diff --git a/research/small-coupled-frame-optimum/.gitattributes b/research/small-coupled-frame-optimum/.gitattributes new file mode 100644 index 0000000000..21d0e37014 --- /dev/null +++ b/research/small-coupled-frame-optimum/.gitattributes @@ -0,0 +1,3 @@ +* -text whitespace=cr-at-eol +# Preserve the archived source's pre-existing extra blank EOF. +evidence/source/frozen/research/native-frame-carrying-swaps/verify.py whitespace=cr-at-eol,-blank-at-eof diff --git a/research/small-coupled-frame-optimum/BRIEF.md b/research/small-coupled-frame-optimum/BRIEF.md new file mode 100644 index 0000000000..1e243082ea --- /dev/null +++ b/research/small-coupled-frame-optimum/BRIEF.md @@ -0,0 +1,31 @@ +# Local result and stopping decision + +**Fixed power price:** at C=15108879/5000000000, exact min-sum over #4994's18 small components/68 contacts reproduces source profile `{1:2201,2:412,3:510,4:127,5:40,8:8}` in both orientations. The1,271-variable component stays at source. Every mapped multiedge and fixed-neighbor unary is retained. Full reconstruction checks all 29,790 mapped containments and includes 8 owned H8 calls. There is no native paid improvement in this restricted domain. + +The fixed-C run uses integer histograms, 119 rigorously signed rational comparisons, 24 terms and no refinement. Normal and isolated optimized semantic receipts agree. The measured first run took 2.58 seconds; the final normal replay took 2.84 seconds. No float selects a cost or assignment. + +**Separate supporting cuts:** exact integer objectives have minima C1=3298 and C2=4395, equal to source. At C3 the minimum is 5075 versus source 5080, with histogram `{1:2223,2:421,3:490,4:132,5:40,8:8}` and unchanged rank mass 5327. Its difference 22H1+9H2−20H3+5H4 is positive at the fixed power price. The proposed all-concave certificate therefore fails, and the authorized extension stops at k3. No k4–8, Pareto frontier, large-component enumeration or physical expansion was run. Normal/optimized cut receipts agree semantically. Portable-publication preparation was stopped under root's condition. + +**Source ABI:** input #4994 ef2810fe43829960789f783e44ee6484d0368f09 uses #4971's frame-carrying native-word representation, preserving the original source invoice 5327. Its frozen native word has SHA256 7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05, shared with the developed #4610 lineage. Source PROOF.md explicitly leaves new physical absolute phases and uniform implementations open. This abstract optimizer does not transfer a new frame schedule into the frozen #4610 literal compiler/caller, does not complete p16, and does not improve kappa. #5016's numerical FULL-domain MILP report is neighboring evidence rather than an exact global certificate; this result concerns only the declared 18 components and makes no global optimality claim. + +**Controls:** original/least/greatest histograms match in both orientations, all domains contain source, and original factor sums equal traceback optima. The author dropped-edge label means only a histogram mismatch, not a mutated validator rejection; CONTROL-CLARIFICATION.md records that limitation. The separate independent reviewer owns stronger private-copy mutation checks. This packet awaits that review. + +Reproduce from this worktree: + + python3 outputs/pr4994-small-frame-dp/optimize.py + python3 -I -O outputs/pr4994-small-frame-dp/optimize.py --output outputs/pr4994-small-frame-dp/OPTIMIZED.json + python3 outputs/pr4994-small-frame-dp/min_rank_cuts.py + python3 -I -O outputs/pr4994-small-frame-dp/min_rank_cuts.py --output-dir outputs/pr4994-small-frame-dp/cuts-optimized + +These commands use the authenticated project-level `outputs/mathematics-paper-research-20261023/frame-optimization` snapshot; `--source-root` can relocate it. The packet is a local result with that explicit external dependency, not a self-contained publication module. + +Frozen hashes: + +- Fixed-C manifest: `389138c4b5389d141090a9b66eba769ef0a70381b7803b248c90eef97399e72d`. +- Fixed-C optimizer: `b1536a86967312bb8c9da7b177dacd54093bea71462bbbfeffdf7325260d96bc`. +- Fixed-C result: `86fe5df320e11db12a0460f9af2d539bf659b14b7498668df3a907e26788ca87`. +- Cut extension manifest: `09844d8e7767cbc82dd576f7f74ac836fe3a0a9d0f73118171367fe8320ba4ee`. +- Cut driver: `d2fb2a56426cc94c9c9149316c93e83536a316f04bbc033603a715e3ae3e82d2`. +- Final cut summary: `c8d86ccc24d91bec4b0dd45b3df26d9e1b9fc1b19cf7d64f7f81914e811eb90a`. + +Credit: 1337isnot1337 supplies #4994's interval/realization theorem, Dugongue supplies #4971's frame-carrying swaps, and Cao Yifan/native predecessors supply the retained word. Astra supplies the source-specific bounded proposal and Dechter theorem fit. This packet supplies the scoped exact implementation and receipts only. diff --git a/research/small-coupled-frame-optimum/HANDOFF-FILES.json b/research/small-coupled-frame-optimum/HANDOFF-FILES.json new file mode 100644 index 0000000000..03a87d1cf9 --- /dev/null +++ b/research/small-coupled-frame-optimum/HANDOFF-FILES.json @@ -0,0 +1,7 @@ +{ + "BRIEF.md": "408ded6ac844b053ad7d35bf3b0515e288f6a4f8eea2389c1cda4b9452d3365b", + "CONTROL-CLARIFICATION.md": "6ccde2634f49bf55e5d88329bec4931e192517acbefb52f3f7d05384dcb0a82c", + "CUT-EXTENSION.md": "3b150ac6a491120e737d6c4442b4a61d4e12cce08b29650269198dcaca9f87e7", + "CUT-FILES.json": "09844d8e7767cbc82dd576f7f74ac836fe3a0a9d0f73118171367fe8320ba4ee", + "FIXED-C-FILES.json": "389138c4b5389d141090a9b66eba769ef0a70381b7803b248c90eef97399e72d" +} diff --git a/research/small-coupled-frame-optimum/LICENSE b/research/small-coupled-frame-optimum/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/small-coupled-frame-optimum/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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New operational packaging is Apache-2.0. The byte-exact evidence retains its original credit and notices. 1337isnot1337 supplies #4994, Dugongue supplies #4971, Cao Yifan and native predecessors supply the retained word, and Astra supplies the source-bound proposal and Dechter fit. Rina Dechter supplies the published bucket-elimination method. Parallel #5016 (numerical full-domain MILP) and #5024 (intact-source-zero-edge-region theorem) retain their distinct credit; neither is claimed as our result. The retained native LICENSE and NOTICE are unchanged. diff --git a/research/small-coupled-frame-optimum/ORIGINS.json b/research/small-coupled-frame-optimum/ORIGINS.json new file mode 100644 index 0000000000..1a3f827144 --- /dev/null +++ b/research/small-coupled-frame-optimum/ORIGINS.json @@ -0,0 +1,62 @@ +{ + "author_packet": "dyadic-full-controller-20261023/outputs/pr4994-small-frame-dp", + "independent_packet_manifest_sha256": "2a54c76896586db9cd3562652531959bd524818d6e438baed39641911073079a", + "retained_ancestor": "a59e3f991c2070287384e354e7453897a8a24e67", + "scope": "Original upstream request pins and exact same bytes retained locally; retained-copy inputs are pinned at the same package paths in the retained ancestor. 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This proves zero saving in this restricted product at this C. Four chosen contact labels change under the tie rule; the source is a minimizer, with no uniqueness claim. + +The separate integer-cut extension stops at cut 3: cuts 1/2 equal source (3298/4395), while cut 3 is **5075 versus source 5080**. Its feasible histogram `{1:2223,2:421,3:490,4:132,5:40,8:8}` differs by `22H1+9H2−20H3+5H4` and costs **+0.077586985710037469603912620755..756** at the fixed power price. Thus the proposed all-concave extension fails. **Cuts 4..8 were not run.** This is neither a global/all-price optimum nor a new physical schedule, caller or κ result. The zero-saving ceiling concerns only the native recursive rank moment at this single C and fixed restricted graph/domain. Equal profiles may have different finite routing, storage or precision costs. Other exponents, the larger component, changed ownership/interfaces and compiler routes are outside the claim; no complete-cost or physical optimality follows. + +[Independent review](evidence/REVIEW.md) explains the mathematical certificate: complete actual subspace domains, every original mapped multiedge and fixed-neighbor unary, finite infeasibility penalty 5328, exact min-sum recurrence/traceback and all 29,790 reconstructed containments. The independent checker does not import the author solver, factor builder, domain generator or price comparator. It checks 8,760 bucket alternatives across the four objectives/two orientations, all 119 strict fixed-price comparisons using a separately pinned rational interval library, and factor-deletion, nonoptimal-argmin and histogram corruption controls. It reuses the authenticated source constructor/frame-DAG; it does not independently replay native phase semantics. + +## Reproduce + +Python3.12+, standard library only. From any directory (replace the path): + +```sh +python3 -I -W error -B research/small-coupled-frame-optimum/verify.py +python3 -I -O -W error -B research/small-coupled-frame-optimum/verify.py +``` + +Each command authenticates the full retained independent packet, runs its unchanged checker, then reruns the unchanged author fixed-price and cut drivers with explicit `--source-root` and private output paths. Semantic comparisons remove only elapsed-time fields and summary receipt hashes that bind those times; underlying receipt data are compared completely. Default commands write only private temporary files, print compact summaries, require no Git/network, and never regenerate frozen results. Expected runtime is under 30 seconds per mode on this workstation. The author driver stops at k=3. Its loop and provisional all-eight status string remain visible unchanged in the archive; the stop receipt and wrapper enforce the actual completed scope. + +Registered checks: + +```sh +python3 -B scripts/research_package.py --package research/small-coupled-frame-optimum --check-only +python3 -B scripts/research_package.py --package research/small-coupled-frame-optimum +python3 -B scripts/check_research_commit.py --package research/small-coupled-frame-optimum --check-source-history +``` + +## Provenance and portability + +Base `f259dabc7d70e0db8d6d36bfda888f008bbfecc1`. Source #4994 `ef2810fe43829960789f783e44ee6484d0368f09`, retaining #4971 `0130b196145a43a7d305de41f49e56e8e8556378`. Independent interval source: `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296:research/higher-moment-strictification/verify.py`. + +The whole 57-file independent input manifest plus its own FILES.json is retained byte-for-byte in `evidence/`, including all frozen author code/results, corrections, timing receipts, source proposal, graph snapshot and original license/NOTICE. [BRIEF.md](BRIEF.md) preserves the author stopping decision, including its historical local-publication status. [ORIGINS.json](ORIGINS.json) maps the original Git requests to their exact retained bytes. SOURCES uses original upstream provenance rows plus same-path live-input pins at a retained ancestor. Both upstream heads are canonical ancestors; publication preflight checks history separately from byte integrity. The archive preserves source line endings and the native verifier's original extra blank EOF; the path-specific whitespace attribute records that exception. No AST/scientific expression rewrite or loader adaptation is needed: the existing author `--source-root` interface is used. Export byte integrity is not authenticated provenance or mathematical acceptance. + +[CONTROL-CLARIFICATION.md](evidence/frozen/CONTROL-CLARIFICATION.md) preserves the original author control limits. The independent controls are stronger and separately described in the review. No historical full suites, native phase/emitter campaign, selected cold replay, large-component enumeration, Pareto search or objectives 4..8 are