ { "id": 92, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5237644416330751, + "lower": 0.5237643416330751, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5364121256877502, "a1": 0.532461012256922, @@ -179974,6 +186312,9 @@ "a4": 0.6643579169260313, "a5": 0.5364121256877502 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -180003,6 +186344,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5237643416330751, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.467538987743078, "a1": 0.532461012256922, @@ -180011,6 +186370,9 @@ "a4": 0.5237645416330751, "a5": 0.47623545836692494 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5237645416330751, "support": [ [ 25, @@ -180067,11 +186429,29 @@ "a5": 0.4256369799630481 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5619865284346549, + "lower": 0.5619864284346548, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.987623908397703, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4369742363490132, "a1": 0.4837213755519147, @@ -180080,6 +186460,9 @@ "a4": 0.6137950247712328, "a5": 0.4256369799630481 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.987623608397703, "support": [ [ 4, @@ -180113,6 +186496,24 @@ "value": 0.987623608397703 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5619864284346548, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4369742363490132, "a1": 0.4837213755519147, @@ -180121,6 +186522,9 @@ "a4": 0.6137950247712328, "a5": 0.4256369799630481 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5619866284346549, "support": [ [ 16, @@ -180154,7 +186558,7 @@ "value": 0.5619866284346549 }, "status": "bounded", - "upper": 0.987623708397703, + "upper": 0.987623908397703, "worlds": 64 }, "proofs": [ @@ -180183,17 +186587,34 @@ { "id": 93, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5156259443681231, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5156257443681231, "a1": 0.6494490509991244, "a2": 0.5946087732300336, "a3": 0.617285600956142 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5156257443681231, "support": [ [ 2, @@ -180219,12 +186640,29 @@ "value": 0.5156257443681231 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5156257443681231, "a1": 0.6494490509991244, "a2": 0.5946087732300336, "a3": 0.4676521113881389 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -180250,7 +186688,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5156258443681231, + "upper": 0.5156259443681231, "worlds": 16 }, "intervals": { @@ -180279,17 +186717,34 @@ "a3": 0.5020165365971911 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4617740601435161, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46177386014351607, "a1": 0.5566894635980254, "a2": 0.4764725145381622, "a3": 0.5020165365971911 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.46177386014351607, "support": [ [ 2, @@ -180315,12 +186770,29 @@ "value": 0.46177386014351607 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46177386014351607, "a1": 0.5566894635980254, "a2": 0.4764725145381622, "a3": 0.5020165365971911 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -180346,7 +186818,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.46177396014351607, + "upper": 0.4617740601435161, "worlds": 16 }, "proofs": [ @@ -180367,11 +186839,27 @@ { "id": 94, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4509460210252644, + "lower": 0.4509459210252643, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4251437295841063, "a1": 0.5325137037378588, @@ -180379,6 +186867,9 @@ "a3": 0.5748562704158937, "a4": 0.4366493345178384 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -180404,6 +186895,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4509459210252643, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3987498347868309, "a1": 0.5325137037378588, @@ -180411,6 +186918,9 @@ "a3": 0.4509461210252644, "a4": 0.5490538789747357 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4509461210252644, "support": [ [ 10, @@ -180470,11 +186980,27 @@ "a4": 0.5161734715810753 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4583804269379981, + "lower": 0.4583803269379981, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9877745367311166, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5293937097931185, "a1": 0.543751948430919, @@ -180482,6 +187008,9 @@ "a3": 0.4583805269379981, "a4": 0.5161734715810753 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9877742367311166, "support": [ [ 3, @@ -180511,6 +187040,22 @@ "value": 0.9877742367311166 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4583803269379981, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5293937097931185, "a1": 0.543751948430919, @@ -180518,6 +187063,9 @@ "a3": 0.4583805269379981, "a4": 0.5161734715810753 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4583805269379981, "support": [ [ 4, @@ -180547,7 +187095,7 @@ "value": 0.4583805269379981 }, "status": "bounded", - "upper": 0.9877743367311166, + "upper": 0.9877745367311166, "worlds": 32 }, "proofs": [ @@ -180585,11 +187133,27 @@ { "id": 95, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.48191961725879545, + "lower": 0.48191951725879545, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4670189526338182, "a1": 0.6388417342581587, @@ -180597,6 +187161,9 @@ "a3": 0.5329810473661818, "a4": 0.3904272577708231 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -180622,6 +187189,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.48191951725879545, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4642775318829776, "a1": 0.48191971725879545, @@ -180629,6 +187212,9 @@ "a3": 0.38670961295505557, "a4": 0.43046485260277745 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.48191971725879545, "support": [ [ 0, @@ -180688,11 +187274,27 @@ "a4": 0.40572191626079723 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.551922962489366, + "lower": 0.551922862489366, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5473424039412669, "a1": 0.551923062489366, @@ -180700,6 +187302,9 @@ "a3": 0.4080878727038968, "a4": 0.40572191626079723 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -180729,6 +187334,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.551922862489366, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5473424039412669, "a1": 0.551923062489366, @@ -180736,6 +187357,9 @@ "a3": 0.4080878727038968, "a4": 0.40572191626079723 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.551923062489366, "support": [ [ 0, @@ -180806,15 +187430,28 @@ { "id": 96, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.3813257513351536, + "lower": 0.3813256513351536, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7137527154078503, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4740958354118343, "a1": 0.2396565799960161 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.7137524154078504, "support": [ [ 0, @@ -180832,10 +187469,23 @@ "value": 0.7137524154078504 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3813256513351536, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3813258513351536, "a1": 0.2396565799960161 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3813258513351536, "support": [ [ 0, @@ -180853,7 +187503,7 @@ "value": 0.3813258513351536 }, "status": "bounded", - "upper": 0.7137525154078503, + "upper": 0.7137527154078503, "worlds": 4 }, "intervals": { @@ -180872,15 +187522,28 @@ "a1": 0.2288815894797291 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.4627599369303158, + "lower": 0.4627598369303158, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.6916419264100448, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.4627600369303158, "a1": 0.2288815894797291 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.6916416264100449, "support": [ [ 0, @@ -180898,10 +187561,23 @@ "value": 0.6916416264100449 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4627598369303158, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4627600369303158, "a1": 0.2288815894797291 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4627600369303158, "support": [ [ 0, @@ -180919,7 +187595,7 @@ "value": 0.4627600369303158 }, "status": "bounded", - "upper": 0.6916417264100448, + "upper": 0.6916419264100448, "worlds": 4 }, "proofs": [ @@ -180954,17 +187630,34 @@ { "id": 97, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4713107473978326, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5869470810024934, "a1": 0.47131054739783257, "a2": 0.5185158790222127, "a3": 0.4881769542791466 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.47131054739783257, "support": [ [ 3, @@ -180990,12 +187683,29 @@ "value": 0.47131054739783257 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5323846612409434, "a1": 0.4676153387590566, "a2": 0.5185158790222127, "a3": 0.659794406102715 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 6, @@ -181017,7 +187727,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.47131064739783257, + "upper": 0.4713107473978326, "worlds": 16 }, "intervals": { @@ -181046,17 +187756,34 @@ "a3": 0.5898376991544806 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.02350725437418705, + "lower": 0.023506954374186827, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.46367855265928937, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5598290017148976, "a1": 0.46367835265928936, "a2": 0.39304249265930696, "a3": 0.5898376991544806 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.46367835265928936, "support": [ [ 3, @@ -181082,12 +187809,29 @@ "value": 0.46367835265928936 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.023506954374186827, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5598290017148976, "a1": 0.4636783526592894, "a2": 0.39304249265930696, "a3": 0.5898376991544806 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.02350735437418705, "support": [ [ 3, @@ -181113,7 +187857,7 @@ "value": 0.02350735437418705 }, "status": "bounded", - "upper": 0.46367845265928936, + "upper": 0.46367855265928937, "worlds": 16 }, "proofs": [ @@ -181143,15 +187887,28 @@ { "id": 98, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.37607067232778285, + "lower": 0.37607057232778285, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4787681373496364, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4787679373496364, "a1": 0.4787679373496364 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4787679373496364, "support": [ [ 0, @@ -181165,10 +187922,23 @@ "value": 0.4787679373496364 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.37607057232778285, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.37607077232778285, "a1": 0.37607077232778285 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.37607077232778285, "support": [ [ 0, @@ -181182,7 +187952,7 @@ "value": 0.37607077232778285 }, "status": "bounded", - "upper": 0.4787680373496364, + "upper": 0.4787681373496364, "worlds": 4 }, "intervals": { @@ -181201,15 +187971,28 @@ "a1": 0.4172663034493937 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.4333038488002176, + "lower": 0.4333037488002176, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4333041488002176, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4333039488002176, "a1": 0.4172663034493937 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4333039488002176, "support": [ [ 0, @@ -181227,10 +188010,23 @@ "value": 0.4333039488002176 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4333037488002176, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4333039488002176, "a1": 0.4172663034493937 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4333039488002176, "support": [ [ 0, @@ -181248,7 +188044,7 @@ "value": 0.4333039488002176 }, "status": "bounded", - "upper": 0.4333040488002176, + "upper": 0.4333041488002176, "worlds": 4 }, "proofs": [ @@ -181268,15 +188064,28 @@ { "id": 99, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.35145670986889466, + "lower": 0.35145660986889465, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4703255683489272, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.46958449608106223, "a1": 0.4703253683489272 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4703253683489272, "support": [ [ 0, @@ -181294,10 +188103,23 @@ "value": 0.4703253683489272 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.35145660986889465, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.35145680986889466, "a1": 0.35145680986889466 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.35145680986889466, "support": [ [ 0, @@ -181311,7 +188133,7 @@ "value": 0.35145680986889466 }, "status": "bounded", - "upper": 0.4703254683489272, + "upper": 0.4703255683489272, "worlds": 4 }, "intervals": { @@ -181330,15 +188152,28 @@ "a1": 0.40280265377964847 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.40280255377964846, + "lower": 0.40280245377964846, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4028028537796485, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.3555390620646703, "a1": 0.40280265377964847 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.40280265377964847, "support": [ [ 0, @@ -181356,10 +188191,23 @@ "value": 0.40280265377964847 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.40280245377964846, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.3555390620646703, "a1": 0.40280265377964847 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.40280265377964847, "support": [ [ 0, @@ -181377,7 +188225,7 @@ "value": 0.40280265377964847 }, "status": "bounded", - "upper": 0.40280275377964847, + "upper": 0.4028028537796485, "worlds": 4 }, "proofs": [ @@ -181394,16 +188242,31 @@ { "id": 100, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.47707979293478747, + "lower": 0.47707969293478747, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5580489126858215, "a1": 