diff --git a/research/pr6621-paid-merge-gate/README.md b/research/pr6621-paid-merge-gate/README.md new file mode 100644 index 0000000000..e18dd27338 --- /dev/null +++ b/research/pr6621-paid-merge-gate/README.md @@ -0,0 +1,137 @@ +# PR #6621 paid-job merge gate + +**Audit; no new κ.** The selected frontier stays 0.00310045. + +## Scope and evidence + +Original card: `supplier-boundary-audit`, refined to one latest candidate. +PR [#6621](https://github.com/CrocSwap/integer-mult-bounds/pull/6621) at +`e772ff8f300f4687bd8fa059f9e8f98719de121c` reports conditional κ = 0.00329700 +by three edits of the PR #6529 native word, on the unchanged PR #6551 caller. +The published signed change per native call is + +```text +paid {1:-3, 3:-1, 4:+1, 5:-1, 6:+1} +targets {8:+1, 9:-1} +``` + +and the complete invoice is that delta times 18. This package checks that +claim against the published receipts and records one coverage gap. It does +not replay the native word or the rational moment engines. + +### What the receipts establish + +Against published PR [#6551](https://github.com/CrocSwap/integer-mult-bounds/pull/6551) +at `11ca568cd1a16776ade02b4df09ea04a784cc674`, the PR #6621 `complete_cost` +histograms differ by exactly `18` times the stated per-call delta. Productive +fields stay 13,756, paid calls fall 67,096 to 67,042, and the rank-mass +surplus stays 760. Both public ordinary-work bounds equal the closed form in +`pricing.py` at 611 caller events, namely 254,932,208. The `+68` native +program events therefore do not move that bound: the formula never reads the +native program length. The local route allowance rises by 1,000, which equals +`1000 * (-3 + 4)` when the per-call paid-job count falls by 3 and one owned +lifetime is added. That is an accounting identity of the published totals, not +a replay. + +The multisets `{1,1,1,3,5,8}` and `{4,6,9}` both sum to 19, and the first is +strictly majorized by the second. For `H(r) = r^t` on `0 < t < 1`, strict +concavity gives + +```text +3 H(1) + H(3) + H(5) + H(8) - H(4) - H(6) - H(9) > 0. +``` + +The same conclusion splits into the two brackets in PR #6621's PROOF.md. +Strict subadditivity of `r^t`, which follows from `s^t > s` for `s, t` in +`(0, 1)`, gives `3 H(1) + H(3) > H(6)` because `1+1+1+3 = 6`. The derivative +`t r^{t-1}` is strictly decreasing, so the unit interval `(4, 5)` contributes +more than `(8, 9)`. The verifier checks the integer comparisons. It does not +replace the concavity argument. + +The native words agree with the event census in the README, independently of +the replay. `word-pr6529.json.gz` is the program inside PR #6551's +`native-source.tar` and is byte-identical to `BASEWORD.json.gz` inside PR +#6621's archive. The new program has length 18,561 rather than 18,493: +`ADD +69`, `MOVE -3`, `INIT +1`, `CLEAR +1`. The only `final` change is index +435, from frame 127 to frame 246. + +### The gap + +`invoice.compare` in the PR #6621 package demands that the candidate differ +from `research/gaussian-root-retirement/RESULT.json` inside its `source.tar` +by only the retirement change + +```text +208*(H41 - H40 - H57 + H56). +``` + +That archived file still carries status +`PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394` and kappa `164697/50000000`. +Its paid and target histograms, local scalar allowance, and raw-root interval +are not the receipt archived by PR #6551. Relative to that unmodified receipt +(sha256 `13639e4770964ded237b79d72ad517448de269b34d724beaa70757dbe0be6fe2`), +the PR #6621 archive already contains the same native merge delta as the +public candidate. The compare gate therefore still sees only the retirement +delta. The rewritten raw-root lower endpoint +`164801644010225711532641/50000000000000000000000000` +lies strictly above the unmodified upper endpoint +`82348659273829759207423/25000000000000000000000000` +and strictly above the kappa string the file still prints, +`164697/50000000`. + +PR #6551's own public histogram really does differ from its own archived +predecessor by the retirement delta. The same numerical gate on PR #6621 does +not additionally certify the merge. The merge is visible only by comparing +the public #6621 receipt with the public #6551 receipt, or with the +unmodified archived predecessor. Neither comparison is the check +`invoice.compare` performs. + +PR [#6554](https://github.com/CrocSwap/integer-mult-bounds/pull/6554) audits +the #6551 retirement cut. It does not inspect this native merge or the +rewritten predecessor receipt. + +## Reproduce + +From the repository root, with Python 3.12: + +```sh +python3 -B research/pr6621-paid-merge-gate/verify.py +python3 scripts/research_package.py --package research/pr6621-paid-merge-gate --check-only +python3.12 scripts/research_package.py --package research/pr6621-paid-merge-gate +``` + +The marker is `PASS_PR6621_MERGE_GATE_DOES_NOT_SEE_THE_MERGE`. + +Vendored bytes, copied from the named commits and checked against the GitHub +blob ids of the two public `RESULT.json` files: + +| File | sha256 | Git blob | +|---|---|---| +| `evidence/pr6551-result.json` | `90e096089e661a82f551feb022ff4fa49a5847b76abb5116c89cb7ed26c3d27f` | `38d840ae0f36b5a922fe288ca422f8d942d0008e` | +| `evidence/pr6621-result.json` | `878e15f5797219311175ae177fea8c4a10f4da5f4c463814721f5bd8b7d6dc27` | `0c31219eccb0d9f8e73b39da7819545795f7d964` | +| `evidence/archive6551-retirement-result.json` | `13639e4770964ded237b79d72ad517448de269b34d724beaa70757dbe0be6fe2` | extracted from PR #6551 `source.tar` | +| `evidence/archive6621-retirement-result.json` | `020728f015b8493b975a6c3d25115e00cef1c4bb62c062148f546723c509b75d` | extracted from PR #6621 `source.tar` | +| `evidence/word-pr6529.json.gz` | `15ca0c4ee15ad5a58dfc178d7b44d89ca202021c2907fbf9ef2ed50ba1ed8513` | `WORD.json.gz` in the #6551 native archive; also `BASEWORD.json.gz` in the #6621 native archive | +| `evidence/word-pr6621.json.gz` | `25b350a56ce11436fccf4c987da466cb002fa28dfc9b7e9d88e8b1b748b79df3` | `WORD.json.gz` in the #6621 native archive | + +PR #6551 `source.tar` blob `025b8b9c6d9b21e31ad7499ebb04132abfa7e88c`. PR #6621 +`source.tar` blob `0c254b78790851e78fc43b0f72b2d47e4723517b`. + +## Open next questions + +1. Replace the archived Gaussian-retirement `RESULT.json` with the unmodified + PR #6551 copy and rerun the published verifier. The first assertion to + inspect is `invoice.compare`. This matters because a green run of the + shipped package does not show the merge. It is blocked here by the nested + replay and moment engines, which this session did not execute. +2. Assign the Gaussian ranks of the two vendored words with an independent + census. The opcode and `final[435]` facts above do not identify ranks + 1, 3, 4, 5, 6, 8 and 9. The rank map is the retained native replay. + +## Credit + +The construction, retirement identity and reported conditional kappa are +DreamingOfClouds' PR #6621, building on Ali Romman's PR #6551 and the retained +PR #6545 / PR #6529 lineage named there. PR #6554 by DLamdata is the open +audit of the retirement cut and is not reused as evidence for the merge. +Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. diff --git a/research/pr6621-paid-merge-gate/SOURCES.json b/research/pr6621-paid-merge-gate/SOURCES.json new file mode 100644 index 0000000000..594089b9c7 --- /dev/null +++ b/research/pr6621-paid-merge-gate/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + } + ] +} diff --git a/research/pr6621-paid-merge-gate/TASK.json b/research/pr6621-paid-merge-gate/TASK.json new file mode 100644 index 0000000000..b126de21f6 --- /dev/null +++ b/research/pr6621-paid-merge-gate/TASK.json @@ -0,0 +1,97 @@ +{ + "schema_version": 1, + "task_id": "supplier-boundary-audit", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "original_card": { + "id": "supplier-boundary-audit", + "question": "Does one changed supplier have complete source-bound native, caller, ordinary and outer admission coverage?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Choose one latest uncovered candidate and build a delta coverage map against the selected review. For P104, #5717 changes owned-lifetime assumptions and #5719 covers exact #5713 causal premises; neither automatically transfers to #5718. For BIT, #5679/#5708 need component admission and compatible outer use. Check controls and exact source identity before reuse; stop with one resolved gap or explicit remaining obligation. A heavy full replay requires a separate serial resource budget.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "supplier admission", + "5717", + "5719", + "5708", + "owned lifetime" + ], + "existing_checks": [ + { + "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.", + "evidence": "research/staged544-mixed-fourth-entry/README.md", + "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.", + "status": "author-checked", + "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3801: successor scatter-boundary decision package.", + "evidence": "research/scatter-boundary-decision/README.md", + "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.", + "status": "author-checked", + "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "refined", + "actual_scope": "Does PR #6621's published paid-job-merge histogram, and its top-level invoice.compare gate against the retained Gaussian-retirement receipt, cover that merge relative to published PR #6551?", + "scope_change_reason": "The card asks for one latest uncovered candidate and a delta coverage map, stopping at one resolved gap. This package audits only PR #6621 head e772ff8f300f4687bd8fa059f9e8f98719de121c against published PR #6551 head 11ca568cd1a16776ade02b4df09ea04a784cc674. It does not transfer the #5719 or #5708 checks, and it does not replay the native word.", + "bottleneck_link": "The selected frontier remains kappa 0.00310045. PR #6621 reports conditional kappa 0.00329700 from three native-word edits on the PR #6551 caller. A maintainer can use that figure only if the signed histogram delta is bound to the published predecessor. This audit separates that arithmetic, which matches the prose, from the compare gate, which does not see the