part of this package. + +## Task, overlap and credit + +The claimed `complex-rank-shape-decoder` card is explicitly **changed** to a supporting exact restricted optimum/independent verification. [TASK.json](TASK.json) retains the original card. Claim/review publication coordination: [#4994 comment](https://github.com/CrocSwap/integer-mult-bounds/pull/4994#issuecomment-6358831540). + +1337isnot1337 supplies [#4994](https://github.com/CrocSwap/integer-mult-bounds/pull/4994)'s interval/realization model; Dugongue supplies [#4971](https://github.com/CrocSwap/integer-mult-bounds/pull/4971)'s frame-carrying swaps; Cao Yifan and native/controller/compiler predecessors supply the retained word. Astra supplies the authenticated source-specific proposal and its fit to Rina Dechter's published min-sum bucket-elimination theorem (1999), cited in the unchanged [PROPOSAL.md](evidence/source/PROPOSAL.md). The new contribution is the bounded exact implementation, certificates, independent reconstruction and portable verification. All source credit and Apache-2.0 notices are retained. + +[#5016](https://github.com/CrocSwap/integer-mult-bounds/pull/5016) is neighboring numerical full-domain MILP evidence, with different coverage from this exact restricted certificate. krzysztofwojt's [#5024](https://github.com/CrocSwap/integer-mult-bounds/pull/5024), head `390d7255f0e128be54e007962d7febb47697a7c5`, proves an all-price global optimum for any number of **intact source zero-edge regions** under its fixed maps/boundaries. Our per-contact small-component domain permits splitting source regions and fixes the big component. These are different restrictions; no dominance claim is made. + +## Open next questions + +A changed physical word or interface needs a source-bound complete favorable invoice before expansion. The 1,271-variable component, broader schedules and physical caller remain open; this package supplies no reason to enumerate them. See the smallest bounded follow-up in TASK.json. 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b/research/small-coupled-frame-optimum/TASK.json @@ -0,0 +1,72 @@ +{ + "actual_scope": "Portable exact verification of the fixed-C optimum on #4994's 18 small components/68 variables with 1271-variable component frozen, plus the separate cut-three counterexample to an all-concave extension.", + "ai_assistance": "Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance; retained predecessor files keep their original authorship and notices.", + "author": "Chris R / Clear1nsight with substantial OpenAI Codex assistance", + "base_commit": "f259dabc7d70e0db8d6d36bfda888f008bbfecc1", + "bottleneck_link": "Tests whether exact per-contact choices in these coupled small components remove paid Gaussian work; at the stated C the best profile equals source. This is a restricted ceiling, not caller admission.", + "budget_minutes": 60, + "evidence": "Independent evidence/REVIEW.md and REVIEW-RESULT.json; frozen author RESULT.json and cuts-normal/CUT-3.json; BRIEF.md stopping decision.", + "open_questions": [ + { + "blocked_by": "No favorable fully bound changed physical mechanism or justified expansion is supplied here.", + "first_step": "Declare a changed source-bound mechanism and its complete optimistic cost before any new search; compare the intact-region #5024 restriction separately.", + "question": "Can a justified changed paid word, helper interface or coupled domain outside this 18-component product improve a complete supplier bill?", + "why_it_matters": "The restricted optimum gives zero saving at one fixed C; it does not settle the large component or global physical caller." + } + ], + "original_card": { + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "id": "complex-rank-shape-decoder", + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ], + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ] + }, + "outcome": "negative-result", + "priority_revision": 7, + "schema_version": 1, + "scope_change_reason": "Explicit donor assignment and public #4994 review claim specialize the rank-shape card to preserving and independently reproducing the exact small-component fixed-price optimum and separate cut-three counterexample; no new decoder or expanded search is claimed.", + "scope_status": "changed", + "stop_rule": "Preserve fixed receipts; replay fixed-C and k1..3 only. 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"source/check_edge_prices.py": "319b26e9af6f616cea0a76937f17ea6ad304802f2c4349e7be614c392bb15482", + "source/frozen/research/carried-warp-frame-intervals/PROOF.md": "ebc23d843e53d5cdb940a9051eb00a756824b06a6d643afae892fcd0bcd81b30", + "source/frozen/research/carried-warp-frame-intervals/RESULT.json": "97cd018c3cb85dbab69aed61cadb0293b9740bed01ca3dcd76026bbedd89f7a5", + "source/frozen/research/carried-warp-frame-intervals/SOURCES.json": "b85a8a51a212d52233f7c1f42b38e2a6f79288d426b1a56c51afaa2ab4588c81", + "source/frozen/research/carried-warp-frame-intervals/frame_dag.py": "2f1277c6467b7219d2a0988138386c2ec5efdfbf6a5c106da6d479b0ede7abd5", + "source/frozen/research/native-frame-carrying-swaps/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "source/frozen/research/native-frame-carrying-swaps/NOTICE": "57d5bcf4f205d6d4c16eb81f37c5a1ab0c99185de26978cab99f0ce82b3147f0", + "source/frozen/research/native-frame-carrying-swaps/SOURCE-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05", + "source/frozen/research/native-frame-carrying-swaps/verify.py": "9e536497b6bf5a1162a933c1aef0ff079f1ec21996095ccfeda40252e0b7b3dd", + "source/inspect_graph.py": "63d158b84c10478ded603cb3ed18c3ac1bd6b7ba7d4998570ccd3cf55b01298b" +} diff --git a/research/small-coupled-frame-optimum/evidence/REPLAY-CHECK.json b/research/small-coupled-frame-optimum/evidence/REPLAY-CHECK.json new file mode 100644 index 0000000000..5a554002c8 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/REPLAY-CHECK.json @@ -0,0 +1,16 @@ +{ + "comparison_excludes": [ + "runtime_seconds", + "total_runtime_seconds", + "receipt_sha256 (summary only: hashes bind elapsed metadata)" + ], + "fresh_author_replays": { + "cuts_normal": "PASS_MATCH_FROZEN_K1_K2_K3_STOP", + "cuts_optimized": "PASS_MATCH_FROZEN_K1_K2_K3_STOP", + "fixed_normal": "PASS_MATCH_FROZEN_SEMANTICS", + "fixed_optimized": "PASS_MATCH_FROZEN_SEMANTICS", + "independent_normal_optimized": "PASS_BYTE_IDENTICAL" + }, + "no_author_frozen_files_written": true, + "status": "PASS" +} diff --git a/research/small-coupled-frame-optimum/evidence/REVIEW-RESULT.json b/research/small-coupled-frame-optimum/evidence/REVIEW-RESULT.json new file mode 100644 index 0000000000..64029eb56d --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/REVIEW-RESULT.json @@ -0,0 +1,259 @@ +{ + "C": "15108879/5000000000", + "all_concave_ceiling": false, + "argmin_alternatives_checked": 8760, + "author_price_imported": false, + "author_solver_imported": false, + "cuts4_to8_executed": false, + "domain_completeness": "All actual domains unique/contained/closed and Gaussian cardinality/source inclusion verified", + "independent_interval_source": { + "head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + "independent_message_states_verified": 8760, + "k3_fixed_C_paid_cost_increase": { + "lower": "0.077586985710037469603912620755", + "upper": "0.077586985710037469603912620756" + }, + "meaningful_independent_controls": { + "map_identity_wrong_containment_witness": [ + 83, + 6540 + ], + "missing_edge_inventory_rejected": true, + "missing_unary_inventory_rejected": true, + "nonoptimal_trace_choice_rejected": true, + "wrong_full_histogram_rejected": true + }, + "new_kappa": null, + "physical_emitter": false, + "results": { + "cut1_backward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut1_forward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_backward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_forward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_backward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_forward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_backward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_forward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + } + }, + "status": "PASS_FIXED_C_AND_K3_DISTINCT_RESULTS", + "strict_author_comparisons_validated": 119 +} diff --git a/research/small-coupled-frame-optimum/evidence/REVIEW.md b/research/small-coupled-frame-optimum/evidence/REVIEW.md new file mode 100644 index 0000000000..03db13d9c0 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/REVIEW.md @@ -0,0 +1,158 @@ +# Independent review: fixed-price optimum and separate cut-three witness + +**PASS within the declared restricted geometric model.** At the exact parameter +`C=15108879/5000000000`, the 18 small components have the source paid histogram +in both orientations: + + {1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}. + +The chosen minimizing assignments change four contact labels under the author's +deterministic tie rule. They have exactly the source histogram; the source +assignment is itself a minimizer. There is no paid saving in this restricted +product. This is not uniqueness of the source assignment. + +The separately authorized integer objectives give source/minimum values +`3298/3298` at k=1, `4395/4395` at k=2, and `5080/5075` at k=3 in both +orientations. The k=3 witness is feasible and has histogram + + {1:2223, 2:421, 3:490, 4:132, 5:40, 8:8}. + +Its source difference is `22H1+9H2−20H3+5H4`; its rank mass remains 5327. +The nine min-rank prefix differences are `[16,10,-5,0,0,0,0,0,0]`. +At the fixed power price it instead increases cost by the rigorously enclosed +interval + + [0.077586985710037469603912620755, + 0.077586985710037469603912620756]. + +Thus the cut-three result and fixed-price optimum are consistent. The cut witness +prevents the proposed source-optimality statement for every concave rank price. +Objectives k=4 through 8 were not executed. No common-minimizer premise, Pareto +enumeration or all-concave ceiling is used. + +## Exact inputs and independence + +The source is #4994 at `ef2810fe43829960789f783e44ee6484d0368f09`, carrying +#4971 at `0130b196145a43a7d305de41f49e56e8e8556378`. The eight frozen source +blobs are authenticated by `source/SOURCE-MANIFEST.json`; the retained source +word SHA256 is `7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05`. +The authenticated retained constructor and frame-DAG implementation supply the +source graph. This review does not independently reimplement that graph or +replay native phase semantics. + +The author's frozen fixed-price manifest is +`389138c4b5389d141090a9b66eba769ef0a70381b7803b248c90eef97399e72d`; +`optimize.py` is +`b1536a86967312bb8c9da7b177dacd54093bea71462bbbfeffdf7325260d96bc`. +The cut manifest is +`09844d8e7767cbc82dd576f7f74ac836fe3a0a9d0f73118171367fe8320ba4ee`; +`min_rank_cuts.py` is +`d2fb2a56426cc94c9c9149316c93e83536a316f04bbc033603a715e3ae3e82d2`. +All these files were copied unchanged and rechecked against the live author +directory after the audit. Their manifests remain in `frozen/`. + +The independent `check.py` imports neither the author's domain generator, +factor builder, solver nor price comparator. It reconstructs the following +items and verifies the stored optimality certificates directly. + +* It derives all variable components from the actual mapped edge list: one + component with 1271 variables and 18 with 68 variables in total. It verifies + the exact solved partition, keeps every other value at source, and checks + every prescribed boundary. +* For every stored domain it checks actual binary subspace closure, uniqueness, + interval containment, source inclusion and the full Gaussian-binomial + cardinality. These together prove that no interval subspace was omitted. + The 68 domains comprise 53 of size 2, 12 of size 5 and 3 of size 16. +* It builds factors from every original mapped multiedge incident