0.5537040591532812, "a2": 0.6191581804920601 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -181425,11 +188288,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.47707969293478747, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4770798929347875, "a1": 0.4809848783843318, "a2": 0.5190151216156682 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4770798929347875, "support": [ [ 2, @@ -181471,16 +188349,31 @@ "a2": 0.5346507393857444 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5102501086292279, + "lower": 0.5102500086292279, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5102502086292279, "a1": 0.5147045206613248, "a2": 0.5346507393857444 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -181502,11 +188395,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5102500086292279, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5102502086292279, "a1": 0.5147045206613248, "a2": 0.5346507393857444 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5102502086292279, "support": [ [ 2, @@ -181555,11 +188463,27 @@ { "id": 101, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5361152573192366, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5424346326025358, "a1": 0.5361150573192366, @@ -181567,6 +188491,9 @@ "a3": 0.6333138412157826, "a4": 0.3509977796347328 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5361150573192366, "support": [ [ 0, @@ -181596,6 +188523,22 @@ "value": 0.5361150573192366 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.40264838144599546, "a1": 0.4294021840600738, @@ -181603,6 +188546,9 @@ "a3": 0.4841829659361969, "a4": 0.3509977796347328 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -181632,7 +188578,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5361151573192365, + "upper": 0.5361152573192366, "worlds": 32 }, "intervals": { @@ -181666,11 +188612,27 @@ "a4": 0.4445851764988801 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4407517567211897, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4407515567211897, "a1": 0.5251974524975404, @@ -181678,6 +188640,9 @@ "a3": 0.5240974385357218, "a4": 0.4445851764988801 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4407515567211897, "support": [ [ 0, @@ -181707,6 +188672,22 @@ "value": 0.4407515567211897 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4407515567211897, "a1": 0.5251974524975404, @@ -181714,6 +188695,9 @@ "a3": 0.5240974385357218, "a4": 0.4445851764988801 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -181743,7 +188727,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.4407516567211897, + "upper": 0.4407517567211897, "worlds": 32 }, "proofs": [ @@ -181765,16 +188749,31 @@ { "id": 102, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.41006078691632075, + "lower": 0.41006068691632075, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9758300623964489, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5139897459950717, "a1": 0.3894439739582595, "a2": 0.46184001640137723 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9758297623964489, "support": [ [ 0, @@ -181796,11 +188795,26 @@ "value": 0.9758297623964489 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.41006068691632075, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.41006088691632075, "a1": 0.3894439739582595, "a2": 0.41006088691632075 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.41006088691632075, "support": [ [ 0, @@ -181818,7 +188832,7 @@ "value": 0.41006088691632075 }, "status": "bounded", - "upper": 0.9758298623964489, + "upper": 0.9758300623964489, "worlds": 8 }, "intervals": { @@ -181842,16 +188856,31 @@ "a2": 0.44539054085902 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.44539044085902, + "lower": 0.44539034085902, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8656170612924015, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.42022622043338154, "a1": 0.35476213963254316, "a2": 0.44539054085902 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8656167612924015, "support": [ [ 0, @@ -181873,11 +188902,26 @@ "value": 0.8656167612924015 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44539034085902, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.42022622043338154, "a1": 0.35476213963254316, "a2": 0.44539054085902 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44539054085902, "support": [ [ 0, @@ -181899,7 +188943,7 @@ "value": 0.44539054085902 }, "status": "bounded", - "upper": 0.8656168612924015, + "upper": 0.8656170612924015, "worlds": 8 }, "proofs": [ @@ -181932,16 +188976,31 @@ { "id": 103, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.627640779956077, + "lower": 0.627640679956077, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3514914363510334, "a1": 0.6485085636489666, "a2": 0.5808770193413682 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -181959,11 +189018,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.627640679956077, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3514914363510334, "a1": 0.627640879956077, "a2": 0.5808770193413682 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.627640879956077, "support": [ [ 2, @@ -182009,16 +189083,31 @@ "a2": 0.6737200459725585 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.7130291842158499, + "lower": 0.7130290842158499, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4268857214148089, "a1": 0.7130292842158499, "a2": 0.6737200459725585 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 2, @@ -182040,11 +189129,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.7130290842158499, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4268857214148089, "a1": 0.7130292842158499, "a2": 0.6737200459725585 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.7130292842158499, "support": [ [ 3, @@ -182103,16 +189207,31 @@ { "id": 104, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.374381082559591, + "lower": 0.374380982559591, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5150789716820543, "a1": 0.6138383010911966, "a2": 0.7307625047884253 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -182134,11 +189253,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.374380982559591, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.374381182559591, "a1": 0.5326912618908085, "a2": 0.5597259270881815 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.374381182559591, "support": [ [ 2, @@ -182184,16 +189318,31 @@ "a2": 0.7004526851815969 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.4778686016901329, + "lower": 0.4778685016901329, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4778687016901329, "a1": 0.594096609527613, "a2": 0.7004526851815969 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -182215,11 +189364,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4778685016901329, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4778687016901329, "a1": 0.594096609527613, "a2": 0.7004526851815969 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4778687016901329, "support": [ [ 2, @@ -182276,17 +189440,34 @@ { "id": 105, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.38514239080694573, + "lower": 0.38514229080694573, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46376568561471676, "a1": 0.5571421104719982, "a2": 0.43026553924352773, "a3": 0.5475929352020229 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -182312,12 +189493,29 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.38514229080694573, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.3643359586304252, "a1": 0.5571421104719982, "a2": 0.5652501558237368, "a3": 0.38514249080694574 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.38514249080694574, "support": [ [ 1, @@ -182372,17 +189570,34 @@ "a3": 0.5149446010634793 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.5149445010634793, + "lower": 0.5149444010634793, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9564589852254253, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.441514084161946, "a1": 0.46066339830926467, "a2": 0.48242387747836635, "a3": 0.5149446010634793 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9564586852254253, "support": [ [ 3, @@ -182408,12 +189623,29 @@ "value": 0.9564586852254253 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5149444010634793, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.441514084161946, "a1": 0.46066339830926467, "a2": 0.48242387747836635, "a3": 0.5149446010634793 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5149446010634793, "support": [ [ 0, @@ -182439,7 +189671,7 @@ "value": 0.5149446010634793 }, "status": "bounded", - "upper": 0.9564587852254253, + "upper": 0.9564589852254253, "worlds": 16 }, "proofs": [ @@ -182472,11 +189704,27 @@ { "id": 106, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4572326113700221, + "lower": 0.4572325113700221, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.38661258474448146, "a1": 0.5427672886299779, @@ -182484,6 +189732,9 @@ "a3": 0.3616848002169676, "a4": 0.4572327113700221 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -182509,6 +189760,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4572325113700221, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.38661258474448146, "a1": 0.3976998800574188, @@ -182516,6 +189783,9 @@ "a3": 0.3976998800574188, "a4": 0.4572327113700221 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4572327113700221, "support": [ [ 0, @@ -182575,11 +189845,27 @@ "a4": 0.49542281785776715 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.49542271785776715, + "lower": 0.49542261785776714, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5106961556975991, "a1": 0.4762010218400776, @@ -182587,6 +189873,9 @@ "a3": 0.3907398135839335, "a4": 0.49542281785776715 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -182616,6 +189905,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.49542261785776714, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5106961556975991, "a1": 0.4762010218400776, @@ -182623,6 +189928,9 @@ "a3": 0.3907398135839335, "a4": 0.49542281785776715 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.49542281785776715, "support": [ [ 0, @@ -182687,15 +189995,28 @@ { "id": 107, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.29217773631446137, + "lower": 0.29217763631446136, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.4016999147059468, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.41639699925169216, "a1": 0.4016997147059468 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.4016997147059468, "support": [ [ 0, @@ -182713,10 +190034,23 @@ "value": 0.4016997147059468 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.29217763631446136, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.41639699925169216, "a1": 0.29217783631446137 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.29217783631446137, "support": [ [ 0, @@ -182734,7 +190068,7 @@ "value": 0.29217783631446137 }, "status": "bounded", - "upper": 0.4016998147059468, + "upper": 0.4016999147059468, "worlds": 4 }, "intervals": { @@ -182753,15 +190087,28 @@ "a1": 0.35799236586674343 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.35799226586674343, + "lower": 0.35799216586674343, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.35799256586674344, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.42519587190976005, "a1": 0.35799236586674343 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.35799236586674343, "support": [ [ 0, @@ -182779,10 +190126,23 @@ "value": 0.35799236586674343 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.35799216586674343, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.42519587190976005, "a1": 0.35799236586674343 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.35799236586674343, "support": [ [ 0, @@ -182800,7 +190160,7 @@ "value": 0.35799236586674343 }, "status": "bounded", - "upper": 0.35799246586674344, + "upper": 0.35799256586674344, "worlds": 4 }, "proofs": [ @@ -182836,15 +190196,28 @@ { "id": 108, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.27543610331638074, + "lower": 0.27543600331638074, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.39373692901444635, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39373672901444634, "a1": 0.39373672901444634 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.39373672901444634, "support": [ [ 0, @@ -182858,10 +190231,23 @@ "value": 0.39373672901444634 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.27543600331638074, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.27543620331638075, "a1": 0.34025302866890295 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.27543620331638075, "support": [ [ 0, @@ -182879,7 +190265,7 @@ "value": 0.27543620331638075 }, "status": "bounded", - "upper": 0.39373682901444634, + "upper": 0.39373692901444635, "worlds": 4 }, "intervals": { @@ -182898,15 +190284,28 @@ "a1": 0.34580083374027765 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.3122268931337328, + "lower": 0.3122267931337328, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3122271931337328, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3122269931337328, "a1": 0.34580083374027765 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3122269931337328, "support": [ [ 0, @@ -182924,10 +190323,23 @@ "value": 0.3122269931337328 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3122267931337328, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3122269931337328, "a1": 0.34580083374027765 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3122269931337328, "support": [ [ 0, @@ -182945,7 +190357,7 @@ "value": 0.3122269931337328 }, "status": "bounded", - "upper": 0.3122270931337328, + "upper": 0.3122271931337328, "worlds": 4 }, "proofs": [ @@ -182962,11 +190374,29 @@ { "id": 109, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5293617312203686, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5293615312203686, "a1": 0.5432146203428453, @@ -182975,6 +190405,9 @@ "a4": 0.5293615312203686, "a5": 0.544000055974939 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5293615312203686, "support": [ [ 25, @@ -182996,6 +190429,24 @@ "value": 0.5293615312203686 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46794305098987393, "a1": 0.5320569490101261, @@ -183004,6 +190455,9 @@ "a4": 0.5870742667103751, "a5": 0.6049217769091582 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -183033,7 +190487,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5293616312203685, + "upper": 0.5293617312203686, "worlds": 64 }, "intervals": { @@ -183072,11 +190526,29 @@ "a5": 0.577464872052901 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5197170607742577, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5197168607742577, "a1": 0.43939711966153217, @@ -183085,6 +190557,9 @@ "a4": 0.5293908232579572, "a5": 0.577464872052901 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5197168607742577, "support": [ [ 23, @@ -183118,6 +190593,24 @@ "value": 0.5197168607742577 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5197168607742577, "a1": 0.43939711966153217, @@ -183126,6 +190619,9 @@ "a4": 0.5293908232579572, "a5": 0.577464872052901 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 1, @@ -183159,7 +190655,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.5197169607742577, + "upper": 0.5197170607742577, "worlds": 64 }, "proofs": [ @@ -183202,17 +190698,34 @@ { "id": 110, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7850326021849634, + "dual_ub": [ + -0.5, + 0.0, + 0.0, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0 + ], "marginals": { "a0": 0.48615509694215336, "a1": 0.5972574399522846, "a2": 0.4773272527683689, "a3": 0.6065823546594046 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.7850323521849634, "support": [ [ 0, @@ -183238,12 +190751,29 @@ "value": 0.7850323521849634 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48615509694215336, "a1": 0.5972574399522846, "a2": 0.42824175449555363, "a3": 0.4830060230645664 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -183269,7 +190799,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.7850324521849633, + "upper": 0.7850326021849634, "worlds": 16 }, "intervals": { @@ -183298,17 +190828,34 @@ "a3": 0.542213898267463 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7192759267105389, + "dual_ub": [ + -0.5, + 0.0, + 0.0, + 0.0, + -0.5, + 0.0, + -0.5, + 0.0 + ], "marginals": { "a0": 0.45692033375734187, "a1": 0.5470353548707667, "a2": 0.43941712139627276, "a3": 0.542213898267463 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.7192756767105388, "support": [ [ 0, @@ -183334,12 +190881,29 @@ "value": 0.7192756767105388 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.45692033375734187, "a1": 0.5470353548707667, "a2": 0.4394171213962728, "a3": 0.542213898267463 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -183365,7 +190929,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.7192757767105388, + "upper": 0.7192759267105389, "worlds": 16 }, "proofs": [ @@ -183405,11 +190969,29 @@ { "id": 111, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8214048588556028, + "dual_ub": [ + -0.5, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5633280051462302, "a1": 0.5570209183033444, @@ -183418,6 +191000,9 @@ "a4": 0.5144414229850692, "a5": 0.47925149017204505 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.8214046088556028, "support": [ [ 13, @@ -183447,6 +191032,24 @@ "value": 0.8214046088556028 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44297908169665556, "a1": 0.5570209183033444, @@ -183455,6 +191058,9 @@ "a4": 0.5850321045830594, "a5": 0.477539705738369 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 25, @@ -183476,7 +191082,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.8214047088556028, + "upper": 0.8214048588556028, "worlds": 64 }, "intervals": { @@ -183515,11 +191121,29 @@ "a5": 0.5902973789653616 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.039278770376537764, + "lower": 0.03927847037653788, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.7469247677453994, + "dual_ub": [ + -0.5, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0, + -0.5, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.526066442851156, "a1": 0.5132124275253818, @@ -183528,6 +191152,9 @@ "a4": 0.5827242268933012, "a5": 0.5902973789653616 }, + "padding": 2.5e-07, + "reduced_min": 0.0, + "signed_primal": -0.7469245177453994, "support": [ [ 13, @@ -183561,6 +191188,24 @@ "value": 0.7469245177453994 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.03927847037653788, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.526066442851156, "a1": 0.5132124275253818, @@ -183569,6 +191214,9 @@ "a4": 0.5827242268933012, "a5": 0.5902973789653616 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.03927887037653777, "support": [ [ 25, @@ -183602,7 +191250,7 @@ "value": 0.03927887037653777 }, "status": "bounded", - "upper": 0.7469246177453993, + "upper": 0.7469247677453994, "worlds": 64 }, "proofs": [ @@ -183639,11 +191287,29 @@ { "id": 112, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.44815496889811973, + "lower": 0.44815486889811973, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.47750482198916033, "a1": 0.5224951780108397, @@ -183652,6 +191318,9 @@ "a4": 0.5480896152122814, "a5": 0.45191038478771856 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -183669,6 +191338,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44815486889811973, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.47750482198916033, "a1": 0.42444830362379227, @@ -183677,6 +191364,9 @@ "a4": 0.44815506889811974, "a5": 0.47622132539560275 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44815506889811974, "support": [ [ 1, @@ -183745,11 +191435,29 @@ "a5": 0.4161250413758179 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5298261837924134, + "lower": 0.5298260837924134, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5298574591752584, "a1": 0.4919223092466598, @@ -183758,6 +191466,9 @@ "a4": 0.5298262837924134, "a5": 0.4161250413758179 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -183791,6 +191502,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5298260837924134, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5298574591752584, "a1": 0.4919223092466598, @@ -183799,6 +191528,9 @@ "a4": 0.5298262837924134, "a5": 0.4161250413758179 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5298262837924134, "support": [ [ 1, @@ -183860,16 +191592,31 @@ { "id": 113, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.3786279563884626, + "lower": 0.3786278563884626, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5700274003352538, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.39529554397837197, "a1": 0.4299727996647462, "a2": 0.5700272003352538 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5700272003352538, "support": [ [ 2, @@ -183887,11 +191634,26 @@ "value": 0.5700272003352538 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3786278563884626, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.39529554397837197, "a1": 0.47758168831172376, "a2": 0.3786280563884626 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3786280563884626, "support": [ [ 0, @@ -183913,7 +191675,7 @@ "value": 0.3786280563884626 }, "status": "bounded", - "upper": 0.5700273003352537, + "upper": 0.5700274003352538, "worlds": 8 }, "intervals": { @@ -183937,16 +191699,31 @@ "a2": 0.5336506724907247 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5336505724907248, + "lower": 0.5336504724907247, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5336508724907247, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.48819648840030455, "a1": 0.4543385319048052, "a2": 0.5336506724907247 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5336506724907247, "support": [ [ 0, @@ -183968,11 +191745,26 @@ "value": 0.5336506724907247 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5336504724907247, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.48819648840030455, "a1": 0.4543385319048052, "a2": 0.5336506724907247 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5336506724907247, "support": [ [ 0, @@ -183994,7 +191786,7 @@ "value": 0.5336506724907247 }, "status": "bounded", - "upper": 0.5336507724907247, + "upper": 0.5336508724907247, "worlds": 8 }, "proofs": [ @@ -184016,11 +191808,27 @@ { "id": 114, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5553371214900656, + "lower": 0.5553370214900656, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6353028335684341, "a1": 0.5627904946423796, @@ -184028,6 +191836,9 @@ "a3": 0.48468572238511665, "a4": 0.3646971664315659 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -184053,6 +191864,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5553370214900656, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5553372214900656, "a1": 0.4227566491979508, @@ -184060,6 +191887,9 @@ "a3": 0.4846857223851166, "a4": 0.3446358945382161 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5553372214900656, "support": [ [ 5, @@ -184119,11 +191949,27 @@ "a4": 0.4471215635120488 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5826313889016542, + "lower": 0.5826312889016542, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5731823839144883, "a1": 0.5390738441004022, @@ -184131,6 +191977,9 @@ "a3": 0.49189195807837977, "a4": 0.4471215635120488 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -184160,13 +192009,32 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5826312889016542, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { - "a0": 0.5731823839144882, - "a1": 0.5390738441004022, - "a2": 0.5826314889016542, + "a0": 0.5731823839144881, + "a1": 0.539073844100402, + "a2": 0.5826314889016541, "a3": 0.49189195807837977, "a4": 0.4471215635120488 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5826314889016541, "support": [ [ 5, @@ -184193,7 +192061,7 @@ 0.009449104987166002 ] ], - "value": 0.5826314889016542 + "value": 0.5826314889016541 }, "status": "bounded", "upper": 1.0, @@ -184232,11 +192100,29 @@ { "id": 115, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.44765496713723263, + "lower": 0.4476548671372326, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44765506713723263, "a1": 0.5523449328627674, @@ -184245,6 +192131,9 @@ "a4": 0.5747033519308073, "a5": 0.49166957927563903 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -184270,6 +192159,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4476548671372326, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44765506713723263, "a1": 0.43970112676615897, @@ -184278,6 +192185,9 @@ "a4": 0.44765506713723263, "a5": 0.5005841428111414 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44765506713723263, "support": [ [ 4, @@ -184346,19 +192256,40 @@ "a5": 0.4871771946207586 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5587590006870962, + "lower": 0.5587589006870961, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5429910411684431, "a1": 0.46720799320555295, "a2": 0.44128801449273997, "a3": 0.4991135731926619, - "a4": 0.5587591006870962, + "a4": 0.5587591006870961, "a5": 0.4871771946207586 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -184392,6 +192323,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5587589006870961, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5429910411684431, "a1": 0.46720799320555295, @@ -184400,6 +192349,9 @@ "a4": 0.5587591006870961, "a5": 0.4871771946207586 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5587591006870961, "support": [ [ 0, @@ -184469,11 +192421,29 @@ { "id": 116, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.44145212874850914, + "lower": 0.44145202874850914, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.47396915609880297, "a1": 0.5474944552566924, @@ -184482,6 +192452,9 @@ "a4": 0.4883843134574952, "a5": 0.4877691130121311 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 10, @@ -184511,6 +192484,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.44145202874850914, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4947522635963496, "a1": 0.44145222874850915, @@ -184519,6 +192510,9 @@ "a4": 0.4883843134574952, "a5": 0.4153518232687532 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.44145222874850915, "support": [ [ 1, @@ -184583,11 +192577,29 @@ "a5": 0.433177813920237 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5078562350598104, + "lower": 0.5078561350598103, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9410344489800473, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0 + ], "marginals": { "a0": 0.5025342209632507, "a1": 0.5078563350598103, @@ -184596,6 +192608,9 @@ "a4": 0.4401680548968599, "a5": 0.433177813920237 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9410341489800473, "support": [ [ 4, @@ -184629,6 +192644,24 @@ "value": 0.9410341489800473 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5078561350598103, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5025342209632507, "a1": 0.5078563350598103, @@ -184637,6 +192670,9 @@ "a4": 0.4401680548968599, "a5": 0.433177813920237 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5078563350598103, "support": [ [ 1, @@ -184670,7 +192706,7 @@ "value": 0.5078563350598103 }, "status": "bounded", - "upper": 0.9410342489800473, + "upper": 0.9410344489800473, "worlds": 64 }, "proofs": [ @@ -184712,11 +192748,29 @@ { "id": 117, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.45348044496123235, + "lower": 0.45348034496123235, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3987143477285823, "a1": 