merge.", + "budget_minutes": 60, + "stop_rule": "Stop after one source-identity gap in the #6621 compare gate. Do not rerun the native column replay or the rational moment engines.", + "outcome": "completed", + "evidence": "verify.py checks the vendored public and archived receipts and the two native words. PASS_PR6621_MERGE_GATE_DOES_NOT_SEE_THE_MERGE.", + "author": "unpaidmoon", + "ai_assistance": "Substantial Cursor Grok assistance.", + "open_questions": [ + { + "question": "Does invoice.compare accept the paid-job merge when the archived Gaussian-retirement RESULT.json is replaced by the unmodified receipt from PR #6551's source.tar?", + "why_it_matters": "The published gate currently differences the candidate against a receipt that already contains the merge, so a passing run does not authenticate the new native histogram.", + "first_step": "Swap research/gaussian-root-retirement/RESULT.json in PR #6621's source.tar for the byte-identical file from PR #6551 source.tar (sha256 13639e4770964ded237b79d72ad517448de269b34d724beaa70757dbe0be6fe2) and rerun the published verify.py, recording the first failing assertion.", + "blocked_by": "The nested native replay and moment engines are outside this package's budget; the expected failure is the compare assertion, but that has not been executed here." + }, + { + "question": "Do the two native words induce the claimed Gaussian rank delta under an independent replay, rather than only under the edited verifier shipped inside PR #6621's native-source.tar?", + "why_it_matters": "The opcode census and final[435] change are independent of that verifier, but the ranks 1, 3, 4, 5, 6, 8 and 9 are assigned by its replay.", + "first_step": "Reimplement the local paid/helper census from the documented event rules on word-pr6529.json.gz and word-pr6621.json.gz, with one mutated opcode as a failure control.", + "blocked_by": "The rank map lives in the retained native replay, which this audit did not reimplement." + } + ] +} diff --git a/research/pr6621-paid-merge-gate/VERIFY.json b/research/pr6621-paid-merge-gate/VERIFY.json new file mode 100644 index 0000000000..67a7932e50 --- /dev/null +++ b/research/pr6621-paid-merge-gate/VERIFY.json @@ -0,0 +1,25 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/pr6621-paid-merge-gate/evidence/archive6551-retirement-result.json", + "research/pr6621-paid-merge-gate/evidence/archive6621-retirement-result.json", + "research/pr6621-paid-merge-gate/evidence/pr6551-result.json", + "research/pr6621-paid-merge-gate/evidence/pr6621-result.json", + "research/pr6621-paid-merge-gate/evidence/word-pr6529.json.gz", + "research/pr6621-paid-merge-gate/evidence/word-pr6621.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 60, + "checks": "Histogram identity of the published #6621 minus #6551 receipts, blindness of invoice.compare to that delta, opcode and final[435] census of the two native words, integer majorization comparisons, and four mutated failure controls." + } + ] +} diff --git a/research/pr6621-paid-merge-gate/evidence/archive6551-retirement-result.json b/research/pr6621-paid-merge-gate/evidence/archive6551-retirement-result.json new file mode 100644 index 0000000000..3bcf9f740b --- /dev/null +++ b/research/pr6621-paid-merge-gate/evidence/archive6551-retirement-result.json @@ -0,0 +1,316 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "candidate": { + "caller": { + "coefficients": 1225, + "event_sha256": "e30e87523bfe8dcf009843965a617a664a1ce802850bb07ac2ca198fa818a124", + "events": 609, + "inputs": 35, + "native_stages": 18 + }, + "complete_cost": { + "compiler": { + "H": 138100200000000, + "N": "2^138100200000000", + "eta": { + "lower": "0.000000000000021343548942378562", + "upper": "0.000000000000021343548942378563" + }, + "gap": "1/1400000000", + "integer_test_exponent": 98643, + "logarithm_power": 2100, + "theta": "63/64", + "uniform_saving": "2305761/700000000", + "word_materialized": false + }, + "derivative_upper": "-709185992340617917271102325360006905223896764960473050137748773/3138550867693340381917894711603833208051177722232017256448", + "full_forward_calls": 18, + "gain": "5641/1000000000", + "kappa": "164697/50000000", + "kappa_decimal": "0.00329394", + "margin_at_previous": { + "lower": "1.294383344079915739634444114064", + "upper": "1.294383344079915739634444114065" + }, + "negative_controls": { + "coarse_tail": "The block tail bound cannot fund this near-limit claim.", + "old_BIT": "An outer inequality fails at BIT saving0.0027.", + "old_completion": "Cutoff16 and floor17 give a ratio above one." + }, + "nonrecursive": { + "local_routes": 5384000, + "local_scalar": 137218, + "paid_rank_mass": 184962, + "peak_owned_fields": 13, + "raw_budget": 1000000000, + "raw_scalar_upper": 254699248, + "scalar_growth_bound": "At most 2^(10^9 + R*f), where R is the full paid rank