to each small + component, including parallel edges and fixed-neighbor unaries. It evaluates + each map on every point of the candidate subspace and authenticates the exact + factor inventory. No cross-component variable factor is discarded. +* For each objective and orientation it verifies every stored separator choice + against every possible eliminated-variable value, constructs the resulting + messages independently, reverses the traceback, and checks the assignment's + cost against the original factors. Across fixed C and k=1,2,3 this verifies + 8760 bucket candidate evaluations; each objective/orientation has 1095. +* It reconstructs the full histogram, including eight owned H8 calls, and checks + all 29790 mapped containments for every resulting assignment. It also checks + the exact list of changed contacts and that the large component is unchanged. + +The finite infeasibility penalty is 5328H1. All factor costs are nonnegative; +the feasible source component cost is at most the full source rank mass 5327 +for these power and integer-cut weights. Therefore a true component minimizer +cannot contain an infeasible factor. The independent full-containment checks +also verify feasibility directly. + +## Arithmetic and recurrence + +The usual min-sum elimination recurrence is correct here: sum the factors +containing the eliminated variable, minimize over its complete finite domain +for each separator assignment, and retain an argmin. Reverse traceback recovers +a minimizing complete assignment. The independent check validates each finite +argmin inequality rather than accepting the author's printed objective value. + +The author's rational logarithm/positive-exponential tail bounds and reciprocal +endpoint ordering were inspected and are valid for ranks 1 through 9 at the +declared C. Every actually used distinct-histogram comparison has a strictly +signed enclosure. Independently, the review uses the frozen interval functions +from `20bb93cd990d2ff683e4d0fc56b87a42cd5d3296`, +`research/higher-moment-strictification/verify.py`, SHA256 +`0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326`. +Its 80-term logarithm bounds, 64-term scaled exponential bounds and outward +192-bit fixed-point rounding produce finer enclosures contained in every +author final weight interval. They independently verify all 119 strict signed +comparison certificates and all reconstructed fixed-price argmin inequalities. +Integer-cut comparisons are exact integer dot products, allowing genuine ties +between distinct histograms. + +The completed capped run does not require an algebraic non-tie theorem or a +claim that all future comparisons terminate. An unresolved comparison would +stop the author solver; none occurred in the reviewed run. + +## Replays and controls + +Fresh author fixed-price and cut-driver normal/optimized replays were run to +private review outputs with an explicit `--source-root`, preserving all author +files. They match the frozen semantic receipts after removal of elapsed-time +metadata. Summary receipt hashes necessarily change when they bind that timing +metadata; comparison still checks every underlying semantic receipt. The cut +driver stops at k=3 in both modes. `REPLAY-CHECK.json` records these comparisons. + +Independent normal and optimized runs produce byte-identical results: + + python3 -I -W error -B outputs/pr4994-small-frame-dp-independent-review/check.py + python3 -I -O -W error -B outputs/pr4994-small-frame-dp-independent-review/check.py + +The checker is read-only unless `--emit` explicitly regenerates its own +`REVIEW-RESULT.json`. All required source bytes are local. It uses only the +Python standard library and does not require Git or a network connection. + +The independent controls delete a unary factor and an edge factor from the +inventory checked by the same validation routine, substitute a strictly +nonminimizing traceback choice in the same argmin validator, and corrupt a full +histogram. Each is rejected. An actual native-map-to-identity containment +counterexample is separately recorded. These controls test specific audit +guards, not a physical native implementation. + +The author's original dropped-edge control only demonstrated a changed +histogram, and its identity-map control exhibited a violated source +containment; they were not full mutated-optimizer replays. The frozen +`CONTROL-CLARIFICATION.md` correctly states that limitation. This review does +not reinterpret the stronger-looking original JSON field names as stronger +tests. + +## Scope and credit + +This establishes a fixed-price zero-saving optimum on the declared 18-component +product with the 1271-variable component fixed at source, plus the distinct +cut-three non-generalization witness. It establishes no optimum on the large +component, intact zero-edge-region campaigns, the global contact model, changed +graphs, helpers, scalars, warps or callers. In particular, chart containment and +rank-difference costs here are the frozen #4994 geometric model; the review +does not emit new native phase-correct words or transfer them to the complete +#4610 compiler. There is no new kappa result. + +Credit remains with 1337isnot1337 for #4994, Dugongue for #4971 and the native +frame work, Cao Yifan and predecessors for the underlying source, Astra for +the authenticated graph proposal and literature fit, and the parent/author +agents for the bounded implementation and authorization. This independent +review and its checker were produced with substantial OpenAI Codex assistance. diff --git a/research/small-coupled-frame-optimum/evidence/check.py b/research/small-coupled-frame-optimum/evidence/check.py new file mode 100644 index 0000000000..a616897cd4 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/check.py @@ -0,0 +1,197 @@ +"""Independent verification of fixed-C and cut1..3 DP certificates. +No author domain/factor/Price/solver implementation is imported. No emitter. +Apache-2.0; substantial OpenAI Codex assistance. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from functools import lru_cache +from hashlib import sha256 +import importlib.util,itertools,json,sys +HERE=Path(__file__).resolve().parent +ZERO=(0,)*10;PENALTY=(0,5328)+(0,)*8;C=Q(15108879,5000000000) +def need(x,m): + if not x:raise ValueError(m) +def load(name,path): + s=importlib.util.spec_from_file_location(name,path);m=importlib.util.module_from_spec(s);sys.modules[name]=m;s.loader.exec_module(m);return m +def add(a,b):return tuple(x+y for x,y in zip(a,b)) +def delta(a,b):return tuple(x-y for x,y in zip(a,b)) +def sem(x): + if isinstance(x,dict):return {k:sem(v)for k,v in x.items()if k not in('runtime_seconds','total_runtime_seconds')} + if isinstance(x,list):return [sem(v)for v in x] + return x +@lru_cache(None) +def image(cols,S): + out=0 + while S: + bit=S&-S;x=bit.bit_length()-1;S-=bit;y=0 + for j,c in enumerate(cols): + if x>>j&1:y^=c + out|=1<>v&1 and not generated>>v&1:basis.append(v);generated=span(basis) + need(generated==S,'subspace closure');return len(basis) +def domain_check(vals,L,H,source): + d=valid_space(H)-valid_space(L);want=0 + for k in range(d+1): + n=Q(1) + for i in range(k):n*=Q((1<<(d-i))-1,(1<<(k-i))-1) + need(n.denominator==1,'Gaussian cardinality');want+=int(n) + need(len(vals)==len(set(vals))==want,'complete unique quotient domain') + for S in vals:valid_space(S);need(S&L==L and S&H==S,'domain containment') + need(source in vals,'source domain fallback') +def inventory(actual,record): + need(len(actual)==record['factor_multiedges'] and sha256(json.dumps(actual,separators=(',',':')).encode()).hexdigest()==record['edge_sha256'],'factor inventory mismatch') +def expect_bad(fn,text): + try:fn() + except ValueError as e:need(text in str(e),'intended independent rejection');return True + raise ValueError('Independent mutation accepted') + +def main(): + f=HERE/'frozen' + for n in ('FIXED-C-FILES.json','CUT-FILES.json'): + for name,h in json.loads((f/n).read_text()).items():need(sha256((f/name).read_bytes()).hexdigest()==h,'author freeze '+name) + pin=json.loads((HERE/'EXTRA-SOURCE.json').read_text());need(sha256((HERE/'interval_source.py').read_bytes()).hexdigest()==pin['sha256'],'independent interval source') + probe=load('independent_dp_source',HERE/'source/inspect_graph.py');data,construct,frame=probe.load() + E=load('independent_dp_intervals',HERE/'interval_source.py') + weights={0:(Q(0),Q(0)),1:(Q(1),Q(1))} + weights.update({r:E.power(r,1-C)for r in range(2,10)}) + def interval(h): + lo=hi=Q(0) + for r,n in enumerate(h): + a,b=weights[r];lo+=n*(a if n>=0 else b);hi+=n*(b if n>=0 else a) + need(lo<=hi,'signed enclosure order');return lo,hi + @lru_cache(None) + def fixedsign(h): + if h==ZERO:return 0 + a,b=interval(h);need(b<0 or a>0,'independent unresolved fixed-C comparison');return -1 if b<0 else 1 + fixed=json.loads((f/'RESULT.json').read_text());need(sem(fixed)==sem(json.loads((f/'OPTIMIZED.json').read_text())),'fixed normal/O semantics') + need(fixed['C']==str(C),'exact fixed C') + for r,ends in fixed['comparison']['final_weight_bounds_rational'].items(): + a,b=map(Q,ends);l,u=weights[int(r)];need(a<=l<=u<=b,'independent finer power enclosure containment') + need(len(fixed['comparison']['certificates'])==119,'119 stored strict comparisons') + for record in fixed['comparison']['certificates']: + need(fixedsign(tuple(record['difference_histogram']))==record['sign'],'independent comparison certificate') + summary=json.loads((f/'cuts-normal/SUMMARY.json').read_text());need(summary['status']=='STOP_LOWER_CUT_FOUND_NO_ALL_CONCAVE_CEILING'and set(summary['objectives'])=={'1','2','3'},'authorized stop exactly k3') + need(sem(summary)==sem(json.loads((f/'cuts-optimized/SUMMARY.json').read_text())) or + {k:v['directions']for k,v in summary['objectives'].items()}=={k:v['directions']for k,v in json.loads((f/'cuts-optimized/SUMMARY.json').read_text())['objectives'].items()},'cut summary normal/O') + cases=[('fixed',None,fixed)]+[(f'cut{k}',k,json.loads((f/f'cuts-normal/CUT-{k}.json').read_text()))for k in (1,2,3)] + controls={};output={};message_states=0;proof_checks=0;badarg_done=False;unary_done=False + for direction,sourceword in data['programs'].items(): + program,_,_=construct(sourceword);schedule=frame.NativeSchedule(data['canonical'],program);g=schedule.graph;L,H=g.bounds();original=schedule.original_values + edges=[(a,b,i,tuple(cols))for b,ps in enumerate(g.parents)for i,(a,cols)in enumerate(ps)] + need(len(edges)==29790 and all(a!=b for a,b,_,_ in edges),'all mapped edge inventory/no self factors') + variable={v for v in range(len(L))if L[v]!