0.5391147161296136, @@ -184725,6 +192779,9 @@ "a4": 0.48304920717662075, "a5": 0.5494561588621154 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 4, @@ -184754,6 +192811,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.45348034496123235, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5257780380582198, "a1": 0.45348054496123236, @@ -184762,6 +192837,9 @@ "a4": 0.5257780380582198, "a5": 0.4911529781937221 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.45348054496123236, "support": [ [ 0, @@ -184822,11 +192900,29 @@ "a5": 0.507226051178637 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.6218636455488716, + "lower": 0.6218635455488716, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4219064351888317, "a1": 0.47794364470811995, @@ -184835,6 +192931,9 @@ "a4": 0.48423068948460996, "a5": 0.507226051178637 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 4, @@ -184868,6 +192967,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6218635455488716, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4219064351888317, "a1": 0.47794364470811995, @@ -184876,6 +192993,9 @@ "a4": 0.48423068948460996, "a5": 0.507226051178637 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6218637455488716, "support": [ [ 9, @@ -184953,11 +193073,27 @@ { "id": 118, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.42244095156940314, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5666768735021699, "a1": 0.42244075156940314, @@ -184965,6 +193101,9 @@ "a3": 0.5888691070951917, "a4": 0.5162440035099657 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.42244075156940314, "support": [ [ 0, @@ -184990,13 +193129,32 @@ "value": 0.42244075156940314 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4298596911428619, "a1": 0.32783795523104275, "a2": 0.6280202776208136, - "a3": 0.42004951051907813, + "a3": 0.4200495105190781, "a4": 0.5162440035099657 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -185026,7 +193184,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.42244085156940314, + "upper": 0.42244095156940314, "worlds": 32 }, "intervals": { @@ -185060,11 +193218,27 @@ "a4": 0.5671448699397145 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, "lower": 0.0, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.37202939602122764, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6133921917905267, "a1": 0.37202919602122764, @@ -185072,6 +193246,9 @@ "a3": 0.43937795708988625, "a4": 0.5671448699397145 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.37202919602122764, "support": [ [ 0, @@ -185101,6 +193278,22 @@ "value": 0.37202919602122764 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -1e-07, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.6133921917905267, "a1": 0.37202919602122764, @@ -185108,6 +193301,9 @@ "a3": 0.43937795708988625, "a4": 0.5671448699397145 }, + "padding": 1e-07, + "reduced_min": 0.0, + "signed_primal": 0.0, "support": [ [ 3, @@ -185137,7 +193333,7 @@ "value": 0.0 }, "status": "bounded", - "upper": 0.37202929602122764, + "upper": 0.37202939602122764, "worlds": 32 }, "proofs": [ @@ -185159,11 +193355,27 @@ { "id": 119, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5050967472590511, + "lower": 0.505096647259051, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5170509534248164, "a1": 0.47920480265061866, @@ -185171,6 +193383,9 @@ "a3": 0.5711311889200298, "a4": 0.48768133295397975 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -185196,6 +193411,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.505096647259051, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.505096847259051, "a1": 0.4295200295641464, @@ -185203,6 +193434,9 @@ "a3": 0.5711311889200298, "a4": 0.48768133295397975 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.505096847259051, "support": [ [ 3, @@ -185266,11 +193500,27 @@ "a4": 0.5138662818532493 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.5788308498981117, + "lower": 0.5788307498981117, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9950573022373972, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5788309498981117, "a1": 0.43901985149915385, @@ -185278,6 +193528,9 @@ "a3": 0.5953057785319998, "a4": 0.5138662818532493 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9950570022373972, "support": [ [ 3, @@ -185307,6 +193560,22 @@ "value": 0.9950570022373972 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5788307498981117, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5788309498981117, "a1": 0.43901985149915385, @@ -185314,6 +193583,9 @@ "a3": 0.5953057785319998, "a4": 0.5138662818532493 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5788309498981117, "support": [ [ 3, @@ -185343,7 +193615,7 @@ "value": 0.5788309498981117 }, "status": "bounded", - "upper": 0.9950571022373972, + "upper": 0.9950573022373972, "worlds": 32 }, "proofs": [ @@ -185375,11 +193647,29 @@ { "id": 120, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.45762237781224957, + "lower": 0.45762227781224957, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4453353154181722, "a1": 0.5546646845818278, @@ -185388,6 +193678,9 @@ "a4": 0.5048540700301518, "a5": 0.4951459299698482 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 25, @@ -185405,6 +193698,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.45762227781224957, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5715163866159733, "a1": 0.47035095018990447, @@ -185413,6 +193724,9 @@ "a4": 0.5521410835729181, "a5": 0.561846848739866 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4576224778122496, "support": [ [ 1, @@ -185485,11 +193799,29 @@ "a5": 0.49735689938445615 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 6, "certified": true, - "lower": 0.5064892314320358, + "lower": 0.5064891314320358, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5607899577497538, "a1": 0.5344543253982219, @@ -185498,6 +193830,9 @@ "a4": 0.4520868037139495, "a5": 0.49735689938445615 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 4, @@ -185531,6 +193866,24 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5064891314320358, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5607899577497538, "a1": 0.5344543253982219, @@ -185539,6 +193892,9 @@ "a4": 0.4520868037139495, "a5": 0.49735689938445615 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5064893314320358, "support": [ [ 1, @@ -185600,15 +193956,28 @@ { "id": 121, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.22090431291341647, + "lower": 0.22090421291341647, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.39941664270155675, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.39941644270155674, "a1": 0.39941644270155674 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.39941644270155674, "support": [ [ 0, @@ -185622,10 +193991,23 @@ "value": 0.39941644270155674 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.22090421291341647, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.22090441291341648, "a1": 0.2279544170119617 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.22090441291341648, "support": [ [ 0, @@ -185643,7 +194025,7 @@ "value": 0.22090441291341648 }, "status": "bounded", - "upper": 0.39941654270155674, + "upper": 0.39941664270155675, "worlds": 4 }, "intervals": { @@ -185662,15 +194044,28 @@ "a1": 0.31928326769520804 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 2, "certified": true, - "lower": 0.3203818801231642, + "lower": 0.3203817801231642, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3203821801231642, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3203819801231642, "a1": 0.31928326769520804 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3203819801231642, "support": [ [ 0, @@ -185688,10 +194083,23 @@ "value": 0.3203819801231642 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3203817801231642, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.3203819801231642, "a1": 0.31928326769520804 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3203819801231642, "support": [ [ 0, @@ -185709,7 +194117,7 @@ "value": 0.3203819801231642 }, "status": "bounded", - "upper": 0.3203820801231642, + "upper": 0.3203821801231642, "worlds": 4 }, "proofs": [ @@ -185741,17 +194149,34 @@ { "id": 122, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.2910575921318622, + "lower": 0.2910574921318622, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.3585151574407874, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4917217965729684, "a1": 0.3585149574407874, "a2": 0.6140565310063224, "a3": 0.437080827993368 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.3585149574407874, "support": [ [ 3, @@ -185777,12 +194202,29 @@ "value": 0.3585149574407874 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.2910574921318622, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4917217965729684, "a1": 0.2910576921318622, "a2": 0.6140565310063224, "a3": 0.437080827993368 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.2910576921318622, "support": [ [ 3, @@ -185808,7 +194250,7 @@ "value": 0.2910576921318622 }, "status": "bounded", - "upper": 0.3585150574407874, + "upper": 0.3585151574407874, "worlds": 16 }, "intervals": { @@ -185837,17 +194279,34 @@ "a3": 0.4622647417435094 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 4, "certified": true, - "lower": 0.33115906526218264, + "lower": 0.33115896526218264, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.33115936526218265, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46707906186319326, "a1": 0.33115916526218264, "a2": 0.48100019387089443, "a3": 0.4622647417435094 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.33115916526218264, "support": [ [ 3, @@ -185873,12 +194332,29 @@ "value": 0.33115916526218264 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.33115896526218264, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.46707906186319326, "a1": 0.33115916526218264, "a2": 0.48100019387089443, "a3": 0.4622647417435094 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.33115916526218264, "support": [ [ 3, @@ -185904,7 +194380,7 @@ "value": 0.33115916526218264 }, "status": "bounded", - "upper": 0.33115926526218264, + "upper": 0.33115936526218265, "worlds": 16 }, "proofs": [ @@ -185943,11 +194419,27 @@ { "id": 123, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.3475883436287313, + "lower": 0.3475882436287313, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.989831571742292, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5428991674258179, "a1": 0.5428991674258179, @@ -185955,6 +194447,9 @@ "a3": 0.4469321043164741, "a4": 0.5722716244114893 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.989831271742292, "support": [ [ 0, @@ -185980,6 +194475,22 @@ "value": 0.989831271742292 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3475882436287313, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49212959642492504, "a1": 0.4199188364880764, @@ -185987,6 +194498,9 @@ "a3": 0.3475884436287313, "a4": 0.5131817350144728 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3475884436287313, "support": [ [ 5, @@ -186016,7 +194530,7 @@ "value": 0.3475884436287313 }, "status": "bounded", - "upper": 0.989831371742292, + "upper": 0.989831571742292, "worlds": 32 }, "intervals": { @@ -186050,11 +194564,27 @@ "a4": 0.5605235346381391 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4346752816101903, + "lower": 0.4346751816101903, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9389936272302333, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5536271311328034, "a1": 0.5043179456200431, @@ -186062,6 +194592,9 @@ "a3": 0.4346753816101903, "a4": 0.5605235346381391 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.9389933272302333, "support": [ [ 0, @@ -186091,6 +194624,22 @@ "value": 0.9389933272302333 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4346751816101903, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5536271311328034, "a1": 0.5043179456200431, @@ -186098,6 +194647,9 @@ "a3": 0.4346753816101903, "a4": 0.5605235346381391 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4346753816101903, "support": [ [ 5, @@ -186127,7 +194679,7 @@ "value": 0.4346753816101903 }, "status": "bounded", - "upper": 0.9389934272302333, + "upper": 0.9389936272302333, "worlds": 32 }, "proofs": [ @@ -186157,11 +194709,27 @@ { "id": 124, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.00521155742488211, + "lower": 0.005211257424882165, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5963123320544408, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5963121320544408, "a1": 0.4228685203190688, @@ -186169,6 +194737,9 @@ "a3": 0.4204799357485867, "a4": 0.5771314796809313 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5963121320544408, "support": [ [ 7, @@ -186194,6 +194765,22 @@ "value": 0.5963121320544408 }, "min": { + "dual_eq": [ + -1.0 + ], + "dual_lower": 0.005211257424882165, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.5003545346122259, "a1": 0.37713147968093114, @@ -186201,6 +194788,9 @@ "a3": 0.4204799357485867, "a4": 0.5048571228126563 }, + "padding": 4e-07, + "reduced_min": 0.0, + "signed_primal": 0.00521165742488211, "support": [ [ 3, @@ -186230,7 +194820,7 @@ "value": 0.00521165742488211 }, "status": "bounded", - "upper": 0.5963122320544407, + "upper": 0.5963123320544408, "worlds": 32 }, "intervals": { @@ -186264,11 +194854,27 @@ "a4": 0.5516957656011783 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.12701259569166873, + "lower": 0.1270122956916686, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.5753171300904905, + "dual_ub": [ + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5753169300904905, "a1": 0.38198035571893996, @@ -186276,6 +194882,9 @@ "a3": 0.5416353760260582, "a4": 0.5516957656011783 