mass." + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "6456127995388481/1960000000000000000", + "fused_gaussian": "6456127986165443/1960000000000000000", + "global_coordinate_router": "14411/4375000", + "group_bit_router": "20175404331767/6125000000000000", + "group_scans": "699999999/700000000", + "main_transform": "6456126595388481/1960000000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "802706127995388481/1960000000000000000" + }, + "parameters": { + "a": "14411/4375000", + "b": "4611521/1400000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "1782706126595388481/1960000000000000000", + "complex_uniform_saving": "2305761/700000000", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "164697/50000000", + "lambda_": "398682423/400000000", + "lambda_prime": "1395388481/1400000000", + "layout": "1/1400000000", + "q": "4611519/1400000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "658789/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "58/546875", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "177293875504611519/980000000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "5595388481/1960000000000000000", + "cap_above_band": "802706126595388481/1960000000000000000", + "cap_below_cell": "177293872004611519/1960000000000000000", + "cap_below_phase_cell_power": "2137293873404611519/1960000000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "39138479/1400000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "5586165443/1960000000000000000", + "gaussian_above_main": "695388481/980000000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "21831767/6125000000000000", + "group_gauge_power_slack": "177293875434611519/980000000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "697694241/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "781484790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "2795388479/1960000000000000000", + "leaf_saving_above_effective": "1395388479/1960000000000000000", + "main_transform_above_kappa": "4195388481/1960000000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "13474423561/175000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395388483/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "2795388479/1960000000000000000", + "q_positive": "4611519/1400000000", + "short_record_fallback": "1395388479/1400000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "796250005595388481/1960000000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 41980, + "16": 1872, + "2": 8154, + "24": 416, + "3": 8838, + "32": 416, + "4": 1926, + "5": 2754, + "56": 416, + "6": 144, + "7": 162, + "8": 18 + }, + "paid_calls": 67096, + "previous_fixed_root": "3288299/1000000000", + "productive_fields": 13756, + "rank_mass_surplus": 760, + "raw_endpoint_margins": { + "lower": { + "first": { + "lower": "0.000000000000000000001070125900", + "upper": "0.000000000000000000001070125901" + }, + "second": { + "lower": "0.000000000000000000001070125900", + "upper": "0.000000000000000000001070125901" + } + }, + "upper": { + "first": { + "lower": "-0.000000000000000000001221858508", + "upper": "-0.000000000000000000001221858507" + }, + "second": { + "lower": "-0.000000000000000000001221858508", + "upper": "-0.000000000000000000001221858507" + } + } + }, + "raw_headroom": [ + "637095319036829691/100000000000000000000000000", + "159273829759207423/25000000000000000000000000" + ], + "raw_root_interval": [ + "329394637095319036829691/100000000000000000000000000", + "82348659273829759207423/25000000000000000000000000" + ], + "refinement_kind": "Independent Gaussian retirement changes the complete productive profile.", + "relative_gain_percent": "564100/3288299", + "strictification": { + "alpha": { + "lower": "0.999999998291106770622495989553", + "upper": "0.999999998291106770622495989554" + }, + "coarse_tail_upper": "1/288230376151711744", + "cutoff": 12, + "delta": { + "lower": "0.964631407891465146160234341582", + "upper": "0.964631407891465146160234341583" + }, + "exact_tail_upper": 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Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_return": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "unearned_central_target": "Every independent reverse caller coefficient", + "unpaid_native_job": "All independent fields and paid calls", + "wrong_cut_sign": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient" + }, + "dual_pair": { + "cut_after": 328, + "cut_pairing": "1", + "input_pairing": "1", + "prefix_column": "P d = S b", + "prefix_row": "a P = S c" + }, + "physical": { + "central_square_columns": 53248, + "central_translations": 17, + "full_calls": 18, + "main_targets": { + "1": 208, + "145": 104, + "16": 104, + "17": 1768, + "25": 416, + "33": 416, + "57": 416, + "73": 208 + }, + "new_paid_jobs": 0, + "ordinary_normalizations": 34, + "physical_contacts": 7488, + "ports": 104, + "route_payload_sha256": "79930ec6c09a8e4930556c925c354bb5431203eaf069d9373f056049c061289b", + "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", + "whole_idle_jobs": { + "16": 1872, + "24": 416, + "32": 416, + "56": 416 + } + }, + "reverse": { + "coefficients": 1225, + "rows": 35 + }, + "source_margin_first": { + "lower": "-1.293834964536877202313242336847", + "upper": "-1.293834964536877202313242336846" + }, + "source_margin_second": { + "lower": "-1.293834964536877202313242336847", + "upper": "-1.293834964536877202313242336846" + } + }, + "selected_frontier_changed": false, + "source_result_sha256": "4e16dd95b28722231e4ee44df3a8cbaa97f2ed1f241a0290fd057e4975fd443e", + "status": "PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394" +} diff --git a/research/pr6621-paid-merge-gate/evidence/archive6621-retirement-result.json b/research/pr6621-paid-merge-gate/evidence/archive6621-retirement-result.json new file mode 100644 index 0000000000..7fd4f6775f --- /dev/null +++ b/research/pr6621-paid-merge-gate/evidence/archive6621-retirement-result.json @@ -0,0 +1,316 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "candidate": { + "caller": { + "coefficients": 1225, + "event_sha256": "e30e87523bfe8dcf009843965a617a664a1ce802850bb07ac2ca198fa818a124", + "events": 609, + "inputs": 35, + "native_stages": 18 + }, + "complete_cost": { + "compiler": { + "H": 138100200000000, + "N": "2^138100200000000", + "eta": { + "lower": "0.000000000000021343548942378562", + "upper": "0.000000000000021343548942378563" + }, + "gap": "1/1400000000", + "integer_test_exponent": 98643, + "logarithm_power": 2100, + "theta": "63/64", + "uniform_saving": "2305761/700000000", + "word_materialized": false + }, + "derivative_upper": "-177182631537858861224422814661394713883828782835986181040446609/784637716923335095479473677900958302012794430558004314112", + "full_forward_calls": 18, + "gain": "5641/1000000000", + "kappa": "164697/50000000", + "kappa_decimal": "0.00329394", + "margin_at_previous": { + "lower": "1.771488269934881361738533375012", + "upper": "1.771488269934881361738533375013" + }, + "negative_controls": { + "coarse_tail": "The block tail bound cannot fund this near-limit claim.", + "old_BIT": "An outer inequality fails at BIT saving0.0027.", + "old_completion": "Cutoff16 and floor17 give a ratio above one." + }, + "nonrecursive": { + "local_routes": 5385000, + "local_scalar": 137866, + "paid_rank_mass": 184944, + "peak_owned_fields": 13, + "raw_budget": 1000000000, + "raw_scalar_upper": 254699248, + "scalar_growth_bound": "At most 2^(10^9 + R*f), where R is the full paid rank mass." + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + 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Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_return": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "unearned_central_target": "Every independent reverse caller coefficient", + "unpaid_native_job": "All independent fields and paid calls", + "wrong_cut_sign": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient" + }, + "dual_pair": { + "cut_after": 328, + "cut_pairing": "1", + "input_pairing": "1", + "prefix_column": "P d = S b", + "prefix_row": "a P = S c" + }, + "physical": { + "central_square_columns": 53248, + "central_translations": 17, + "full_calls": 18, + "main_targets": { + "1": 208, + "145": 104, + "16": 104, + "17": 1768, + "25": 416, + "33": 416, + "57": 416, + "73": 208 + }, + "new_paid_jobs": 0, + "ordinary_normalizations": 34, + "physical_contacts": 7488, + "ports": 104, + "route_payload_sha256": "79930ec6c09a8e4930556c925c354bb5431203eaf069d9373f056049c061289b", + "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", + "whole_idle_jobs": { + "16": 1872, + "24": 416, + "32": 416, + "56": 416 + } + }, + "reverse": { + "coefficients": 1225, + "rows": 35 + }, + "source_margin_first": { + "lower": "-0.815914776941227711468204576504", + "upper": "-0.815914776941227711468204576503" + }, + "source_margin_second": { + "lower": "-0.815914776941227711468204576504", + "upper": "-0.815914776941227711468204576503" + } + }, + "selected_frontier_changed": false, + "source_result_sha256": "35c7df5205d4e2f740af61979a2562b7ea1d9e1aef32885b9e384386e2108bdf", + "status": "PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394" +} diff --git a/research/pr6621-paid-merge-gate/evidence/pr6551-result.json b/research/pr6621-paid-merge-gate/evidence/pr6551-result.json new file mode 100644 index 0000000000..38d840ae0f --- /dev/null +++ b/research/pr6621-paid-merge-gate/evidence/pr6551-result.json @@ -0,0 +1,356 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], 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"tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", + "whole_idle_jobs": { + "16": 1768, + "24": 416, + "32": 416, + "40": 312, + "56": 208 + } + }, + "reverse": { + "coefficients": 1225, + "rows": 35 + }, + "source_margin_first": { + "lower": "-0.223153821753303547838006215777", + "upper": "-0.223153821753303547838006215776" + }, + "source_margin_second": { + "lower": "-0.223153821753303547838006215777", + "upper": "-0.223153821753303547838006215776" + } + }, + "selected_frontier_changed": false, + "source_head": "775722aa94a5e85b05d1d704d7dca10cbf016f0c", + "source_result_sha256": "13639e4770964ded237b79d72ad517448de269b34d724beaa70757dbe0be6fe2", + "status": "PASS_REBALANCED_RETIREMENT_KAPPA_00329492" +} diff --git a/research/pr6621-paid-merge-gate/evidence/pr6621-result.json b/research/pr6621-paid-merge-gate/evidence/pr6621-result.json new file mode 