=H[v]};adj={v:set()for v in variable} + for a,b,_,_ in edges: + if a in variable and b in variable:adj[a].add(b);adj[b].add(a) + unseen=set(variable);derived=[] + while unseen: + todo=[unseen.pop()];component=set(todo) + while todo: + for w in adj[todo.pop()]&unseen:unseen.remove(w);component.add(w);todo.append(w) + derived.append(frozenset(component)) + need(len(derived)==19 and sorted(map(len,derived))==[1]*8+[2]*3+[3]*3+[9,10,11,15,1271],'independent components') + expected_components={x for x in derived if len(x)<1271};expected_small=set().union(*expected_components) + need(len(expected_small)==68,'independent small component scope') + def full_hist(values): + h=list(ZERO);h[8]=8 + for v,pinned in enumerate(g.fixed):need(pinned is None or values[v]==pinned,'prescribed boundary') + for a,b,ei,cols in edges: + need(image(cols,values[a])&values[b]==image(cols,values[a]),'full mapped containment') + r=dim(values[b])-dim(values[a]);need(r>=0,'full nonnegative rank') + if r:h[r]+=1 + return tuple(h) + old=full_hist(original);need(sum(r*n for r,n in enumerate(old))==5327,'source rankmass') + for label,k,result in cases: + if k: + need(sem(result)==sem(json.loads((f/f'cuts-optimized/CUT-{k}.json').read_text())),'cut normal/O semantics') + need(result['objective']['k']==k,'actual integer objective') + compare=lambda x,y: (sum(n*min(r,k)for r,n in enumerate(delta(x,y)))>0)-(sum(n*min(r,k)for r,n in enumerate(delta(x,y)))<0) + else:compare=lambda x,y:fixedsign(delta(x,y)) + rec=result['directions'][direction];D={int(v):list(map(int,vals))for v,vals in rec['all_domains'].items()};small=set(D) + need(small==expected_small and {frozenset(x['nodes'])for x in rec['components']}==expected_components and len(rec['components'])==18,'exact independent small scope/partition') + for v,vals in D.items():domain_check(vals,L[v],H[v],original[v]) + values=list(original);totalstates=0 + for component in rec['components']: + comp=set(component['nodes']);order=component['order'];need(set(order)==comp and len(order)==len(comp),'complete order') + factors=[];ids=[] + for a,b,ei,cols in edges: + if a not in comp and b not in comp:continue + scope=tuple(sorted(v for v in(a,b)if v in comp));table={} + for ix in itertools.product(*(range(len(D[v]))for v in scope)): + env={v:D[v][j]for v,j in zip(scope,ix)};av=env.get(a,original[a]);bv=env.get(b,original[b]);moved=image(cols,av) + if moved&bv==moved: + r=dim(bv)-dim(av);need(r>=0,'feasible edge rank');table[ix]=tuple(int(i==r and r>0)for i in range(10)) + else:table[ix]=PENALTY + factors.append((scope,table));ids.append([a,b,ei,list(cols)]) + inventory(ids,component) + if not unary_done: + unary=next(i for i,(scope,table)in enumerate(factors)if len(scope)==1) + controls['missing_unary_inventory_rejected']=expect_bad(lambda:inventory(ids[:unary]+ids[unary+1:],component),'factor inventory');unary_done=True + controls['missing_edge_inventory_rejected']=expect_bad(lambda:inventory(ids[1:],component),'factor inventory') + trace=component['traceback'];need(len(trace)==len(order),'trace length');active=list(factors);records=[];states=0 + for v,t in zip(order,trace,strict=True): + need(v==t[0],'trace order');bucket=[x for x in active if v in x[0]];active=[x for x in active if v not in x[0]] + sep=tuple(sorted({w for scope,tab in bucket for w in scope}-{v}));need(list(sep)==t[1],'actual separator') + choices={tuple(ix):j for ix,j in t[2]};keys=list(itertools.product(*(range(len(D[w]))for w in sep))) + need(set(choices)==set(keys),'complete separator choices');table={} + for ix in keys: + env=dict(zip(sep,ix));costs=[] + for j in range(len(D[v])): + env[v]=j;h=ZERO + for scope,tab in bucket:h=add(h,tab[tuple(env[w]for w in scope)]) + costs.append(h);states+=1 + arg=choices[ix];need(0<=arg0),None) + if bad is not None:controls['nonoptimal_trace_choice_rejected']=expect_bad(lambda:validate_choice(bad),'nonoptimal argmin');badarg_done=True + table[ix]=chosen + active.append((sep,table));records.append((v,sep,choices)) + need(all(not scope for scope,tab in active),'all variables eliminated');opt=ZERO + for scope,tab in active:opt=add(opt,tab[()]) + need(list(opt)==component['histogram'],'independent message optimum histogram') + indices={} + for v,sep,ch in reversed(records):indices[v]=ch[tuple(indices[w]for w in sep)] + need(indices=={int(v):j for v,j in component['assignment_indices'].items()},'independent reverse traceback') + direct=ZERO;source_h=ZERO + for scope,tab in factors: + direct=add(direct,tab[tuple(indices[v]for v in scope)]) + source_h=add(source_h,tab[tuple(D[v].index(original[v])for v in scope)]) + need(direct==opt and list(source_h)==component['source_histogram'],'direct factors versus messages/source') + for v,j in indices.items():values[v]=D[v][j] + need(states==component['bucket_states'],'exact bucket states');totalstates+=states + need(totalstates==1095,'all small bucket states');message_states+=totalstates + need(all(values[v]==original[v]for v in range(len(values))if v not in small),'big/determined frozen source') + need({str(v):str(values[v])for v in small}==rec['assignment'],'complete chosen assignment') + need([v for v in sorted(small)if values[v]!=original[v]]==rec['changed_nodes'],'exact changed-node census') + full=full_hist(values);need(list(full)==rec['optimal_full_histogram']and list(old)==rec['original_histogram'],'full histogram equality') + need(sum(r*n for r,n in enumerate(full))==5327,'candidate rankmass') + if not k:need(full==old,'fixed-C source histogram optimum') + output[label+'_'+direction]={'full_histogram':list(full),'prefix_differences':[sum(n*min(r,j)for r,n in enumerate(delta(full,old)))for j in range(1,10)],'changed_nodes':len(rec['changed_nodes']),'states_verified':totalstates,'all_containments':29790} + # This tests the actual containment predicate with an incorrect retained map, + # not a claim that the author reran a mutated optimization. + a,b,ei,cols=next(e for e in edges if image(e[3],original[e[0]])&original[e[1]]==image(e[3],original[e[0]])and original[e[0]]&original[e[1]]!=original[e[0]]) + controls['map_identity_wrong_containment_witness']=[a,b] + tampered=list(old);r=next(i for i,n in enumerate(old)if i and n);tampered[r]-=1 + controls['wrong_full_histogram_rejected']=expect_bad(lambda:need(tuple(tampered)==old,'full histogram mismatch'),'full histogram') + need(badarg_done and unary_done,'meaningful mutation controls reached') + expected=(0,2223,421,490,132,40,0,0,8,0) + need(all(tuple(output['cut3_'+d]['full_histogram'])==expected for d in data['programs']),'exact k3 witness') + h=delta(expected,tuple(fixed['directions']['forward']['original_histogram']));need(h==(0,22,9,-20,5,0,0,0,0,0),'k3 delta') + lo,hi=interval(h);need(lo>0,'k3 witness is worse at fixed C') + result={'status':'PASS_FIXED_C_AND_K3_DISTINCT_RESULTS','C':str(C),'independent_message_states_verified':message_states,'argmin_alternatives_checked':proof_checks,'author_solver_imported':False,'author_price_imported':False,'domain_completeness':'All actual domains unique/contained/closed and Gaussian cardinality/source inclusion verified','independent_interval_source':pin,'strict_author_comparisons_validated':119,'results':output,'meaningful_independent_controls':controls,'k3_fixed_C_paid_cost_increase':E.display((lo,hi)),'all_concave_ceiling':False,'cuts4_to8_executed':False,'physical_emitter':False,'new_kappa':None} + print(json.dumps(result,indent=2,sort_keys=True)) + if '--emit'in sys.argv:(HERE/'REVIEW-RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') +if __name__=='__main__':main() diff --git a/research/small-coupled-frame-optimum/evidence/frozen/CONTROL-CLARIFICATION.md b/research/small-coupled-frame-optimum/evidence/frozen/CONTROL-CLARIFICATION.md new file mode 100644 index 0000000000..2dcc2fd1b7 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/CONTROL-CLARIFICATION.md @@ -0,0 +1,7 @@ +# Original control labels + +The immutable fixed-C receipt's `dropped_edge_histogram_rejected` label means that deleting one known positive-rank mapped edge changes the recomputed full invoice. The implementation constructs that decremented histogram and checks inequality. It does **not** feed a mutated factor inventory into a separate validator, so the label is stronger than the control performed. REPORT.md describes the actual histogram-change check. + +Likewise the map-to-identity control exhibits an actual original edge for which the source subspaces fail containment under identity, although they pass under the retained native map. It tests that containment predicate directly rather than rerunning a mutated optimization. The bad-assignment control does run the full graph validator and requires rejection. + +The independent reviewer is adding private-copy factor/inventory mutation controls. These should be identified as independent evidence, without retroactively attributing them to the frozen author run. This clarification changes no source, optimizer, selected assignment, comparison certificate or fixed-C receipt. diff --git a/research/small-coupled-frame-optimum/evidence/frozen/CUT-EXTENSION.md b/research/small-coupled-frame-optimum/evidence/frozen/CUT-EXTENSION.md new file mode 100644 index 0000000000..247d150eab --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/CUT-EXTENSION.md @@ -0,0 +1,21 @@ +# Supporting integer cut extension: stopped at k=3 + +After the fixed-C freeze, root amended the public claim before authorizing a separate exact test of min-rank cuts C_k=sum_r n_r min(r,k), on the identical 18 components/68 contacts with the large component at source. `min_rank_cuts.py` imports the byte-pinned frozen optimizer; it substitutes exact integer cut weights for the rational power-price comparator. It changes no domain, factor, ordering, finite penalty, graph check or traceback contract. Distinct histograms can tie exactly under these integer objectives, and deterministic first-index ties remain permitted. + +Both orientations give the same results: + +| k | Source cut | Restricted minimum | +|---|---:|---:| +| 1 | 3298 | 3298 | +| 2 | 4395 | 4395 | +| 3 | 5080 | 5075 | + +The authorized stopping rule was triggered at k3. Objectives4 through8 were not executed. There was no Pareto-frontier enumeration, large-component search or physical emission. Each objective evaluated1,095 bucket states per orientation,6,570 states across the three executed objectives and two orientations. Separate normal/optimized receipts retain each objective's full domains, factors' hashes, minimizing traceback, assignment, containments and integer comparison differences. + +The k3 minimizing histogram in both orientations is + + {1:2223,2:421,3:490,4:132,5:40,8:8}, + +with source difference22H1+9H2−20H3+5H4 and unchanged rank mass5327. It is a lower k3 cut, not a lower power price at the fixed C. The earlier fixed-C optimum remains the source histogram. The k3 result prevents the proposed proof that the source minimizes every concave rank price over this restricted domain. No all-concave source ceiling is claimed, and the conditional portable-publication preparation was stopped. + +The imported optimizer's generic JSON status identifies an exact restricted optimum for its supplied objective. Each cut receipt explicitly replaces its objective metadata and comparison method with integer min-rank-cut weights and removes the power-price C field. Its `delta_interval` display is therefore an integer cut difference, not a power-moment difference. `SUMMARY.json` carries `STOP_LOWER_CUT_FOUND_NO_ALL_CONCAVE_CEILING` to make the limited conclusion explicit. diff --git a/research/small-coupled-frame-optimum/evidence/frozen/CUT-FILES.json b/research/small-coupled-frame-optimum/evidence/frozen/CUT-FILES.json new file mode 100644 index 0000000000..53ba4b8c4d --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/CUT-FILES.json @@ -0,0 +1,15 @@ +{ + "CONTROL-CLARIFICATION.md": "6ccde2634f49bf55e5d88329bec4931e192517acbefb52f3f7d05384dcb0a82c", + "CUT-EXTENSION.md": "3b150ac6a491120e737d6c4442b4a61d4e12cce08b29650269198dcaca9f87e7", + "cuts-normal.log": "c2ecb232a777b04410cba59a2e881a83c27456daeaf93197890eb2bb646ec95f", + "cuts-normal/CUT-1.json": "2257b48c1373a6e53da86bc96e06190d267fb2f47c11f8bbc14bcc7ba8acfc9e", + "cuts-normal/CUT-2.json": "ba849fdaddbf0ca8154c6e8720b8c5083f424314ffe885de8301d6e647446e96", + "cuts-normal/CUT-3.json": "1e753c481369f26506ec1d3548cb2bd88b13bddc37bcdb84739f510a19c35997", + "cuts-normal/SUMMARY.json": "c8d86ccc24d91bec4b0dd45b3df26d9e1b9fc1b19cf7d64f7f81914e811eb90a", + "cuts-optimized.log": "5fedf5218c346f89c088f93064c4292cbf9b809f6aad72ab3718e8d3709fd3ab", + "cuts-optimized/CUT-1.json": "7a34dfeb19352d83738211a0568323c56e877e0b9496f539bfd77e99192712ea", + "cuts-optimized/CUT-2.json": "86f28774de3f1ca46872cdf6a4afdda9a9095f5c500bf16eb50509b3652efc33", + "cuts-optimized/CUT-3.json": "c9c78c8b18fdfde82f78a1626a34f8e8b95f77255aaec1695d19b50736d3be53", + "cuts-optimized/SUMMARY.json": "99b4a58a1f6ef84e401df5429e9b59454b8ae2c3ab0daea4d17f1bb5cc52f3d6", + "min_rank_cuts.py": "d2fb2a56426cc94c9c9149316c93e83536a316f04bbc033603a715e3ae3e82d2" +} diff --git a/research/small-coupled-frame-optimum/evidence/frozen/FIXED-C-FILES.json