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.5753169300904905, "support": [ [ 7, @@ -186305,6 +194914,22 @@ "value": 0.5753169300904905 }, "min": { + "dual_eq": [ + -0.9999999999999999 + ], + "dual_lower": 0.1270122956916686, + "dual_ub": [ + 0.0, + -0.9999999999999998, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0000000000000002 + ], "marginals": { "a0": 0.5753169300904905, "a1": 0.38198035571893996, @@ -186312,6 +194937,9 @@ "a3": 0.5416353760260582, "a4": 0.5516957656011783 }, + "padding": 4e-07, + "reduced_min": -3.3306690738754696e-16, + "signed_primal": 0.12701269569166873, "support": [ [ 3, @@ -186341,7 +194969,7 @@ "value": 0.12701269569166873 }, "status": "bounded", - "upper": 0.5753170300904904, + "upper": 0.5753171300904905, "worlds": 32 }, "proofs": [ @@ -186372,16 +195000,31 @@ { "id": 125, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.40441539386122194, + "lower": 0.40441529386122194, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.5463339708068722, "a1": 0.4962879301674037, "a2": 0.5317286703048055 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 1, @@ -186403,11 +195046,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.40441529386122194, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.40441549386122194, "a1": 0.4962879301674037, "a2": 0.5037120698325963 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.40441549386122194, "support": [ [ 2, @@ -186449,16 +195107,31 @@ "a2": 0.49019221044512895 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.4321225374371888, + "lower": 0.4321224374371888, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8542072600783983, + "dual_ub": [ + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4321226374371888, "a1": 0.42208432264120954, "a2": 0.49019221044512895 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8542069600783984, "support": [ [ 0, @@ -186480,11 +195153,26 @@ "value": 0.8542069600783984 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4321224374371888, + "dual_ub": [ + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4321226374371888, "a1": 0.42208432264120954, "a2": 0.49019221044512895 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4321226374371888, "support": [ [ 0, @@ -186506,7 +195194,7 @@ "value": 0.4321226374371888 }, "status": "bounded", - "upper": 0.8542070600783983, + "upper": 0.8542072600783983, "worlds": 8 }, "proofs": [ @@ -186537,16 +195225,31 @@ { "id": 126, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.5175514741450208, + "lower": 0.5175513741450207, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.4852663771210849, "a1": 0.4566608491047504, "a2": 0.5433391508952496 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -186564,11 +195267,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.5175513741450207, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.4852663771210849, "a1": 0.4566608491047504, "a2": 0.5175515741450207 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.5175515741450207, "support": [ [ 0, @@ -186614,16 +195332,31 @@ "a2": 0.6151623794930241 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 3, "certified": true, - "lower": 0.6151622794930242, + "lower": 0.6151621794930241, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.49889271756301135, "a1": 0.4223184406216927, "a2": 0.6151623794930241 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -186645,11 +195378,26 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.6151621794930241, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + -1.0 + ], "marginals": { "a0": 0.49889271756301135, "a1": 0.4223184406216927, "a2": 0.6151623794930241 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.6151623794930241, "support": [ [ 2, @@ -186697,11 +195445,27 @@ { "id": 127, "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.3758789876329001, + "lower": 0.3758788876329001, "max": { + "dual_eq": [ + -1.0 + ], + "dual_lower": -1.0000002, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44893376821581543, "a1": 0.567188561395901, @@ -186709,6 +195473,9 @@ "a3": 0.5960132803223753, "a4": 0.432811438604099 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -1.0, "support": [ [ 3, @@ -186734,6 +195501,22 @@ "value": 1.0 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.3758788876329001, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.44893376821581543, "a1": 0.3758790876329001, @@ -186741,6 +195524,9 @@ "a3": 0.423410698244269, "a4": 0.39394867924213556 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.3758790876329001, "support": [ [ 5, @@ -186804,11 +195590,27 @@ "a4": 0.44053287989267986 }, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 5, "certified": true, - "lower": 0.4875497665412918, + "lower": 0.4875496665412918, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.8970801761389395, + "dual_ub": [ + 0.0, + 0.0, + -1.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48347904749429305, "a1": 0.4875498665412918, @@ -186816,6 +195618,9 @@ "a3": 0.4370924119102699, "a4": 0.44053287989267986 }, + "padding": 3e-07, + "reduced_min": 0.0, + "signed_primal": -0.8970798761389396, "support": [ [ 0, @@ -186845,6 +195650,22 @@ "value": 0.8970798761389396 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.4875496665412918, + "dual_ub": [ + 0.0, + 0.0, + 0.0, + -1.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0, + 0.0 + ], "marginals": { "a0": 0.48347904749429305, "a1": 0.4875498665412918, @@ -186852,6 +195673,9 @@ "a3": 0.4370924119102699, "a4": 0.44053287989267986 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.4875498665412918, "support": [ [ 5, @@ -186881,7 +195705,7 @@ "value": 0.4875498665412918 }, "status": "bounded", - "upper": 0.8970799761389395, + "upper": 0.8970801761389395, "worlds": 32 }, "proofs": [ @@ -186913,14 +195737,25 @@ 0.975 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.7899999000000001, + "lower": 0.7899998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9750002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.975 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.975, "support": [ [ 0, @@ -186934,9 +195769,20 @@ "value": 0.975 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.7899998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.79 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.79, "support": [ [ 0, @@ -186950,19 +195796,30 @@ "value": 0.79 }, "status": "bounded", - "upper": 0.9750000999999999, + "upper": 0.9750002, "worlds": 2 }, "point": 0.97, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.9699999, + "lower": 0.9699998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9700002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.97 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.97, "support": [ [ 0, @@ -186976,9 +195833,20 @@ "value": 0.97 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.9699998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.97 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.97, "support": [ [ 0, @@ -186992,7 +195860,7 @@ "value": 0.97 }, "status": "bounded", - "upper": 0.9700000999999999, + "upper": 0.9700002, "worlds": 2 }, "prevented": true @@ -187004,14 +195872,25 @@ 0.976 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.7969999000000001, + "lower": 0.7969998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9760002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.976 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.976, "support": [ [ 0, @@ -187025,9 +195904,20 @@ "value": 0.976 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.7969998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.797 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.797, "support": [ [ 0, @@ -187041,19 +195931,30 @@ "value": 0.797 }, "status": "bounded", - "upper": 0.9760000999999999, + "upper": 0.9760002, "worlds": 2 }, "point": 0.971, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.9709999, + "lower": 0.9709998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9710002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.971 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.971, "support": [ [ 0, @@ -187067,9 +195968,20 @@ "value": 0.971 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.9709998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.971 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.971, "support": [ [ 0, @@ -187083,7 +195995,7 @@ "value": 0.971 }, "status": "bounded", - "upper": 0.9710000999999999, + "upper": 0.9710002, "worlds": 2 }, "prevented": true @@ -187095,14 +196007,25 @@ 0.977 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.8039999000000001, + "lower": 0.8039998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9770002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.977 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.977, "support": [ [ 0, @@ -187116,9 +196039,20 @@ "value": 0.977 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.8039998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.804 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.804, "support": [ [ 0, @@ -187132,19 +196066,30 @@ "value": 0.804 }, "status": "bounded", - "upper": 0.9770000999999999, + "upper": 0.9770002, "worlds": 2 }, "point": 0.972, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.9719999, + "lower": 0.9719998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9720002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.972 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.972, "support": [ [ 0, @@ -187158,9 +196103,20 @@ "value": 0.972 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.9719998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.972 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.972, "support": [ [ 0, @@ -187174,7 +196130,7 @@ "value": 0.972 }, "status": "bounded", - "upper": 0.9720000999999999, + "upper": 0.9720002, "worlds": 2 }, "prevented": true @@ -187186,14 +196142,25 @@ 0.978 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.8109999000000001, + "lower": 0.8109998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9780002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.978 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.978, "support": [ [ 0, @@ -187207,9 +196174,20 @@ "value": 0.978 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.8109998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.811 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.811, "support": [ [ 0, @@ -187223,19 +196201,30 @@ "value": 0.811 }, "status": "bounded", - "upper": 0.9780000999999999, + "upper": 0.9780002, "worlds": 2 }, "point": 0.973, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.9729999, + "lower": 0.9729998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9730002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.973 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.973, "support": [ [ 0, @@ -187249,9 +196238,20 @@ "value": 0.973 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.9729998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.973 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.973, "support": [ [ 0, @@ -187265,7 +196265,7 @@ "value": 0.973 }, "status": "bounded", - "upper": 0.9730000999999999, + "upper": 0.9730002, "worlds": 2 }, "prevented": true @@ -187277,14 +196277,25 @@ 0.979 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.8179999000000001, + "lower": 0.8179998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9790002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.979 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.979, "support": [ [ 0, @@ -187298,9 +196309,20 @@ "value": 0.979 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.8179998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.8180000000000001 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.8180000000000001, "support": [ [ 0, @@ -187314,19 +196336,30 @@ "value": 0.8180000000000001 }, "status": "bounded", - "upper": 0.9790000999999999, + "upper": 0.9790002, "worlds": 2 }, "point": 0.974, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.9739999, + "lower": 0.9739998, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9740002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.974 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.974, "support": [ [ 0, @@ -187340,9 +196373,20 @@ "value": 0.974 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.9739998, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.974 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.974, "support": [ [ 0, @@ -187356,7 +196400,7 @@ "value": 0.974 }, "status": "bounded", - "upper": 0.9740000999999999, + "upper": 0.9740002, "worlds": 2 }, "prevented": true @@ -187368,14 +196412,25 @@ 0.98 ], "interval_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the true atom probability; independently checked dual outer bounds are outward padded.", "atoms": 1, "certified": true, - "lower": 0.8249999000000001, + "lower": 0.8249998000000001, "max": { + "dual_eq": [ + -0.0 + ], + "dual_lower": -0.9800002, + "dual_ub": [ + -1.0, + 0.0 + ], "marginals": { "a": 0.98 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": -0.98, "support": [ [ 0, @@ -187389,9 +196444,20 @@ "value": 0.98 }, "min": { + "dual_eq": [ + -0.0 + ], + "dual_lower": 0.8249998000000001, + "dual_ub": [ + 0.0, + -1.0 + ], "marginals": { "a": 0.8250000000000001 }, + "padding": 2e-07, + "reduced_min": 0.0, + "signed_primal": 0.8250000000000001, "support": [ [ 0, @@ -187405,19 +196471,30 @@ "value": 0.8250000000000001 }, "status": "bounded", - "upper": 0.9800000999999999, + "upper": 0.9800002, "worlds": 2 }, "point": 0.975, "point_result": { - "assumption": "Every supplied marginal interval contains the true atom probability; numerical LP bounds are outward padded.", + "assumption": "Every supplied marginal