100644 index 0000000000..0c31219ecc --- /dev/null +++ b/research/pr6621-paid-merge-gate/evidence/pr6621-result.json @@ -0,0 +1,356 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "candidate": { + "caller": { + "coefficients": 1225, + "event_sha256": "5f0fd5f0f8fabcc568a32c60093a0496e90409e855a47a33e33d7a74c2194d47", + "events": 611, + "inputs": 35, + "native_stages": 18 + }, + "changes": { + "gain_formula": "208*(H41-H40-H57+H56)", + "paid": { + "16": -104, + "40": 312, + "56": -208 + }, + "rank_mass_change": -832, + "signed": { + "40": -208, + "41": 208, + "56": 208, + "57": -208 + }, + "targets": { + "16": -104, + "40": 104, + "41": 208, + "57": -208 + } + }, + "child_sizes": [ + 7, + 2, + 5, + 4 + ], + "complete_cost": { + "compiler": { + "H": 138100200000000, + "N": "2^138100200000000", + "eta": { + "lower": "0.000000000000020728450160865176", + "upper": "0.000000000000020728450160865177" + }, + "gap": "1/1400000000", + "integer_test_exponent": 98643, + 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+ "power": 1920, + "reserve": "1/1000000000000000000000000000", + "tail_decay": "97/100", + "tail_offset": "1/7", + "tested": "659401/200000000" + }, + "targets": { + "1": 460, + "145": 104, + "17": 1768, + "2": 144, + "25": 416, + "3": 72, + "33": 416, + "4": 1926, + "40": 104, + "41": 208, + "5": 270, + "57": 208, + "6": 54, + "7": 162, + "73": 208, + "8": 720, + "9": 6516 + }, + "thin_queries": 17, + "whole_idle_jobs": 3120 + }, + "controls": { + "extra_gaussian_credit": "All main target phases and ranks", + "missing_boundary": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_cut": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_idle": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_idle_one": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_lambda": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_local": "Every native stage exactly once", + "missing_q_power": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_query": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "missing_return": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient", + "unearned_central_target": "Every independent reverse caller coefficient", + "unpaid_native_job": "All independent fields and paid calls", + "wrong_cut_sign": "Every Q(i)[Q,D]/(Q^4-1) endpoint coefficient" + }, + "dual_pair": { + "cut_after": 328, + "cut_pairing": "1", + "input_pairing": "1", + "prefix_column": "P d = S b", + "prefix_row": "a P = S c" + }, + "internal_node_sizes": { + "2": 8, + "3": 2, + "4": 2, + "5": 1, + "7": 1 + }, + "physical": { + "central_square_columns": 53248, + "central_translations": 19, + "full_calls": 18, + "main_targets": { + "1": 208, + "145": 104, + "17": 1768, + "25": 416, + "33": 416, + "40": 104, + "41": 208, + "57": 208, + "73": 208 + }, + "new_paid_jobs": 0, + "ordinary_normalizations": 34, + "physical_contacts": 7488, + "ports": 104, + "route_payload_sha256": "79930ec6c09a8e4930556c925c354bb5431203eaf069d9373f056049c061289b", + "tensor_rule": "Factorwise native maps; scalar signs stay outside the tensor power.", + "whole_idle_jobs": { + "16": 1768, + "24": 416, + "32": 416, + "40": 312, + "56": 208 + } + }, + "reverse": { + "coefficients": 1225, + "rows": 35 + }, + "source_margin_first": { + "lower": "-0.221520283237361776197662543960", + "upper": "-0.221520283237361776197662543959" + }, + "source_margin_second": { + "lower": "-0.221520283237361776197662543960", + "upper": "-0.221520283237361776197662543959" + } + }, + "selected_frontier_changed": false, + "source_head": "775722aa94a5e85b05d1d704d7dca10cbf016f0c", + "source_result_sha256": "020728f015b8493b975a6c3d25115e00cef1c4bb62c062148f546723c509b75d", + "status": "PASS_PAID_JOB_MERGES_KAPPA_00329700" +} diff --git a/research/pr6621-paid-merge-gate/evidence/word-pr6529.json.gz b/research/pr6621-paid-merge-gate/evidence/word-pr6529.json.gz new file mode 100644 index 0000000000..91baa371a7 Binary files /dev/null and b/research/pr6621-paid-merge-gate/evidence/word-pr6529.json.gz differ diff --git a/research/pr6621-paid-merge-gate/evidence/word-pr6621.json.gz b/research/pr6621-paid-merge-gate/evidence/word-pr6621.json.gz new file mode 100644 index 0000000000..3e8f74fc90 Binary files /dev/null and b/research/pr6621-paid-merge-gate/evidence/word-pr6621.json.gz differ diff --git a/research/pr6621-paid-merge-gate/verify.py b/research/pr6621-paid-merge-gate/verify.py new file mode 100644 index 0000000000..40dd503924 --- /dev/null +++ b/research/pr6621-paid-merge-gate/verify.py @@ -0,0 +1,224 @@ +#!