b/research/small-coupled-frame-optimum/evidence/frozen/FIXED-C-FILES.json new file mode 100644 index 0000000000..4ed750c714 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/FIXED-C-FILES.json @@ -0,0 +1,8 @@ +{ + "OPTIMIZED.json": "3fb9cb2d3a926fad97892bd4c6413606b57e44f9f547cb1d8f5bd12bb391f340", + "REPORT.md": "bf3d1cd3bee25fac8245c206c8af27b51ad8ec2ad83642e6f961d8ea5f573f40", + "RESULT.json": "86fe5df320e11db12a0460f9af2d539bf659b14b7498668df3a907e26788ca87", + "normal.log": "451d0d48bbbfe09542250610a7b14b6b70d7e7222a3b95d2261c24604d19f504", + "optimize.py": "b1536a86967312bb8c9da7b177dacd54093bea71462bbbfeffdf7325260d96bc", + "optimized.log": "a5490c57ef829b9d39761e0ad38cc0a90aecb3291b0ce828157f7b7f08be98cd" +} diff --git a/research/small-coupled-frame-optimum/evidence/frozen/OPTIMIZED.json b/research/small-coupled-frame-optimum/evidence/frozen/OPTIMIZED.json new file mode 100644 index 0000000000..6dfcc4ccdf --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/OPTIMIZED.json @@ -0,0 +1,11565 @@ +{ + "C": "15108879/5000000000", + "comparison": { + "certificates": [ + { + "difference_histogram": [ + 0, + 2, + 2, + -2, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "interval_decimal": [ + "0.011516160830993310915788590061", + "0.011516160830993310915788595844" + ], + "series_terms": 24, + "sign": 1 + }, + { + "difference_histogram": [ + 0, + -5327, + 2, + -2, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "interval_decimal": [ + "-5328.988483839169006689084211409939", + "-5328.988483839169006689084211404156" + ], + "series_terms": 24, + "sign": -1 + }, + { + "difference_histogram": [ + 0, + 3, + 3, + -3, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "interval_decimal": [ + "0.017274241246489966373682885092", + "0.017274241246489966373682893766" + ], + "series_terms": 24, + "sign": 1 + }, + { + "difference_histogram": [ + 0, + 3, + 2, + -1, + -1, + 0, + 0, + 0, + 0, + 0 + ], + "interval_decimal": [ + "0.018294629017508745210459862303", + "0.018294629017508745210459870972" + ], + "series_terms": 24, + "sign": 1 + }, + { + "difference_histogram": [ + 0, + -10658, + 0, + 0, + 0, + 0, + 0, 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b/research/small-coupled-frame-optimum/evidence/frozen/REPORT.md @@ -0,0 +1,57 @@ +# Exact restricted small-component optimum at the fixed power price + +The 18 small components in both source orientations have the **same optimal paid histogram as the source**, at the exact parameter C=15108879/5000000000=0.0030217758. The optimum is + + {1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}. + +Its histogram difference from the source is identically zero. There is no favorable native paid delta in this restricted domain, so this result does not justify a physical expansion. It does not optimize the 1,271-variable large component or any changed contact, scalar, warp, helper or caller contract. + +## Source and domain + +The input is 1337isnot1337's #4994 at ef2810fe43829960789f783e44ee6484d0368f09, retaining Dugongue's #4971 at 0130b196145a43a7d305de41f49e56e8e8556378. Astra's authenticated eight-blob SOURCE-MANIFEST and inspect_graph.py loader are reused, with their hashes recorded in RESULT.json. The loader executes only the retained swap constructor and loads the frozen frame-DAG code. This is an independent optimizer implementation using that source graph, not an independent reimplementation of the source graph or physical native semantics. + +#4994 PROOF.md, “Binding the graph to the native word,” identifies its input as #4971's frame-carrying representation of Cao Yifan's native round-three source. Its SOURCES.json has base #4971 and pins SOURCE-WORD.json.gz SHA256 7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05, the retained native source used in the #4610 stream. The original histogram above reproduces that source's invoice, including eight owned rank8 calls. The graph representation and potential new frame realizations are successor contracts. Equal or improved local prices do not by themselves transfer the literal #4610 phase implementation, complete p16 caller, finite compiler reserve, rounding or outer theorem. No such transfer is claimed here. + +For each small variable v the domain is every actual binary subspace S satisfying L_v<=S<=H_v. The implementation selects a complement of L_v in H_v, lists all quotient vectors and closes the set of possible subspaces under adjoining each quotient vector. Every quotient subspace is spanned by such vectors, so this procedure is complete. Actual subspaces are represented by 512-bit pointset integers, deduplicated and sorted. It checks binary closure, interval containment, complete Gaussian-binomial cardinality and source inclusion. The 68 domains are exactly 53 of size2,12 of size5 and3 of size16. The stored domain lists and chosen indices are in RESULT.json. + +All 1,271 large-component variables and every determined contact remain at their original source subspaces. The 18 small components are derived from the variable graph; their node sets are compared with the frozen source-specific elimination ordering. No factor connects a small component to another variable component. Fixed neighbors become unary factors and remain in the objective. All parallel mapped edges are retained separately. + +## Factors, recurrence and traceback + +For every original mapped edge a→b with map G, its factor is H_(dim(S_b)−dim(S_a)) when G(S_a)<=S_b and is 5328 H1 otherwise. H0=0 and Hr=r^(1−C). This includes all internal multiedges and every fixed-neighbor unary. Edges with neither endpoint in the solved component are a constant and are excluded only from that component's minimization. Full reconstruction prices every one of the 29,790 mapped edges and adds the eight owned H8 calls. + +The finite penalty is genuine: it is stored as 5328 units of H1, not discarded or silently converted to infinity. Every factor is nonnegative. The source provides a feasible component assignment whose cost is at most its rank mass, at most5327. Hence a minimizing component cannot pay even one infeasibility penalty. Full graph containment is independently checked after traceback rather than inferred from the objective. + +At variable v, collect all factors whose scope contains v, sum them, and minimize over the complete domain of v for each assignment of the union scope minus v. Store both the resulting separator factor and the first minimizing domain index. Subsequent buckets operate on those exact factors. Reversing the elimination order reconstructs each v from its stored separator assignment. The original factor sum at the reconstructed assignment is checked equal to the bucket optimum. The source assignment's original factor cost is evaluated separately in every component and must be no smaller than the optimum. Equal histograms use the first sorted domain index, so ties are deterministic. Distinct unresolved histograms never use a source preference or floating-point tiebreak. + +The fixed order visits 1,095 bucket assignments per orientation; its largest bucket has125 assignments. These are measured enumeration counts, separate from elapsed time. Both orientations select four contact changes under the equal-histogram tie rule. The source assignment itself is also optimal; these changes produce no improvement. + +## Certified arithmetic + +Costs remain integer histograms throughout summation and elimination. For a signed difference d, its interval uses d_r*lower(Hr) on a nonnegative coefficient and d_r*upper(Hr) on a negative coefficient for the lower endpoint; the upper endpoint reverses these choices. + +The weights use rational series bounds. Write r=2^k u with1<=u<2. For x=2 or u put z=(x−1)/(x+1), so0<=z<=1/3. With n terms, + + A=2 sum_(j=0)^(n−1) z^(2j+1)/(2j+1), + A <= ln(x) <= A+2 z^(2n+1)/((2n+1)(1−z²)). + +Combine these bounds to bound ln(r). For positive y=C ln(r), bound exp(y) by the degree-n positive Taylor sum. The first omitted term is t_n*y/(n+1), and successive tail ratios are at most y/(n+2); therefore dividing that first term by1−y/(n+2) is an upper tail bound. Reciprocal bounds then enclose Hr=r/exp(C ln(r)). H1=1 and H0=0 are exact. + +Start with24 terms. Each distinct histogram comparison must have a strictly signed rational enclosure; otherwise double the term count through at most384 and STOP on an unresolved distinct histogram. The executed runs required119 distinct comparisons,24 terms and zero refinements. The receipt retains each signed histogram difference, sign, series length and outward decimal interval, together with exact rational final weight endpoints. These decimals are display certificates derived by integer floor/ceiling; they never select an optimum. No floating-point number is used in the cost arithmetic. Runtime metadata alone uses a clock. + +## Replays and controls + +Run from this worktree: + + python3 outputs/pr4994-small-frame-dp/optimize.py + python3 -I -O outputs/pr4994-small-frame-dp/optimize.py --output outputs/pr4994-small-frame-dp/OPTIMIZED.json + +The default source path is the project-level outputs/mathematics-paper-research-20261023/frame-optimization snapshot. An explicit --source-root can replace its location; the loader still authenticates all eight frozen source hashes. No source file is written. The only generated artifact is the requested output JSON. The normal and optimized semantic receipts agree after removing elapsed-time fields. Logs retain measured runtimes. + +Both orientations reproduce all original/least/greatest profiles, making six exact source-profile controls. Additional controls reject an actual out-of-interval full-space contact assignment by the full graph checker; detect the histogram change from removing a paid mapped edge; and exhibit an actual mapped edge where replacing its native map with identity violates the source containment. The source fallback, complete domain census, original-factor traceback equality, all29,790 final containments and fixed large-component assignment are checked in both normal and optimized runs. The implementation uses explicit checks rather than Python assert, so optimized mode retains them. + +The later independent review must audit these domains, factors, arithmetic bounds and traceback before this packet is treated as independently verified. No phase, physical emitter, arbitrary-input native replay, compiler or kappa campaign is included. Any extension to other price objectives requires its own authorization; this fixed-C result alone is not an all-concave optimality theorem. + +## Credit and open boundary + +1337isnot1337 supplies #4994's sharp intervals and realization contract; Dugongue supplies #4971's weighted frame-carrying swaps; Cao Yifan and the native/helper lineage supply the underlying source. Astra supplies the published bucket-elimination fit and bounded source-specific proposal. Rina Dechter's 1999 min-sum bucket elimination theorem supplies the general recurrence. This packet implements and executes only the declared18-component restricted optimization. 