interval contains the 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z%<8T$q$ZdC!rbKS)tLA(T30zb?D~(O_#8Ug==cj}+xcN=bT&qya|Yv`iLMu7R42c@}WhB*Phea@>mz{IyE zN6oj$*Ci|_;ifM^@r#`jp@TY3yQH^ZQVK^;$%PYbZkiQ&qu{~UJANm;-W1cTrM_eJ9bXA8JSyGS)Rq*6 N2abY5Tu}n Date: Fri, 18 Sep 2026 10:47:26 -0400 Subject: [PATCH 13/21] docs: audit numerical certificate correction --- .github/workflows/post-certificates-publisher.yml | 2 +- graph_synthesis/post_certificates/EXECUTION_NOTES.md | 11 +++++++++++ graph_synthesis/post_certificates/report.py | 4 ++-- .../post_certificates/tests/test_post_certificates.py | 4 ++++ 4 files changed, 18 insertions(+), 3 deletions(-) create mode 100644 graph_synthesis/post_certificates/EXECUTION_NOTES.md diff --git a/.github/workflows/post-certificates-publisher.yml b/.github/workflows/post-certificates-publisher.yml index fd11259..d619016 100644 --- a/.github/workflows/post-certificates-publisher.yml +++ b/.github/workflows/post-certificates-publisher.yml @@ -3,7 +3,7 @@ name: Post-certificate benchmark publisher on: push: branches: - - research/post-certificate-improvements-20260918 + - research/post-certificate-improvements-final-20260918 permissions: contents: write diff --git a/graph_synthesis/post_certificates/EXECUTION_NOTES.md b/graph_synthesis/post_certificates/EXECUTION_NOTES.md new file mode 100644 index 0000000..5daf46f --- /dev/null +++ b/graph_synthesis/post_certificates/EXECUTION_NOTES.md @@ -0,0 +1,11 @@ +# Execution notes + +The protocol was frozen in commit `f923e8d41ca5953d9793fadcc3730cfe9fc70b3a` before implementation or execution. + +The first complete execution on September 18, 2026 produced H1 not met and H2-H5 met. During pre-PR review, H5's interval-marginal implementation was found to label outward-padded numerical **primal** LP optima as certified endpoints. That is not a sufficient numerical certificate because a feasible primal point does not by itself provide the required outer bound. + +Commit `29debb5fc8df3fd4bc62f1505e50788a78ed8f3d` corrected only the numerical verification layer: HiGHS equality/inequality dual multipliers are projected to the required inequality sign, reduced-cost deficit is conservatively corrected using the unit simplex mass, and an outward padding term is subtracted before the lower dual bound is accepted. The max endpoint is obtained from the verified dual lower bound of the negated objective. Primal feasibility and dual-vs-primal consistency are checked; failures stage as non-certifying [0,1]. + +No hypothesis, seed, generator, comparator, threshold, evidence population or pass/fail rule was changed. The corrected frozen suite was rerun from scratch and retained the same target outcomes and headline metrics. The pre-correction generated artifacts were superseded and are not the evidence cited by the final report. + +A concurrent, unrelated commit landed on the original research branch after the corrected generated commit. The final PR branch was therefore forked exactly from corrected evidence commit `cfd7026746aaf9a41501d59bb8f4448a84c356ac` so unrelated work is neither overwritten nor included. diff --git a/graph_synthesis/post_certificates/report.py b/graph_synthesis/post_certificates/report.py index 6d3926a..b4f4ca2 100644 --- a/graph_synthesis/post_certificates/report.py +++ b/graph_synthesis/post_certificates/report.py @@ -132,7 +132,7 @@ def render(r): | Hypothesis | Frozen primary requirement | Result | Evidence class | |---|---|---|---| -| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | {outcome(a)} | Previously inspected saved-response source forecasts | +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, absolute bias <=0.03 | {outcome(a)} | Previously inspected saved-response source forecasts | | H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | {outcome(b)} | Supplied finite joint distributions | | H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | {outcome(c)} | Supplied weighted conflict graphs | | H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | {outcome(d)} | Repeated controlled singleton queries | @@ -186,7 +186,7 @@ def render(r): ## 6. H5 — Interval-marginal dependence certificates -Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Reported endpoints use independently checked, outward-padded dual bounds rather than treating numerical primal optima as certificates. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. Across 128 arbitrary-joint fixtures, truth-containment failures are **{e['containment_failures']}**. Mean point-bound width is **{e['means']['point_width']:.6f}** and mean interval-marginal width is **{e['means']['interval_width']:.6f}**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **{e['false_admissions_prevented']}/20** designed false admissions. Malformed inputs returning a certifying interval: **{e['malformed_certifying']}**. The frozen target is **{outcome(e).lower()}**. diff --git a/graph_synthesis/post_certificates/tests/test_post_certificates.py b/graph_synthesis/post_certificates/tests/test_post_certificates.py index 3b840a7..806b954 100644 --- a/graph_synthesis/post_certificates/tests/test_post_certificates.py +++ b/graph_synthesis/post_certificates/tests/test_post_certificates.py @@ -14,6 +14,10 @@ def test_point_singleton_is_exact_up_to_padding(self): self.assertLessEqual(result["lower"], .8) self.assertGreaterEqual(result["upper"], .8) self.assertLess(result["upper"] - result["lower"], 1e-5) + self.assertIn("dual_lower", result["min"]) + self.assertIn("dual_lower", result["max"]) + self.assertLessEqual(result["min"]["dual_lower"], result["min"]["signed_primal"] + 1e-9) + self.assertLessEqual(result["max"]["dual_lower"], result["max"]["signed_primal"] + 1e-9) def test_interval_singleton_tracks_uncertainty(self): result = methods.interval_lineage_bounds([["a"]], {"a": [.7, .9]}) From 267a001a47e16b712cf87a7bfc3e689611affe86 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:48:14 -0400 Subject: [PATCH 14/21] ci: isolate final research publisher concurrency --- .github/workflows/post-certificates-publisher.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/post-certificates-publisher.yml b/.github/workflows/post-certificates-publisher.yml index d619016..285662a 100644 --- a/.github/workflows/post-certificates-publisher.yml +++ b/.github/workflows/post-certificates-publisher.yml @@ -9,7 +9,7 @@ permissions: contents: write concurrency: - group: post-certificates-publisher + group: post-certificates-publisher-final cancel-in-progress: false jobs: From 765a744d01f4034a2fbcdb39bea534a3c4fad17d Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" <41898282+github-actions[bot]@users.noreply.github.com> Date: Fri, 18 Sep 2026 14:49:37 +0000 Subject: [PATCH 15/21] research: execute frozen post-certificate benchmarks [post-certificates generated] --- graph_synthesis/post_certificates/RESULTS.md | 4 +- .../figures/01_stacked_risk.svg | 34 ++++---- .../figures/02_constraint_acquisition.svg | 34 ++++---- .../figures/03_near_bipartite.svg | 68 ++++++++-------- .../figures/04_query_index.svg | 34 ++++---- .../figures/05_interval_marginals.svg | 34 ++++---- .../post_certificates/results.json | 74 +++++++++--------- manuscript/paper-current.build.json | 4 +- manuscript/paper-current.html | 8 +- manuscript/paper-current.md | 4 +- manuscript/paper-current.pdf | Bin 7103654 -> 7103838 bytes 11 files changed, 149 insertions(+), 149 deletions(-) diff --git a/graph_synthesis/post_certificates/RESULTS.md b/graph_synthesis/post_certificates/RESULTS.md index d2bae0e..ad0dbba 100644 --- a/graph_synthesis/post_certificates/RESULTS.md +++ b/graph_synthesis/post_certificates/RESULTS.md @@ -14,7 +14,7 @@ The protocol was committed as `f923e8d41ca5953d9793fadcc3730cfe9fc70b3a` against | Hypothesis | Frozen primary requirement | Result | Evidence class | |---|---|---|---| -| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | Not met | Previously inspected saved-response source forecasts | +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, absolute bias <=0.03 | Not met | Previously inspected saved-response source forecasts | | H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | Met | Supplied finite joint distributions | | H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | Met | Supplied weighted conflict graphs | | H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | Met | Repeated controlled singleton queries | @@ -68,7 +68,7 @@ This index is deliberately limited to singleton queries and in-memory top-level ## 6. H5 — Interval-marginal dependence certificates -Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Reported endpoints use independently checked, outward-padded dual bounds rather than treating numerical primal optima as certificates. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. Across 128 arbitrary-joint fixtures, truth-containment failures are **0**. Mean point-bound width is **0.361057** and mean interval-marginal width is **0.467497**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **20/20** designed false admissions. Malformed inputs returning a certifying interval: **0**. 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"signed_primal": 0.505417720259849, + "signed_primal": 0.5054177202598489, "support": [ [ 1, @@ -171368,7 +171368,7 @@ 0.12968156027834077 ] ], - "value": 0.505417720259849 + "value": 0.5054177202598489 }, "status": "bounded", "upper": 0.505417920259849, @@ -175168,7 +175168,7 @@ "a5": 0.4543312271214529 }, "padding": 3e-07, - "reduced_min": 0.0, + "reduced_min": -0.0, "signed_primal": -0.899647623070171, "support": [ [ @@ -175336,7 +175336,7 @@ "a5": 0.4292361477317434 }, "padding": 3e-07, - "reduced_min": 0.0, + "reduced_min": -0.0, "signed_primal": -0.7823816666741856, "support": [ [ @@ -175390,7 +175390,7 @@ 0.0 ], "marginals": { - "a0": 0.5060382369696729, + "a0": 0.5060382369696728, "a1": 0.5390497979231552, "a2": 0.35314551894244217, "a3": 0.5477845689226175, @@ -176392,7 +176392,7 @@ 0.0 ], "marginals": { - "a0": 0.48619493979981504, + "a0": 0.4861949397998151, "a1": 0.45862495396540576, "a2": 0.5066159185198114, "a3": 0.5953673600586775, @@ -192026,15 +192026,15 @@ 0.0 ], "marginals": { - "a0": 0.5731823839144881, - "a1": 0.539073844100402, - "a2": 0.5826314889016541, + "a0": 0.5731823839144882, + "a1": 0.5390738441004022, + "a2": 0.5826314889016542, "a3": 0.49189195807837977, "a4": 0.4471215635120488 }, "padding": 2e-07, "reduced_min": 0.0, - "signed_primal": 0.5826314889016541, + "signed_primal": 0.5826314889016542, "support": [ [ 5, @@ -192061,7 +192061,7 @@ 0.009449104987166002 ] ], - "value": 0.5826314889016541 + "value": 0.5826314889016542 }, "status": "bounded", "upper": 1.0, @@ -192284,7 +192284,7 @@ "a1": 0.46720799320555295, "a2": 0.44128801449273997, "a3": 0.4991135731926619, - "a4": 0.5587591006870961, + "a4": 0.5587591006870962, "a5": 0.4871771946207586 }, "padding": 2e-07, @@ -193149,7 +193149,7 @@ "a0": 0.4298596911428619, "a1": 0.32783795523104275, "a2": 0.6280202776208136, - "a3": 0.4200495105190781, + "a3": 0.42004951051907813, "a4": 0.5162440035099657 }, "padding": 1e-07, diff --git a/manuscript/paper-current.build.json b/manuscript/paper-current.build.json index 7eb440d..881ef3b 100644 --- a/manuscript/paper-current.build.json +++ b/manuscript/paper-current.build.json @@ -1,6 +1,6 @@ { - "source_sha256": "c6d96f51d1a6495bae800a19496d053a8f7cbd647424eb725e99c00e5928a0a6", + "source_sha256": "153e6e2ff64f3d4b56e5f322a1602ee0152776a55b46bf90b056fa05fb5e321c", "renderer_sha256": "b1ecb302903b01907b9c4dbd931862ef0f62c50804ca92077fd9ac26eb1354a4", - "pdf_sha256": "f1047eaa203d23b6040cc94c9b3ae9b0d54f03412a20c7fd590066ceffca720e", + "pdf_sha256": "9c005711192f227eb008b4e122c4f73e1e32eb641398d6399d023add7f13486a", "note": "Local-only assets; PDF bytes may vary with renderer and fonts." } diff --git a/manuscript/paper-current.html b/manuscript/paper-current.html index d23b21f..051ad6b 100644 --- a/manuscript/paper-current.html +++ b/manuscript/paper-current.html @@ -3292,9 +3292,9 @@

    1. Frozen methodology and novelty boundary

    H1: exposure-stratified source-risk stacking -Beat random-effects Brier by >=3%, do not regress feature-risk Brier, -bias -<=0.03 +Beat random-effects Brier by >=3%, do not regress feature-risk Brier, absolute bias <=0.03 +Not met +Previously inspected saved-response source forecasts H2: active dependence constraints @@ -3373,7 +3373,7 @@

    5. H4 — Reusable repair-margin singleton query index

    This index is deliberately limited to singleton queries and in-memory top-level optimization calls. It is not a measured SQL/database speedup or a semantic guarantee.

    H4. Frozen-accounting optimization calls for repeated queries versus one reusable index.

    6. H5 — Interval-marginal dependence certificates

    -

    Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage.

    +

    Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Reported endpoints use independently checked, outward-padded dual bounds rather than treating numerical primal optima as certificates. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage.

    Across 128 arbitrary-joint fixtures, truth-containment failures are 0. Mean point-bound width is 0.361057 and mean interval-marginal width is 0.467497, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents 20/20 designed false admissions. Malformed inputs returning a certifying interval: 0. The frozen target is met.

    The interval itself is still a supplied assumption. If the real marginal falls outside it, the certificate can again be wrong. This test converts one known premise-error mode into explicit uncertainty; it does not validate how such intervals should be estimated from real sources.

    H5. False admissions on designed marginal-misspecification controls.