/usr/bin/env python3 +"""Coverage gap for the PR #6621 paid-job merge gate. + +The checker uses the vendored receipts and native words. It does not import +the candidate pricing engine or replay the word. Integer comparisons decide +the histogram identities. A mutated receipt and a mutated word are failure +controls. +""" +from collections import Counter +from fractions import Fraction +from gzip import GzipFile +from pathlib import Path +import json + +HERE = Path(__file__).resolve().parent +EVIDENCE = HERE / "evidence" +STATUS = "PASS_PR6621_MERGE_GATE_DOES_NOT_SEE_THE_MERGE" + +MERGE_PAID = {1: -54, 3: -18, 4: 18, 5: -18, 6: 18} +MERGE_TARGETS = {8: 18, 9: -18} +PER_CALL_PAID = {1: -3, 3: -1, 4: 1, 5: -1, 6: 1} +PER_CALL_TARGETS = {8: 1, 9: -1} +RETIREMENT_PAID = {16: -104, 40: 312, 56: -208} +RETIREMENT_TARGETS = {16: -104, 40: 104, 41: 208, 57: -208} +CALLS = 18 + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def load_json(name): + return json.loads((EVIDENCE / name).read_text(encoding="utf-8")) + + +def load_word(name): + with GzipFile(EVIDENCE / name) as raw: + return json.loads(raw.read().decode("utf-8")) + + +def histogram(cost, key): + return {int(rank): int(count) for rank, count in cost[key].items()} + + +def difference(after, before): + ranks = set(after) | set(before) + return {rank: after.get(rank, 0) - before.get(rank, 0) + for rank in ranks if after.get(rank, 0) != before.get(rank, 0)} + + +def scale(counts, factor): + return {rank: factor * count for rank, count in counts.items()} + + +def ordinary_raw(caller_events): + """Closed form of the ordinary-work expression in PR #6621 pricing.py.""" + return 18 * 10**7 + 17 * 1664 + 32 * 35 * 104 * caller_events + 35 * 104 * (26 + 1000) + + +def partial_sums(ranks): + ordered = sorted(ranks, reverse=True) + total = 0 + sums = [] + for rank in ordered: + total += rank + sums.append(total) + return sums + + +def assert_merge_shape(paid_delta, target_delta): + need(paid_delta == MERGE_PAID, "paid merge delta") + need(target_delta == MERGE_TARGETS, "target merge delta") + need(scale(PER_CALL_PAID, CALLS) == MERGE_PAID, "eighteen calls times the per-call paid edit") + need(scale(PER_CALL_TARGETS, CALLS) == MERGE_TARGETS, "eighteen calls times the per-call target edit") + need(sum(PER_CALL_PAID.values()) == -3, "three fewer paid jobs per call") + need(sum(rank * count for rank, count in PER_CALL_PAID.items()) == -1, "paid rank mass falls by one") + need(sum(rank * count for rank, count in PER_CALL_TARGETS.items()) == -1, "target rank mass falls by one") + + +def assert_majorization(): + """The gaining multiset is strictly majorized by the paying multiset. + + Both have sum 19. For H(r) = r^t with 0 < t < 1, strict concavity and + Karamata's inequality then give a positive signed gain. The analytic step + is the written argument in README.md; this function checks every integer + comparison that argument uses. + """ + gaining = (1, 1, 1, 3, 5, 8) + paying = (4, 6, 9) + need(sum(gaining) == sum(paying) == 19, "equal rank mass") + left, right = partial_sums(gaining), partial_sums(paying) + need(len(left) == len(right) + 3, "three extra summands on the gaining side") + # Compare the largest k parts. The paying side has three parts; pad the + # remaining prefix with the already-exhausted sum. + padded = right + [right[-1]] * (len(left) - len(right)) + need(all(a < b for a, b in zip(left[:-1], padded[:-1])), "strict partial sums") + need(left[-1] == padded[-1] == 19, "the full sums meet") + # Subadditivity bracket: 1+1+1+3 = 6, and the integral bracket is 5 against 9. + need(1 + 1 + 1 + 3 == 6, "merge preserves rank mass") + need(5 - 4 == 1 and 9 - 8 == 1, "edit C compares adjacent unit intervals") + + +def assert_gate(candidate_vs_archive, archive_vs_published_predecessor): + need(candidate_vs_archive == {"paid": RETIREMENT_PAID, "targets": RETIREMENT_TARGETS}, + "top-level gate sees only the retirement delta") + need(archive_vs_published_predecessor == {"paid": MERGE_PAID, "targets": MERGE_TARGETS}, + "archived predecessor already contains the merge") + + +def word_census(before, after): + need(before["schema"] == after["schema"] == "p104-accumulated-block-composition/2", "word schema") + stable = [key for key in before if key not in ("program", "final")] + need(all(before[key] == after[key] for key in stable), "public word fields other than program and final") + changed = [index for index, (left, right) in enumerate(zip(before["final"], after["final"])) + if left != right] + need(changed == [435], "only final[435] changes") + need((before["final"][435], after["final"][435]) == (127, 246), "helper 435 moves from frame 127 to 246") + before_ops = Counter(event[0] for event in before["program"]) + after_ops = Counter(event[0] for event in after["program"]) + delta = {name: after_ops[name] - before_ops[name] + for name in set(before_ops) | set(after_ops) + if after_ops[name] != before_ops[name]} + need(len(before["program"]) == 18493 and len(after["program"]) == 18561, "program lengths") + need(delta == {"ADD": 69, "MOVE": -3, "INIT": 1, "CLEAR": 1}, "opcode census") + need(before["owned_fields"] == after["owned_fields"] == 29, "owned-field count") + + +def expect_failure(action, label): + try: + action() + except ValueError: + return + raise ValueError("failure control accepted a bad " + label) + + +def main(): + public_old = load_json("pr6551-result.json") + public_new = load_json("pr6621-result.json") + archive_old = load_json("archive6551-retirement-result.json") + archive_new = load_json("archive6621-retirement-result.json") + need(public_old["status"] == "PASS_REBALANCED_RETIREMENT_KAPPA_00329492", "PR #6551 status") + need(public_new["status"] == "PASS_PAID_JOB_MERGES_KAPPA_00329700", "PR #6621 status") + need(archive_old["status"] == archive_new["status"] == "PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394", + "both archived predecessor receipts keep the old status") + old_cost = public_old["candidate"]["complete_cost"] + new_cost = public_new["candidate"]["complete_cost"] + old_archive = archive_old["candidate"]["complete_cost"] + new_archive = archive_new["candidate"]["complete_cost"] + + paid_delta = difference(histogram(new_cost, "paid"), histogram(old_cost, "paid")) + target_delta = difference(histogram(new_cost, "targets"), histogram(old_cost, "targets")) + assert_merge_shape(paid_delta, target_delta) + need(old_cost["paid_calls"] == 67096 and new_cost["paid_calls"] == 67042, "paid-call totals") + need(old_cost["productive_fields"] == new_cost["productive_fields"] == 13756, "productive fields") + need(old_cost["rank_mass_surplus"] == new_cost["rank_mass_surplus"] == 760, "rank-mass surplus") + need(old_cost["kappa"] == "82373/25000000" and new_cost["kappa"] == "3297/1000000", "published kappa strings") + need(public_old["candidate"]["changes"] == public_new["candidate"]["changes"], + "machine-readable changes blocks are identical") + need(public_new["candidate"]["changes"]["gain_formula"] == "208*(H41-H40-H57+H56)", + "changes block still names the retirement formula") + need(public_new["candidate"]["changes"]["paid"] == {str(k): v for k, v in RETIREMENT_PAID.items()}, + "changes paid map is the retirement delta") + retirement_mass = sum(rank * count for rank, count in RETIREMENT_TARGETS.items()) + need(retirement_mass == -832 == public_new["candidate"]["changes"]["rank_mass_change"], + "retirement target rank-mass change") + + need(old_cost["nonrecursive"]["raw_scalar_upper"] == new_cost["nonrecursive"]["raw_scalar_upper"] + == ordinary_raw(611) == 254932208, "public ordinary-work bound uses 611 caller events") + need(old_archive["nonrecursive"]["raw_scalar_upper"] == new_archive["nonrecursive"]["raw_scalar_upper"] + == ordinary_raw(609) == 254699248, "archived ordinary-work bound uses 609 caller events") + need(new_cost["nonrecursive"]["local_scalar"] - old_cost["nonrecursive"]["local_scalar"] == 648, "local scalar") + need(new_cost["nonrecursive"]["local_routes"] - old_cost["nonrecursive"]["local_routes"] == 1000, "local routes") + need(1000 == 1000 * (sum(PER_CALL_PAID.values()) + 4), + "route delta matches one extra lifetime and three fewer per-call paid jobs") + + archive_paid = difference(histogram(new_archive, "paid"), histogram(old_archive, "paid")) + archive_targets = difference(histogram(new_archive, "targets"), histogram(old_archive, "targets")) + gate_paid = difference(histogram(new_cost, "paid"), histogram(new_archive, "paid")) + gate_targets = difference(histogram(new_cost, "targets"), histogram(new_archive, "targets")) + published_gate_paid = difference(histogram(old_cost, "paid"), histogram(old_archive, "paid")) + published_gate_targets = difference(histogram(old_cost, "targets"), histogram(old_archive, "targets")) + assert_gate({"paid": gate_paid, "targets": gate_targets}, + {"paid": archive_paid, "targets": archive_targets}) + need(published_gate_paid == RETIREMENT_PAID and published_gate_targets == RETIREMENT_TARGETS, + "PR #6551 really does differ from its own archived predecessor by the retirement delta") + need(old_archive["kappa"] == new_archive["kappa"] == "164697/50000000", + "archived kappa string is unchanged") + old_root = [Fraction(item) for item in old_archive["raw_root_interval"]] + new_root = [Fraction(item) for item in new_archive["raw_root_interval"]] + need(old_root[0] <= old_root[1] < new_root[0] <= new_root[1], + "rewritten predecessor crossing moved strictly upward") + need(new_root[0] > Fraction(old_archive["kappa"]), + "rewritten predecessor crossing is above its own stated kappa") + + word_census(load_word("word-pr6529.json.gz"), load_word("word-pr6621.json.gz")) + assert_majorization() + + expect_failure(lambda: assert_merge_shape({**MERGE_PAID, 1: -53}, MERGE_TARGETS), "paid delta") + expect_failure(lambda: assert_majorization_mutated(), "majorization") + expect_failure( + lambda: assert_gate({"paid": MERGE_PAID, "targets": MERGE_TARGETS}, + {"paid": MERGE_PAID, "targets": MERGE_TARGETS}), + "compare gate") + bad_word = load_word("word-pr6621.json.gz") + bad_word["final"][435] = 127 + expect_failure(lambda: word_census(load_word("word-pr6529.json.gz"), bad_word), "final frame") + print(STATUS) + + +def assert_majorization_mutated(): + """Equal multisets have equal partial sums, so the strict inequality fails.""" + gaining = (4, 6, 9) + paying = (9, 6, 4) + left, right = partial_sums(gaining), partial_sums(paying) + width = max(len(left), len(right)) + left += [left[-1]] * (width - len(left)) + right += [right[-1]] * (width - len(right)) + need(sum(gaining) == sum(paying), "mutated sums") + need(all(a < b for a, b in zip(left[:-1], right[:-1])), "mutated partial sums") + + +if __name__ == "__main__": + main()