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"total_runtime_seconds": 2.541147 +} diff --git a/research/small-coupled-frame-optimum/evidence/frozen/cuts-optimized/SUMMARY.json b/research/small-coupled-frame-optimum/evidence/frozen/cuts-optimized/SUMMARY.json new file mode 100644 index 0000000000..25f122bc83 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/cuts-optimized/SUMMARY.json @@ -0,0 +1,142 @@ +{ + "fixed_c_script_sha256": "b1536a86967312bb8c9da7b177dacd54093bea71462bbbfeffdf7325260d96bc", + "objectives": { + "1": { + "directions": { + "backward": { + "bucket_states": 1095, + "changed_nodes": [ + 10249, + 10261, + 10272, + 10273, + 10282, + 12388 + ], + "minimum": 3298, + "source": 3298 + }, + "forward": { + "bucket_states": 1095, + "changed_nodes": [ + 10249, + 10261, + 10272, + 10273, + 10282, + 12388 + ], + "minimum": 3298, + "source": 3298 + } + }, + "receipt_sha256": "7a34dfeb19352d83738211a0568323c56e877e0b9496f539bfd77e99192712ea" + }, + "2": { + "directions": { + "backward": { + "bucket_states": 1095, + "changed_nodes": [ + 9773, + 9811, + 9821, + 9840, + 10261, + 10272, + 10273, + 11481, + 12146, + 12158, + 12388 + ], + "minimum": 4395, + "source": 4395 + }, + "forward": { + "bucket_states": 1095, + "changed_nodes": [ + 9773, + 9811, + 9821, + 9840, + 10261, + 10272, + 10273, + 11481, + 12146, + 12158, + 12388 + ], + "minimum": 4395, + "source": 4395 + } + }, + "receipt_sha256": "86f28774de3f1ca46872cdf6a4afdda9a9095f5c500bf16eb50509b3652efc33" + }, + "3": { + "directions": { + "backward": { + "bucket_states": 1095, + "changed_nodes": [ + 9773, + 9798, + 9811, + 9821, + 9840, + 9899, + 10248, + 10261, + 10272, + 10273, + 10282, + 10353, + 10354, + 10377, + 10378, + 10706, + 11368, + 11369, + 11481, + 12146, + 12158, + 12388 + ], + "minimum": 5075, + "source": 5080 + }, + "forward": { + "bucket_states": 1095, + "changed_nodes": [ + 9773, + 9798, + 9811, + 9821, + 9840, + 9899, + 10248, + 10261, + 10272, + 10273, + 10282, + 10353, + 10354, + 10377, + 10378, + 10706, + 11368, + 11369, + 11481, + 12146, + 12158, + 12388 + ], + "minimum": 5075, + "source": 5080 + } + }, + "receipt_sha256": "c9c78c8b18fdfde82f78a1626a34f8e8b95f77255aaec1695d19b50736d3be53" + } + }, + "scope": "Same18smallcomponents/68variables; large1271at source; no Pareto search", + "status": "STOP_LOWER_CUT_FOUND_NO_ALL_CONCAVE_CEILING" +} diff --git a/research/small-coupled-frame-optimum/evidence/frozen/min_rank_cuts.py b/research/small-coupled-frame-optimum/evidence/frozen/min_rank_cuts.py new file mode 100644 index 0000000000..2e18c41b20 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/min_rank_cuts.py @@ -0,0 +1,61 @@ +#!/usr/bin/env python3 +"""Separately authorized exact integer cut objectives on the frozen DP.""" +import argparse +import hashlib +import importlib.util +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE=Path(__file__).resolve().parent +FROZEN='b1536a86967312bb8c9da7b177dacd54093bea71462bbbfeffdf7325260d96bc' + +def main(): + p=argparse.ArgumentParser();p.add_argument('--source-root',type=Path) + p.add_argument('--output-dir',type=Path,default=HERE/'cuts-normal');args=p.parse_args() + need=HERE/'optimize.py' + if hashlib.sha256(need.read_bytes()).hexdigest()!=FROZEN:raise ValueError('Frozen fixed-C implementation changed') + spec=importlib.util.spec_from_file_location('frozen_small_frame_dp',need) + dp=importlib.util.module_from_spec(spec);spec.loader.exec_module(dp) + args.output_dir.mkdir(exist_ok=True) + summary={'status':'PASS_ALL_EIGHT_SOURCE_CUT_MINIMA','scope':'Same18smallcomponents/68variables; large1271at source; no Pareto search','objectives':{},'fixed_c_script_sha256':FROZEN} + for k in range(1,9): + class IntegerPrice: + def __init__(self): + self.n=0;self.refinements=0;self.comparisons=0;self.certificates=[];self.cache={} + def prepare(self):self.bounds={r:(Q(min(r,k)),Q(min(r,k)))for r in range(10)} + def interval(self,h): + x=Q(sum(n*min(r,k)for r,n in enumerate(h))) + return x,x + def compare(self,a,b): + if a==b:return 0 + diff=dp.sub(a,b) + if diff in self.cache:return self.cache[diff] + self.comparisons+=1;x=self.interval(diff)[0];s=(x>0)-(x<0) + self.cache[diff]=s;self.cache[tuple(-v for v in diff)]=-s + self.certificates.append({'difference_histogram':list(diff),'integer_difference':int(x),'sign':s}) + return s + dp.Price=IntegerPrice + output=args.output_dir/f'CUT-{k}.json' + sys.argv=[str(need),'--output',str(output)] + if args.source_root:sys.argv+=['--source-root',str(args.source_root)] + dp.main() + result=json.loads(output.read_text()) + result['objective']={'name':'min_rank_cut','k':k,'exact_integer_weights':[min(r,k)for r in range(10)]} + result.pop('C');result['driver_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest() + result['comparison']['method']='Exact integer min-rank-cut weighted histogram comparison; distinct histograms may tie exactly' + rows={} + for d,entry in result['directions'].items(): + old=sum(n*min(r,k)for r,n in enumerate(entry['original_histogram'])) + new=sum(n*min(r,k)for r,n in enumerate(entry['optimal_full_histogram'])) + rows[d]={'source':old,'minimum':new,'changed_nodes':entry['changed_nodes'],'bucket_states':entry['bucket_states']} + if newold:raise ValueError('Source fallback failed') + output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + summary['objectives'][str(k)]={'directions':rows,'receipt_sha256':hashlib.sha256(output.read_bytes()).hexdigest()} + print(json.dumps({'cut':k,'directions':rows,'status':summary['status']}),flush=True) + if summary['status']!='PASS_ALL_EIGHT_SOURCE_CUT_MINIMA':break + (args.output_dir/'SUMMARY.json').write_text(json.dumps(summary,indent=2,sort_keys=True)+'\n') + +if __name__=='__main__':main() diff --git a/research/small-coupled-frame-optimum/evidence/frozen/normal.log b/research/small-coupled-frame-optimum/evidence/frozen/normal.log new file mode 100644 index 0000000000..6fdef5a5c4 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/normal.log @@ -0,0 +1,3 @@ +{"direction": "backward", "bucket_states": 1095, "changed": 4, "histogram": [0, 2201, 412, 510, 127, 40, 0, 0, 8, 0], "delta": ["0.000000000000000000000000000000", "0.000000000000000000000000000000"], "seconds": 1.4063} +{"direction": "forward", "bucket_states": 1095, "changed": 4, "histogram": [0, 2201, 412, 510, 127, 40, 0, 0, 8, 0], "delta": ["0.000000000000000000000000000000", "0.000000000000000000000000000000"], "seconds": 1.263874} +{"status": "PASS_EXACT_RESTRICTED_OPTIMUM", "total_seconds": 2.835547, "comparisons": 119, "refinements": 0} diff --git a/research/small-coupled-frame-optimum/evidence/frozen/optimize.py b/research/small-coupled-frame-optimum/evidence/frozen/optimize.py new file mode 100644 index 0000000000..27abd784d7 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/optimize.py @@ -0,0 +1,233 @@ +#!/usr/bin/env python3 +"""Exact restricted frame-domain min-sum; no physical emitter or large search.""" +import argparse +import hashlib +import importlib.util +import itertools +import json +import time +from collections import Counter +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +DEFAULT = HERE.parents[2] / 'outputs/mathematics-paper-research-20261023/frame-optimization' +C = Q(15108879, 5000000000) +ZERO = (0,) * 10 +PENALTY = (0, 5328) + (0,) * 8 + +def need(x, message): + if not x: raise ValueError(message) + +def add(a,b): return tuple(x+y for x,y in zip(a,b)) +def sub(a,b): return tuple(x-y for x,y in zip(a,b)) +def singleton(r): return tuple(int(i==r and r>0) for i in range(10)) + +def log_bounds(r, n): + # ln(r)=k ln(2)+ln(r/2^k); each atanh argument is in [0,1/3]. + def series(x): + z=(x-1)/(x+1) + total=sum((z**(2*j+1)/Q(2*j+1) for j in range(n)), Q(0))*2 + tail=2*z**(2*n+1)/(Q(2*n+1)*(1-z*z)) + return total,total+tail + k=r.bit_length()-1 + a,b=series(Q(2));d,e=series(Q(r,2**k)) + return k*a+d,k*b+e + +def exp_bounds(x,n): + # Positive x<1. Tail ratios after n are bounded by x/(n+2). + term=Q(1);total=term + for j in range(1,n+1): + term*=x/j;total+=term + first=term*x/(n+1) + return total,total+first/(1-x/Q(n+2)) + +class Price: + def __init__(self): + self.n=24;self.cache={};self.bounds={};self.refinements=0;self.comparisons=0;self.certificates=[] + def prepare(self): + self.bounds={0:(Q(0),Q(0)),1:(Q(1),Q(1))} + for r in range(2,10): + lo,hi=log_bounds(r,self.n) + elo,_=exp_bounds(C*lo,self.n) + _,ehi=exp_bounds(C*hi,self.n) + self.bounds[r]=(Q(r)/ehi,Q(r)/elo) + def interval(self,h): + lo=hi=Q(0) + for r,a in enumerate(h): + l,u=self.bounds[r] + lo+=a*(l if a>=0 else u);hi+=a*(u if a>=0 else l) + return lo,hi + def compare(self,a,b): + if a==b:return 0 + d=sub(a,b) + if d in self.cache:return self.cache[d] + self.comparisons+=1 + while True: + lo,hi=self.interval(d) + if hi<0: sign=-1;break + if lo>0: sign=1;break + self.n*=2;self.refinements+=1 + need(self.n<=384,'STOP_UNRESOLVED_DISTINCT_HISTOGRAM') + self.prepare() + self.cache[d]=sign;self.cache[tuple(-x for x in d)]=-sign + self.certificates.append({'difference_histogram':list(d),'sign':sign, + 'series_terms':self.n,'interval_decimal':decimal_bounds((lo,hi))}) + return sign + +def decimal_bounds(pair,digits=30): + scale=10**digits + lo,hi=pair + def show(n): + sign='-' if n<0 else '';n=abs(n) + return sign+str(n//scale)+'.'+str(n%scale).zfill(digits) + return [show(lo.numerator*scale//lo.denominator), + show(-((-hi.numerator*scale)//hi.denominator))] + +def domain(frame,lo,hi): + # Select an independent complement of lo inside hi. Enumerate the ENTIRE + # quotient subspace lattice by repeated adjoining of each quotient vector. + comp=[];span=lo + for v in frame.basis(hi): + if not (span>>v)&1: + comp.append(v);span=frame.join(span,frame.space([v])) + need(span==hi,'Complement spans upper') + qspace=frame.space(comp) + vectors=[v for v in range(1,512) if (qspace>>v)&1] + vals={lo} + for v in vectors: + vals|={frame.join(s,frame.space([v])) for s in tuple(vals)} + result=sorted(vals) + need(all(s&lo==lo and s&hi==s for s in result),'Domain interval') + need(all(frame.space(frame.basis(s))==s for s in result),'Actual subspace closure') + expect={0:1,1:2,2:5,3:16}[len(comp)] + need(len(result)==expect,'Complete quotient cardinality') + return result + +def histogram(frame,graph,values): + graph.check(values) + h=list(ZERO);h[8]=8 + for b,parents in enumerate(graph.parents): + for a,g in parents: + need(frame.image(g,values[a])&values[b]==frame.image(g,values[a]),'Mapped containment') + r=frame.dimension(values[b])-frame.dimension(values[a]) + need(r>=0,'Ascending rank') + if r:h[r]+=1 + return tuple(h) + +def solve_component(order,domains,factors,price): + factors=list(factors);records=[];states=0;largest=0 + for v in order: + bucket=[f for f in factors if v in f[0]] + factors=[f for f in factors if v not in f[0]] + need(bucket,'Nonempty variable bucket') + scope=tuple(sorted({w for s,t in bucket for w in s}));sep=tuple(w for w in scope if w!=v) + table={};choice={} + for indices in itertools.product(*(range(len(domains[w])) for w in sep)): + env=dict(zip(sep,indices));best=None;arg=None + for j in range(len(domains[v])): + env[v]=j;value=ZERO;states+=1 + for s,t in bucket:value=add(value,t[tuple(env[w] for w in s)]) + if best is None or price.compare(value,best)<0:best,arg=value,j + table[indices]=best;choice[indices]=arg + largest=max(largest,len(table)*len(domains[v])) + factors.append((sep,table));records.append((v,sep,choice)) + need(all(not s for s,t in factors),'Elimination complete') + optimum=ZERO + for s,t in factors:optimum=add(optimum,t[()]) + assignment={} + for v,sep,choices in reversed(records):assignment[v]=choices[tuple(assignment[w]for w in sep)] + return optimum,assignment,states,largest,records + +def main(): + parser=argparse.ArgumentParser();parser.add_argument('--source-root',type=Path,default=DEFAULT) + parser.add_argument('--output',type=Path,default=HERE/'RESULT.json');args=parser.parse_args() + start=time.monotonic();src=args.source_root.resolve() + spec=importlib.util.spec_from_file_location('authenticated_frame_probe',src/'inspect_graph.py') + probe=importlib.util.module_from_spec(spec);spec.loader.exec_module(probe) + data,construct,frame=probe.load() + frozen=json.loads((src/'GRAPH-STRUCTURE.json').read_text()) + published=json.loads((probe.FROZEN/'research/carried-warp-frame-intervals/RESULT.json').read_text()) + price=Price();price.prepare();result={'status':'PASS_EXACT_RESTRICTED_OPTIMUM','C':str(C),'directions':{},'physical_emitter':False,'new_kappa':None} + for direction,source in data['programs'].items(): + tick=time.monotonic();program,swaps,unequal=construct(source) + need((swaps,unequal)==(534,43),'Frozen constructor census') + schedule=frame.NativeSchedule(data['canonical'],program);graph=schedule.graph + lower,upper=graph.bounds();original=schedule.original_values + need(len(graph.fixed)==15935 and sum(map(len,graph.parents))==29790,'Complete graph census') + need(Counter(e[-1]for e in program if e[0]=='center')=={8:8},'Owned centres constant') + variable={v for v in range(len(lower))if lower[v]!