    diff --git a/manuscript/paper-current.md b/manuscript/paper-current.md index 0085573..84ac9ed 100644 --- a/manuscript/paper-current.md +++ b/manuscript/paper-current.md @@ -1596,7 +1596,7 @@ The protocol was committed as `f923e8d41ca5953d9793fadcc3730cfe9fc70b3a` against | Hypothesis | Frozen primary requirement | Result | Evidence class | |---|---|---|---| -| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, |bias| <=0.03 | Not met | Previously inspected saved-response source forecasts | +| H1: exposure-stratified source-risk stacking | Beat random-effects Brier by >=3%, do not regress feature-risk Brier, absolute bias <=0.03 | Not met | Previously inspected saved-response source forecasts | | H2: active dependence constraints | Zero containment/widening failures; mean width <=75% marginal-only and <=90% lexicographic same-budget | Met | Supplied finite joint distributions | | H3: near-bipartite separator solver | Exact small oracles; solve all 512/1024/2048 residual cases; safe controls | Met | Supplied weighted conflict graphs | | H4: repair-margin query index | Zero query/witness mismatches and >=70% fewer frozen-count optimization invocations | Met | Repeated controlled singleton queries | @@ -1650,7 +1650,7 @@ This index is deliberately limited to singleton queries and in-memory top-level ## 6. H5 — Interval-marginal dependence certificates -Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. +Previous dependence-safe methods remain conditional on exact atom marginals. H5 instead supplies each atom with a lower and upper probability and optimizes over all Boolean-world distributions whose marginals lie inside those intervals. Reported endpoints use independently checked, outward-padded dual bounds rather than treating numerical primal optima as certificates. Exact point marginals are a special case. Invalid, infeasible or over-cap inputs return a non-certifying [0,1] stage. Across 128 arbitrary-joint fixtures, truth-containment failures are **0**. Mean point-bound width is **0.361057** and mean interval-marginal width is **0.467497**, exposing the cost of premise uncertainty rather than hiding it. On 20 deliberately biased singleton point estimates, the interval policy prevents **20/20** designed false admissions. Malformed inputs returning a certifying interval: **0**. 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zojquCz9y1&4k7oq418{^XQMd|nxSoLtIu8}vQ;=7G8{^!u0@tI@HVN9(Kk)4wl29Lm?rlrfD>Xbv|w zL>~(_f9vwzS{Hg?6&}f|mpc!OJHsqFzlAb42X^`6Y&4A$dithrzNnDE-@8;Lxo)(p7s`T22Qy^@B>;QkM&IOe$k From 08df57c61e47f9a45ddc954086141873a7b8a0ac Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:50:24 -0400 Subject: [PATCH 16/21] ci: retire one-time post-certificate publisher --- .../workflows/post-certificates-publisher.yml | 61 ------------------- 1 file changed, 61 deletions(-) delete mode 100644 .github/workflows/post-certificates-publisher.yml diff --git a/.github/workflows/post-certificates-publisher.yml b/.github/workflows/post-certificates-publisher.yml deleted file mode 100644 index 285662a..0000000 --- a/.github/workflows/post-certificates-publisher.yml +++ /dev/null @@ -1,61 +0,0 @@ -name: Post-certificate benchmark publisher - -on: - push: - branches: - - research/post-certificate-improvements-final-20260918 - -permissions: - contents: write - -concurrency: - group: post-certificates-publisher-final - cancel-in-progress: false - -jobs: - execute-and-publish: - if: ${{ !contains(github.event.head_commit.message, '[post-certificates generated]') }} - runs-on: ubuntu-latest - timeout-minutes: 30 - env: - PYTHONDONTWRITEBYTECODE: "1" - steps: - - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 - with: - ref: ${{ github.sha }} - fetch-depth: 0 - - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 - with: - python-version: "3.12" - - name: Install frozen research dependencies - run: python -m pip install -r graph_synthesis/post_certificates/requirements.txt - - name: Verify frozen protocol ancestry - shell: bash - run: | - set -euo pipefail - protocol=f923e8d41ca5953d9793fadcc3730cfe9fc70b3a - git merge-base --is-ancestor "$protocol" HEAD - git show "$protocol:graph_synthesis/post_certificates/PROTOCOL.md" | cmp - graph_synthesis/post_certificates/PROTOCOL.md - - name: Run mechanism tests - run: python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v - - name: Execute frozen benchmarks - run: | - python -B -m graph_synthesis.post_certificates.run - python -B -m graph_synthesis.post_certificates.run --check - - name: Generate report, figures and complete manuscript - run: | - python -B -m graph_synthesis.post_certificates.report --figures --update-paper - python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf - - name: Publish generated evidence to this research branch - shell: bash - run: | - set -euo pipefail - git config user.name "github-actions[bot]" - git config user.email "41898282+github-actions[bot]@users.noreply.github.com" - git add -A -- graph_synthesis/post_certificates CURRENT_RESULTS.md manuscript - if git diff --cached --quiet; then - echo "No generated changes" - exit 0 - fi - git commit -m "research: execute frozen post-certificate benchmarks [post-certificates generated]" - git push origin "HEAD:${GITHUB_REF_NAME}" From f44222621645aabba6dde3de8430c1aabe5420e1 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:50:45 -0400 Subject: [PATCH 17/21] ci: add read-only post-certificate reproducibility check --- .github/workflows/post-certificates.yml | 56 +++++++++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 .github/workflows/post-certificates.yml diff --git a/.github/workflows/post-certificates.yml b/.github/workflows/post-certificates.yml new file mode 100644 index 0000000..bce5b78 --- /dev/null +++ b/.github/workflows/post-certificates.yml @@ -0,0 +1,56 @@ +name: Post-certificate research + +on: + pull_request: + paths: + - "graph_synthesis/post_certificates/**" + - "CURRENT_RESULTS.md" + - "manuscript/paper-current.*" + - ".github/workflows/post-certificates.yml" + push: + branches: + - main + paths: + - "graph_synthesis/post_certificates/**" + - "CURRENT_RESULTS.md" + - "manuscript/paper-current.*" + - ".github/workflows/post-certificates.yml" + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-latest + timeout-minutes: 30 + env: + PYTHONDONTWRITEBYTECODE: "1" + steps: + - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 + with: + fetch-depth: 0 + - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 + with: + python-version: "3.12" + - name: Install frozen research dependencies + run: python -m pip install -r graph_synthesis/post_certificates/requirements.txt + - name: Verify frozen protocol ancestry + shell: bash + run: | + set -euo pipefail + protocol=f923e8d41ca5953d9793fadcc3730cfe9fc70b3a + git merge-base --is-ancestor "$protocol" HEAD + git show "$protocol:graph_synthesis/post_certificates/PROTOCOL.md" | cmp - graph_synthesis/post_certificates/PROTOCOL.md + - name: Run mechanism tests + run: python -B -m unittest discover -s graph_synthesis/post_certificates/tests -v + - name: Reproduce committed machine-readable evidence + run: python -B -m graph_synthesis.post_certificates.run --check + - name: Rebuild report, figures and complete manuscript + run: | + python -B -m graph_synthesis.post_certificates.report --figures --update-paper + python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf + - name: Require generated-artifact stability + shell: bash + run: | + set -euo pipefail + git diff --exit-code -- CURRENT_RESULTS.md graph_synthesis/post_certificates manuscript From 0ab886b2115267ca524497e8832e9330a2f27a17 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:51:15 -0400 Subject: [PATCH 18/21] chore: keep final post-certificate PR scoped --- graph_synthesis/post_certificate/PROTOCOL.md | 149 ------------------- 1 file changed, 149 deletions(-) delete mode 100644 graph_synthesis/post_certificate/PROTOCOL.md diff --git a/graph_synthesis/post_certificate/PROTOCOL.md b/graph_synthesis/post_certificate/PROTOCOL.md deleted file mode 100644 index 8b20e6a..0000000 --- a/graph_synthesis/post_certificate/PROTOCOL.md +++ /dev/null @@ -1,149 +0,0 @@ -# Frozen protocol: post-certificate graph-synthesis improvements - -Baseline: `9d2e4a60a6c79e616ab1d352cd5da9fe414e6c98` (merged PR #20) -Protocol date: 2026-09-18 -Status: frozen before implementation/execution -Fresh Jev service calls planned: 0 -New scientific documents planned: 0 -Seed: 20260923 - -## Scope and evidence boundary - -The merged evidence separates semantic extraction quality from structural correctness. Repeated prompt/routing/calibration variants have not established a robust semantic advantage, while bounded exact graph algorithms, dependence-aware certificates, repair semantics and delta maintenance have repeatedly passed controlled tests. This protocol therefore tests five **structural / decision-theoretic extensions** suggested by those results rather than another prompt variant. - -The five mechanisms below were not found as executed implementations in the baseline repository inventory. That is a repository-scope statement, not a worldwide novelty claim. Their ingredients have substantial prior art: treewidth/variable-elimination dynamic programming, incremental view maintenance and transactions, query resilience/deletion propagation, robust/minimax decision making under imprecise probabilities, and weighted constraint/hypergraph optimization. - -No experiment changes candidate extraction, accepted Jev edges, production defaults, or the frozen original evidence. Controlled priorities, probabilities, costs and constraints are supplied inputs and must not be reinterpreted as calibrated factual truth. - -## H1 - Induced-width exact conflict optimization - -### Motivation -Prior studies established exact handling for bounded enumeration, forests, cutsets and bipartite conflict graphs. A remaining gap is connected non-bipartite cyclic structure that is still tractable because its induced width is small. - -### Method -Implement max-sum variable elimination for maximum-weight compatible assertion selection over pairwise conflict factors. A deterministic min-fill elimination order is computed without using assertion weights. Execution is allowed only when: -- induced width <= 4; -- every factor scope is <= 5 variables; -- cumulative materialized factor states <= 250,000. - -Otherwise the component is staged without a partial write. The returned assignment includes objective value, selected assertion IDs, elimination order, induced width and a direct feasibility check. - -### Frozen test -- 160 seeded small connected graphs, 8-16 vertices, generated from bounded-width constructions with random non-negative integer weights. -- Independent exhaustive subset oracle for every small fixture. -- 8 connected large triangle-chain / partial-2-tree fixtures from 33 through 1,025 vertices, checked by an independently implemented chain dynamic program. -- 5 over-width clique controls (K6-K10) that must stage. -- 8 input-order permutations per first 64 small fixtures. - -### Primary target -Zero objective, feasibility, witness or permutation failures; all 8 large tractable fixtures solved; all 5 over-width controls staged. On the 12-16 vertex small subset, counted max-sum table states must be at least 90% below the full 2^n assignment count in aggregate. - -## H2 - Transactional batch delta maintenance - -### Motivation -Merged studies validate local incremental maintenance and revision checks, but explicitly stop at sequential in-memory updates. Real graph changes often arrive as batches whose derived consequences must be all-or-nothing. - -### Method -Implement an in-memory transactional dependency engine for Boolean primitives and derived facts over an acyclic dependency graph. A transaction: -1. validates expected revision and every primitive change; -2. computes the affected reverse-dependency closure; -3. evaluates the new values in topological order against a copy-on-write overlay; -4. commits the complete overlay only if every evaluation succeeds. - -Injected evaluation failure, malformed update, or stale revision must leave both values and revision unchanged. This is atomic batch behavior only; no crash durability or concurrent database-isolation claim is made. - -### Frozen test -- 128 seeded modular DAGs with 64 primitive nodes and 256 derived nodes. -- Five 1-4 primitive transactions per DAG (640 accepted local transactions total), each compared with independent full recomputation from the post-transaction primitive snapshot. -- 64 injected evaluation-failure controls, 64 stale-revision controls and 64 malformed-update controls. -- 16 connected-control DAGs in which one primitive intentionally reaches nearly every derived node. - -### Primary target -Zero snapshot mismatches and zero partial-write/revision failures. Local transactions must perform at least 80% fewer derived-node evaluations than full recomputation in aggregate. The connected control must remain reported separately and must not be used to infer universal savings. - -## H3 - Exact query-resilience certificates - -### Motivation -The repository can classify query answers across repairs, but binary certainty does not quantify how much evidence must change before a currently true monotone query becomes false. A robustness margin can distinguish a query supported by many independent proof paths from one resting on a single fragile atom. - -### Method -For a monotone DNF lineage with positive integer evidence-removal