=upper[v]} + adjacency={v:set()for v in variable} + for b in variable: + for a,g in graph.parents[b]: + if a in variable:adjacency[a].add(b);adjacency[b].add(a) + comps=probe.components(adjacency);need(len(comps)==19 and len(comps[0])==1271,'Components') + small=set.union(*comps[1:]);need(len(small)==68,'Small variable scope') + domains={v:domain(frame,lower[v],upper[v])for v in sorted(small)} + need(Counter(map(len,domains.values()))=={2:53,5:12,16:3},'Domain census') + need(all(original[v]in domains[v]for v in small),'Source fallback inclusion') + controls={} + for name,values in [('original_contacts',original),('least',lower),('greatest',upper)]: + h=histogram(frame,graph,values) + expected={int(k):v for k,v in published['directions'][direction]['schedules'][name]['paid'].items()} + need({r:n for r,n in enumerate(h)if n}==expected,'Known profile '+name) + controls[name]=list(h) + values=list(original);comp_results=[];total_states=0 + for ci,comp in enumerate(comps[1:],1): + order=frozen['directions'][direction]['elimination_components'][ci]['ordering'] + need(set(order)==comp,'Frozen order exact component') + factors=[];edge_ids=[] + for b,parents in enumerate(graph.parents): + for ei,(a,g)in enumerate(parents): + if a not in comp and b not in comp:continue + scope=tuple(sorted(v for v in (a,b)if v in comp)) + need(not ((a in variable and a not in comp)or(b in variable and b not in comp)),'No omitted variable neighbor') + table={} + for ix in itertools.product(*(range(len(domains[v]))for v in scope)): + env={v:domains[v][j]for v,j in zip(scope,ix)} + av=env.get(a,original[a]);bv=env.get(b,original[b]) + moved=frame.image(g,av) + table[ix]=singleton(frame.dimension(bv)-frame.dimension(av))if moved&bv==moved else PENALTY + factors.append((scope,table));edge_ids.append([a,b,ei,list(g)]) + optimum,assignment,states,largest,trace=solve_component(order,domains,factors,price) + direct=ZERO + for scope,table in factors:direct=add(direct,table[tuple(assignment[v]for v in scope)]) + need(direct==optimum,'Traceback original factor objective') + source_h=ZERO + for scope,table in factors:source_h=add(source_h,table[tuple(domains[v].index(original[v])for v in scope)]) + need(price.compare(optimum,source_h)<=0,'Source fallback cost') + for v,j in assignment.items():values[v]=domains[v][j] + total_states+=states + comp_results.append({'nodes':sorted(comp),'order':order,'factor_multiedges':len(factors),'edge_sha256':hashlib.sha256(json.dumps(edge_ids,separators=(',',':')).encode()).hexdigest(),'bucket_states':states,'largest_bucket_states':largest,'histogram':list(optimum),'source_histogram':list(source_h),'domain_sizes':{str(v):len(domains[v])for v in sorted(comp)},'assignment_indices':assignment,'traceback':[[v,list(sep),[[list(k),j]for k,j in sorted(ch.items())]]for v,sep,ch in trace]}) + need(total_states==1095,'Measured bucket states match declared domain') + need(all(values[v]==original[v]for v in range(len(values))if v not in small),'Large and determined contacts untouched') + full=histogram(frame,graph,values);old=histogram(frame,graph,original) + delta=sub(full,old);cmp=price.compare(full,old) + # Three source-bound semantic rejection controls. + bad=list(values);v=next(v for v in small if upper[v]!=graph.full);bad[v]=graph.full + try:graph.check(bad) + except ValueError:bad_rejected=True + else:bad_rejected=False + need(bad_rejected,'Out-of-interval/fixed-neighbor mutation rejected') + positive_edge=next((a,b,g)for b,ps in enumerate(graph.parents)for a,g in ps if frame.dimension(original[b])>frame.dimension(original[a])) + a,b,g=positive_edge;dropped=list(old);dropped[frame.dimension(original[b])-frame.dimension(original[a])]-=1 + need(tuple(dropped)!=old,'Dropped multiplicity changes full invoice') + map_witness=None + for b,ps in enumerate(graph.parents): + for a,g in ps: + if g!=graph.identity and original[a]&original[b]!=original[a]:map_witness=[a,b];break + if map_witness:break + need(map_witness is not None,'Actual map-to-identity containment failure control') + result['directions'][direction]={'small_variables':68,'large_variables_held_source':1271,'mapped_edges_checked':29790,'components':comp_results,'all_domains':{str(v):list(map(str,domains[v]))for v in sorted(small)},'assignment':{str(v):str(values[v])for v in sorted(small)},'changed_nodes':[v for v in sorted(small)if values[v]!=original[v]],'original_histogram':list(old),'optimal_full_histogram':list(full),'delta_histogram':list(delta),'delta_interval_rational':list(map(str,price.interval(delta))),'delta_interval_decimal':decimal_bounds(price.interval(delta)),'strict_improvement':cmp<0,'six_profile_controls_this_direction':controls,'semantic_controls':{'bad_assignment_rejected':bad_rejected,'dropped_edge_histogram_rejected':True,'map_to_identity_containment_rejected_at':map_witness},'bucket_states':total_states,'runtime_seconds':round(time.monotonic()-tick,6)} + print(json.dumps({'direction':direction,'bucket_states':total_states,'changed':len(result['directions'][direction]['changed_nodes']),'histogram':full,'delta':result['directions'][direction]['delta_interval_decimal'],'seconds':result['directions'][direction]['runtime_seconds']}),flush=True) + result['comparison']={'log_and_exp_terms':price.n,'refinements':price.refinements,'distinct_comparisons':price.comparisons,'method':'exact rational atanh log and positive exp Taylor bounds; signed histogram coefficients enclosed outward', + 'final_weight_bounds_rational':{str(r):list(map(str,b))for r,b in price.bounds.items()}, + 'certificates':price.certificates} + result['source_manifest']=json.loads((src/'SOURCE-MANIFEST.json').read_text()) + result['loader_sha256']=hashlib.sha256((src/'inspect_graph.py').read_bytes()).hexdigest() + result['script_sha256']=hashlib.sha256(Path(__file__).read_bytes()).hexdigest() + result['total_runtime_seconds']=round(time.monotonic()-start,6) + args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'total_seconds':result['total_runtime_seconds'],'comparisons':price.comparisons,'refinements':price.refinements})) + +if __name__=='__main__':main() diff --git a/research/small-coupled-frame-optimum/evidence/frozen/optimized.log b/research/small-coupled-frame-optimum/evidence/frozen/optimized.log new file mode 100644 index 0000000000..15c56a39cc --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/frozen/optimized.log @@ -0,0 +1,3 @@ +{"direction": "backward", "bucket_states": 1095, "changed": 4, "histogram": [0, 2201, 412, 510, 127, 40, 0, 0, 8, 0], "delta": ["0.000000000000000000000000000000", "0.000000000000000000000000000000"], "seconds": 1.352627} +{"direction": "forward", "bucket_states": 1095, "changed": 4, "histogram": [0, 2201, 412, 510, 127, 40, 0, 0, 8, 0], "delta": ["0.000000000000000000000000000000", "0.000000000000000000000000000000"], "seconds": 1.182672} +{"status": "PASS_EXACT_RESTRICTED_OPTIMUM", "total_seconds": 2.751234, "comparisons": 119, "refinements": 0} diff --git a/research/small-coupled-frame-optimum/evidence/independent-normal.json b/research/small-coupled-frame-optimum/evidence/independent-normal.json new file mode 100644 index 0000000000..64029eb56d --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/independent-normal.json @@ -0,0 +1,259 @@ +{ + "C": "15108879/5000000000", + "all_concave_ceiling": false, + "argmin_alternatives_checked": 8760, + "author_price_imported": false, + "author_solver_imported": false, + "cuts4_to8_executed": false, + "domain_completeness": "All actual domains unique/contained/closed and Gaussian cardinality/source inclusion verified", + "independent_interval_source": { + "head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + "independent_message_states_verified": 8760, + "k3_fixed_C_paid_cost_increase": { + "lower": "0.077586985710037469603912620755", + "upper": "0.077586985710037469603912620756" + }, + "meaningful_independent_controls": { + "map_identity_wrong_containment_witness": [ + 83, + 6540 + ], + "missing_edge_inventory_rejected": true, + "missing_unary_inventory_rejected": true, + "nonoptimal_trace_choice_rejected": true, + "wrong_full_histogram_rejected": true + }, + "new_kappa": null, + "physical_emitter": false, + "results": { + "cut1_backward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut1_forward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_backward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_forward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_backward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_forward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_backward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_forward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + } + }, + "status": "PASS_FIXED_C_AND_K3_DISTINCT_RESULTS", + "strict_author_comparisons_validated": 119 +} diff --git a/research/small-coupled-frame-optimum/evidence/independent-optimized.json b/research/small-coupled-frame-optimum/evidence/independent-optimized.json new file mode 100644 index 0000000000..64029eb56d --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/independent-optimized.json @@ -0,0 +1,259 @@ +{ + "C": "15108879/5000000000", + "all_concave_ceiling": false, + "argmin_alternatives_checked": 8760, + "author_price_imported": false, + "author_solver_imported": false, + "cuts4_to8_executed": false, + "domain_completeness": "All actual domains unique/contained/closed and Gaussian cardinality/source inclusion verified", + "independent_interval_source": { + "head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296", + "path": "research/higher-moment-strictification/verify.py", + "sha256": "0ce7e7137422d5ffeda22085c81fa88471bbe963100fdad62e659f1e3bf89326" + }, + "independent_message_states_verified": 8760, + "k3_fixed_C_paid_cost_increase": { + "lower": "0.077586985710037469603912620755", + "upper": "0.077586985710037469603912620756" + }, + "meaningful_independent_controls": { + "map_identity_wrong_containment_witness": [ + 83, + 6540 + ], + "missing_edge_inventory_rejected": true, + "missing_unary_inventory_rejected": true, + "nonoptimal_trace_choice_rejected": true, + "wrong_full_histogram_rejected": true + }, + "new_kappa": null, + "physical_emitter": false, + "results": { + "cut1_backward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut1_forward": { + "all_containments": 29790, + "changed_nodes": 6, + "full_histogram": [ + 0, + 2198, + 418, + 507, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_backward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut2_forward": { + "all_containments": 29790, + "changed_nodes": 11, + "full_histogram": [ + 0, + 2213, + 406, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 6, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_backward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "cut3_forward": { + "all_containments": 29790, + "changed_nodes": 22, + "full_histogram": [ + 0, + 2223, + 421, + 490, + 132, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 16, + 10, + -5, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_backward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + }, + "fixed_forward": { + "all_containments": 29790, + "changed_nodes": 4, + "full_histogram": [ + 0, + 2201, + 412, + 510, + 127, + 40, + 0, + 0, + 8, + 0 + ], + "prefix_differences": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "states_verified": 1095 + } + }, + "status": "PASS_FIXED_C_AND_K3_DISTINCT_RESULTS", + "strict_author_comparisons_validated": 119 +} diff --git a/research/small-coupled-frame-optimum/evidence/interval_source.py b/research/small-coupled-frame-optimum/evidence/interval_source.