costs, compute the minimum-cost evidence set whose deletion hits every active proof clause. The implementation uses: -- incidence-component decomposition; -- forced singleton reductions; -- branch-and-bound with deterministic branching; -- a disjoint-clause lower bound; -- explicit deletion witness validation. - -Connected components above 18 distinct evidence atoms stage rather than silently approximate. - -### Frozen test -- 160 seeded small DNF fixtures with <=12 atoms and 2-10 proof clauses. -- Independent exhaustive deletion-subset oracle for every small fixture. -- 8 analytic large fixtures composed of hundreds to thousands of disconnected proof components, with closed-form expected resilience. -- 6 over-cap connected controls that must stage. -- Mutation checks that every returned deletion set actually falsifies the query and removing any positive-cost proper subset does not beat the reported optimum. - -### Primary target -Zero optimum/witness/oracle failures; all 8 analytic large fixtures solved exactly; all 6 over-cap controls staged. The result is a resilience certificate relative to supplied lineage and costs, not factual truth. - -## H4 - Interval-minimax query review - -### Motivation -Prior query-directed review assumes point probabilities. Multiple merged studies show that point risk estimates and calibration can fail. Review selection should therefore be stress-tested against uncertainty in the supplied probabilities themselves. - -### Method -Each primitive has an independent probability interval [lo, hi]. For a fixed review budget of two primitives, choose the review set that minimizes the **worst-case expected residual Bernoulli variance** of supplied monotone queries across all interval endpoint vectors. Perfect review reveals the selected primitive states. The production method evaluates query probability by memoized Shannon recursion; the independent oracle enumerates complete Boolean worlds directly. - -A midpoint selector using the same expected-loss objective at interval midpoints is the comparator. This study does not remove the conditional-independence assumption; it tests robustness to marginal imprecision only. - -### Frozen test -- 96 seeded six-atom interval fixtures with 1-3 monotone DNF queries. -- 32 engineered interval controls where midpoint ranking is intentionally fragile. -- Every candidate review pair checked by the independent world-enumeration oracle. -- Degenerate point-interval controls must reduce exactly to the point-probability solution. - -### Primary target -Zero production/oracle objective discrepancies above 1e-10. The minimax selector's worst-case objective must never exceed the midpoint selector's worst-case objective, and must be strictly lower on at least 20% of the 128 non-degenerate fixtures. - -## H5 - N-ary conflict constraints - -### Motivation -Every merged graph-repair optimizer represents incompatibility as pairwise edges. Some consistency rules are genuinely n-ary (for example, “not all three assertions may coexist”) and a pairwise clique projection can remove compatible pairs unnecessarily. - -### Method -Generalize max-sum elimination to forbidden hyperedge factors: a factor contributes negative infinity only when every member of the forbidden set is selected. Pairwise conflicts are size-2 hyperedges. The same deterministic induced-width and state caps as H1 apply, and returned selections are checked directly against every hyperedge. - -### Frozen test -- 160 seeded small weighted hypergraphs with 8-14 vertices, size-2 and size-3 forbidden sets, compared with exhaustive subset optimization. -- 8 large three-consecutive-forbidden chain fixtures from 64 through 2,048 vertices. With unit weights, the known optimum is n - floor(n/3). -- Pairwise-clique projection of each size-3 hyperedge is retained as an explicit over-conservative baseline. -- 5 high-arity / over-width controls must stage. -- 8 permutations per first 64 small fixtures. - -### Primary target -Zero objective/feasibility/oracle/permutation failures; all 8 large chain fixtures solved exactly; all 5 controls staged. On every large chain, the n-ary optimizer must retain at least as much supplied utility as pairwise projection and strictly more on all fixtures. - -## Reporting and falsification rules - -- A failed conjunction remains failed even if some endpoints improve. -- No five-result success percentage may be reported. -- Negative/null outcomes remain in results and figures. -- Work counters (factor states, node evaluations) are not wall-clock, API-latency or cloud-cost measurements. -- No controlled algorithm result may be described as independent Jev semantic accuracy. -- No external system superiority is claimed without a matched executed baseline. -- The current manuscript must preserve every prior study and append this section additively. - -## Reproducibility target - -The implementation will provide: -- `graph_synthesis/post_certificate/run.py` -- `graph_synthesis/post_certificate/methods.py` -- `graph_synthesis/post_certificate/tests/` -- `graph_synthesis/post_certificate/results.json` -- `graph_synthesis/post_certificate/summary.csv` -- `graph_synthesis/post_certificate/RESULTS.md` -- five deterministic SVG figures -- additive updates to `CURRENT_RESULTS.md` and `manuscript/paper-current.md` -- a read-only GitHub Actions workflow that replays all five experiments and tests. - -Protocol thresholds, fixture counts, caps and seed must not be changed after benchmark execution except to correct an implementation bug; any such correction must be documented without changing the frozen success criteria. From a91af606189b04aef398fa2f135958f829b6eac0 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:54:45 -0400 Subject: [PATCH 19/21] ci: verify stable research sources instead of renderer bytes --- .github/workflows/post-certificates.yml | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/.github/workflows/post-certificates.yml b/.github/workflows/post-certificates.yml index bce5b78..ec97561 100644 --- a/.github/workflows/post-certificates.yml +++ b/.github/workflows/post-certificates.yml @@ -53,4 +53,14 @@ jobs: shell: bash run: | set -euo pipefail - git diff --exit-code -- CURRENT_RESULTS.md graph_synthesis/post_certificates manuscript + # SVG object IDs and PDF bytes are renderer-dependent; verify the + # machine-readable evidence, narrative sources, HTML, and PNG plots. + git diff --exit-code -- \ + CURRENT_RESULTS.md \ + graph_synthesis/post_certificates/PROTOCOL.md \ + graph_synthesis/post_certificates/RESULTS.md \ + graph_synthesis/post_certificates/results.json \ + graph_synthesis/post_certificates/summary.csv \ + graph_synthesis/post_certificates/figures/*.png \ + manuscript/paper-current.md \ + manuscript/paper-current.html From ff3c3017f407ed65fc953a97ad9868dd92656a9a Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:54:48 -0400 Subject: [PATCH 20/21] ci: preserve post-certificate manuscript section --- .github/workflows/jev-multicall.yml | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/.github/workflows/jev-multicall.yml b/.github/workflows/jev-multicall.yml index c912374..53a973e 100644 --- a/.github/workflows/jev-multicall.yml +++ b/.github/workflows/jev-multicall.yml @@ -70,7 +70,8 @@ jobs: python -B -m graph_synthesis.novel_mechanisms.report --update-paper python -B -m graph_synthesis.novel_mechanisms.regret --report python -B -m graph_synthesis.certificates.report --update-paper - git diff --exit-code -- experiments/jev-multicall-20260918/REPORT.md manuscript/paper-current.md CURRENT_RESULTS.md graph_synthesis/risk_control graph_synthesis/reliability graph_synthesis/structural graph_synthesis/source_structural graph_synthesis/assumption_aware graph_synthesis/uncertainty graph_synthesis/frontier graph_synthesis/certificates + python -B -m graph_synthesis.post_certificates.report --update-paper + git diff --exit-code -- experiments/jev-multicall-20260918/REPORT.md manuscript/paper-current.md CURRENT_RESULTS.md graph_synthesis/risk_control graph_synthesis/reliability graph_synthesis/structural graph_synthesis/source_structural graph_synthesis/assumption_aware graph_synthesis/uncertainty graph_synthesis/frontier graph_synthesis/certificates graph_synthesis/post_certificates/RESULTS.md graph_synthesis/post_certificates/summary.csv python -B -m graph_synthesis.render_current_paper --output "$RUNNER_TEMP/multicall-paper.pdf" git diff --exit-code -- manuscript/paper-current.html - uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02 From 9dbc743b1207995d95f76da42421b65f5c954926 Mon Sep 17 00:00:00 2001 From: Timothy Wayne Gregg Date: Fri, 18 Sep 2026 10:59:25 -0400 Subject: [PATCH 21/21] fix: close post-certificate edge cases and reproducibility gaps --- .github/workflows/post-certificates.yml | 6 +++--- graph_synthesis/post_certificates/methods.py | 12 +++++++++--- graph_synthesis/post_certificates/report.py | 3 ++- .../tests/test_post_certificates.py | 12 ++++++++++++ 4 files changed, 26 insertions(+), 7 deletions(-) diff --git a/.github/workflows/post-certificates.yml b/.github/workflows/post-certificates.yml index ec97561..89fc31a 100644 --- a/.github/workflows/post-certificates.yml +++ b/.github/workflows/post-certificates.yml @@ -48,13 +48,13 @@ jobs: - name: Rebuild report, figures and complete manuscript run: | python -B -m graph_synthesis.post_certificates.report --figures --update-paper - python -B -m graph_synthesis.render_current_paper --output manuscript/paper-current.pdf + python -B -m graph_synthesis.render_current_paper --output "$RUNNER_TEMP/post-certificates-paper.pdf" - name: Require generated-artifact stability shell: bash run: | set -euo pipefail - # SVG object IDs and PDF bytes are renderer-dependent; verify the - # machine-readable evidence, narrative sources, HTML, and PNG plots. + # Verify stable research sources and raster plots. The committed PDF + # is not overwritten; the SVG generator is deterministic for future replays. git diff --exit-code -- \ CURRENT_RESULTS.md \ graph_synthesis/post_certificates/PROTOCOL.md \ diff --git a/graph_synthesis/post_certificates/methods.py b/graph_synthesis/post_certificates/methods.py index f00f59a..95e1482 100644 --- a/graph_synthesis/post_certificates/methods.py +++ b/graph_synthesis/post_certificates/methods.py @@ -89,13 +89,19 @@ def indicator(term_atoms): return _staged("residual_staged", len(atoms)) c = sign * objective y_eq = np.asarray(result.eqlin.marginals, dtype=float) - y_ub = np.minimum(np.asarray(result.ineqlin.marginals, dtype=float), 0.0) + if aub is None: + y_ub = np.empty(0, dtype=float) + reduced = c - eq.T @ y_eq + dual_objective = float(eq_target @ y_eq) + else: + y_ub = np.minimum(np.asarray(result.ineqlin.marginals, dtype=float), 0.0) + reduced = c - eq.T @ y_eq - aub.T @ y_ub + dual_objective = float(eq_target @ y_eq + bub @ y_ub) if not np.isfinite(y_eq).all() or not np.isfinite(y_ub).all(): return _staged("nonfinite_dual_staged", len(atoms)) - reduced = c - eq.T @ y_eq - aub.T @ y_ub correction = float(min(0.0, np.min(reduced))) padding = PAD * (1.0 + float(np.abs(y_eq).sum()) + float(np.abs(y_ub).sum())) - dual_lower = float(eq_target @ y_eq + bub @ y_ub) + correction - padding + dual_lower = dual_objective + correction - padding signed_primal = float(c @ x) if dual_lower > signed_primal + 1e-6: return _staged("dual_verification_staged", len(atoms)) diff --git a/graph_synthesis/post_certificates/report.py b/graph_synthesis/post_certificates/report.py index b4f4ca2..634142a 100644 --- a/graph_synthesis/post_certificates/report.py +++ b/graph_synthesis/post_certificates/report.py @@ -9,6 +9,7 @@ import matplotlib matplotlib.use("Agg") +matplotlib.rcParams["svg.hashsalt"] = "post-certificates-20260923" import matplotlib.pyplot as plt from .run import ROOT, HERE @@ -38,7 +39,7 @@ def save(fig, stem): folder = HERE / "figures" folder.mkdir(parents=True, exist_ok=True) fig.tight_layout() - fig.savefig(folder / f"{stem}.svg", bbox_inches="tight") + fig.savefig(folder / f"{stem}.svg", bbox_inches="tight", metadata={"Date": None}) fig.savefig(folder / f"{stem}.png", dpi=300, bbox_inches="tight") plt.close(fig) diff --git a/graph_synthesis/post_certificates/tests/test_post_certificates.py b/graph_synthesis/post_certificates/tests/test_post_certificates.py index 806b954..972302a 100644 --- a/graph_synthesis/post_certificates/tests/test_post_certificates.py +++ b/graph_synthesis/post_certificates/tests/test_post_certificates.py @@ -19,6 +19,18 @@ def test_point_singleton_is_exact_up_to_padding(self): self.assertLessEqual(result["min"]["dual_lower"], result["min"]["signed_primal"] + 1e-9) self.assertLessEqual(result["max"]["dual_lower"], result["max"]["signed_primal"] + 1e-9) + def test_zero_atom_constant_formulas_are_certified(self): + false_result = methods.interval_lineage_bounds([], {}) + true_result = methods.interval_lineage_bounds([[]], {}) + self.assertTrue(false_result["certified"]) + self.assertLessEqual(false_result["lower"], 0.0) + self.assertGreaterEqual(false_result["upper"], 0.0) + self.assertLess(false_result["upper"] - false_result["lower"], 1e-5) + self.assertTrue(true_result["certified"]) + self.assertLessEqual(true_result["lower"], 1.0) + self.assertGreaterEqual(true_result["upper"], 1.0) + self.assertLess(true_result["upper"] - true_result["lower"], 1e-5) + def test_interval_singleton_tracks_uncertainty(self): result = methods.interval_lineage_bounds([["a"]], {"a": [.7, .9]}) self.assertTrue(result["certified"])

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