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/interval_source.py @@ -0,0 +1,421 @@ +#!/usr/bin/env python3 +"""Higher-moment strictification and a polynomial-logarithm compiler bound. + +New arithmetic is independent of predecessor interval code. The unchanged +invoice replay and two outer ledgers are credited, byte-pinned oracles. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import ast +from collections import Counter +from contextlib import redirect_stdout +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256, sha1 +import io +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 2**192 +C = Q('0.00268648') +KAPPA = Q('0.00268647') +T = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} +P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + +def source_environment(path): + env = {'__file__': str(path), '__name__': 'pinned_source_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +def authenticate(): + result = {} + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + path = HERE/'vendor'/Path(row['path']).relative_to( + 'research/higher-moment-strictification/vendor') + digest = sha256(path.read_bytes()).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + raw = path.read_bytes() + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def invoice_oracle(): + """Run #4426 unchanged, rebinding only its two file-location globals.""" + path = HERE/'vendor/invoice-review/verify.py' + env = source_environment(path) + env.update(ROOT=path.parent, PHASES='DATA-PHASES.json') + output = io.StringIO() + with redirect_stdout(output): + env['main']() + result = json.loads(output.getvalue()) + need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle') + need({int(k): v for k, v in result['targets'].items()} == T + and {int(k): v for k, v in result['paid'].items()} == P, + 'exact literal-word invoice') + return result + + +def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)): + t = 1-C + need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks') + need(t+u >= 1, 'tail moment exponent at least one') + target, paid = moment(T, t), moment(P, t) + alpha = divide(paid, target) + gamma = divide(moment(P, t+u), mul(power(cutoff, u), target)) + delta = divide((Q(sum(T.values())*floor),)*2, + mul(power(cutoff, C), target)) + limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500)) + for name, bounds, limit in zip(('alpha', 'gamma', 'delta'), + (alpha, gamma, delta), limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit') + a, g, d = limits + bound = 1/(1+v*(1-a))+2*g**v+2*d**v + need(bound < 1, 'complete charged normalized moment') + old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2, + mul(power(cutoff, C), target)) + old_lower = alpha[0]**v+2*old_gamma[0]**v + need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power') + return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor, + 'paid_moment_exponent': t+u, 'tail_offset_u': u, + 'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma), + 'delta': display(delta), 'rational_upper_limits': limits, + 'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2), + 'old_rank_one_gamma': display(old_gamma), + 'old_rank_one_bound_lower': display((old_lower, old_lower)), + 'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v), + 'maximum_paid': str(cutoff)+'^'+str(v), + 'productive_fields_before_uniform_compiler': '7688^'+str(v), + 'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v), + 'materialized_product_or_uniform_word': False} + + +def uniform_rank(v): + t, p, theta = 1-C, 13, Q(6, 7) + gap = (C-KAPPA)/7 + uniform_saving = C-gap + need(10**7 < 15**6, 'theta upper bound') + need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality') + eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t) + need(eta[0] > theta**p, 'exit contraction below complement capacity') + base = exp_interval(scale(log_bounds(121), v*C)) + need(base[1] < 2**p, 'entire ordinary base range fits') + # Integer grid: gap*H is integral, avoiding enormous rational powers. + step = gap.denominator + need(gap.numerator == 1, 'chosen rational gap grid') + + def passes(j): + H = step*j + return (H+1)**p < 2**j + + lo, hi = 1, 2 + while not passes(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (lo+hi)//2 + if passes(mid): + hi = mid + else: + lo = mid + H = step*hi + need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison') + need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails') + return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap, + 'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta), + 'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)), + 'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H), + 'integer_test': {'left_base': H+1, 'left_exponent': p, + 'right_base': 2, 'right_exponent': hi}, + 'grid_step': step, 'previous_grid_point_rejected': True, + 'smaller_logarithmic_power_rejected': True} + + +def power_majorant_comparison(v, uniform_saving): + """Retain #4416's older power proof, changing only the new unit's ranks.""" + t, z, h = 1-C, 1-uniform_saving, Q(1, 7) + z0 = (t+z)/2 + delta = z0-t + B, debt = (4+7*h)*v, 1+7*v*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold') + need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), + 'strict power-majorant comparison and previous-rank control') + return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h, + 'scope': 'Tail transformation alone, retaining the older power majorant.'} + + +def outer_ledger(uniform_saving): + d = (C-KAPPA)/7 + params = {'kappa': KAPPA, 'tested_saving': C, + 'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d, + 'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + env = source_environment(HERE/'vendor/outer_endpoint.py') + row = env['ledger'](params) + need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3, + 'complete first outer ledger') + need(all(v > 0 for group in ('strict_checks', 'functional_checks') + for v in row[group].values()), 'all outer predicates') + frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer'] + need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger') + parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes()) + function = next(n for n in parsed.body + if isinstance(n, ast.FunctionDef) and n.name == 'ledger') + constants = [n for n in parsed.body if isinstance(n, ast.Assign) + and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_') + for t in n.targets)] + eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a')) + grid = 10**10 + backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA + need(backoff > 0, 'strict derived oracle grid backoff') + oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8), + 'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff, + 'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2), + 'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16), + 'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'], + 'online': Q('0.001730970419199163702738'), + 'old': Q('0.001730970419199163702738')} + code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[])) + exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle) + second = oracle['ledger']('higher_moment_smaller_ranks') + need(second['kappa'] == KAPPA and second['margins'] == row['margins'], + 'all nine rows match both ledgers') + need(len(second['strict_checks']) == 63 and + all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates') + controls = {} + for name, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': C}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + bad = env['ledger'](dict(params, **updates)) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'outer control rejected: '+name) + controls[name] = failed + for name, options in [('old_per_axis_scan', {'old_scan': True}), + ('group_equals_dimension', {'beta_': eps})]: + bad = oracle['ledger']('reject_'+name, **options) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'legacy control rejected: '+name) + controls[name] = failed + return {'ledger': row, 'legacy_63_checks': second['strict_checks'], + 'legacy_grid': grid, 'legacy_backoff': backoff, + 'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA, + 'rejected_controls': controls} + + +def finite_controls(): + def tensor(histogram): + out = Counter() + for k, n in histogram.items(): + for h, b in histogram.items(): + out[k*h] += n*b + return out + + def split(histogram, cutoff): + out = Counter() + for k, n in histogram.items(): + q, r = divmod(k, cutoff) + out[cutoff] += q*n + if r: + out[r] += n + return +out + + target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1}) + padded, completion = Counter(), Counter() + for k, n in target.items(): + padded[max(k, 9)] += n + if k < 9: + completion[9-k] += n + final = split(paid+completion, 4) + mass = lambda x: sum(k*n for k, n in x.items()) + need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass') + need(min(padded) > max(final), 'exact toy separation') + need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory') + # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension. + invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1] + need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting') + return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13, + 'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2', + 'sigma': '3/4', 'actual_charge': 100, + 'invalid_upper': display((invalid, invalid))}} + + +def verify(): + sources = authenticate() + invoice = invoice_oracle() + tail = tail_certificate() + rank = uniform_rank(tail['tensor_power']) + endpoint = outer_ledger(rank['uniform_saving']) + controls = finite_controls() + rejected = [] + for name, updates, expected in [ + ('too_short_product', {'v': 100}, 'complete charged normalized moment'), + ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'), + ('lost_separation', {'floor': 10}, 'strict finite ranks'), + ]: + try: + tail_certificate(**updates) + except ValueError as error: + need(str(error) == expected, 'wrong rejection: '+name) + rejected.append({'mutation': name, 'failed_at': str(error)}) + else: + raise ValueError('accepted mutation: '+name) + old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler'] + return encoded({'schema': 'higher-moment-native-strictification/1', + 'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA, + 'invoice_oracle': invoice, 'strictification': tail, + 'uniform_rank': rank, 'outer': endpoint, + 'tail_only_power_majorant': power_majorant_comparison( + tail['tensor_power'], rank['uniform_saving']), + 'finite_controls': controls, 'rejected_mutations': rejected, + 'predecessor_H': old['H1'], + 'rank_exponent_reduction_factor': Q(old['H1'], rank['H']), + 'tensor_power_reduction_factor': Q(6240, tail['tensor_power']), + 'source_sha256': sources, + 'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = verify() + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'], + 'uniform_rank': result['uniform_rank']['N'], + 'strict_moment_gap': result['strictification']['strict_moment_gap'], + 'kappa': result['kappa']})) + + +if __name__ == '__main__': + main() diff --git a/research/small-coupled-frame-optimum/evidence/replays/author-cuts-normal.log b/research/small-coupled-frame-optimum/evidence/replays/author-cuts-normal.log new file mode 100644 index 0000000000..eb353ee2e2 --- /dev/null +++ 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a/research/small-coupled-frame-optimum/evidence/source/PROPOSAL.md b/research/small-coupled-frame-optimum/evidence/source/PROPOSAL.md new file mode 100644 index 0000000000..d1ca86fca1 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/source/PROPOSAL.md @@ -0,0 +1,89 @@ +# Bounded exact optimization of the 18 small frame components + +Prepared 2026-10-23 with OpenAI Codex assistance. **Status: proposal only; optimization and candidate emission are held for the team leader's live ownership and independent-review gate.** The 1,271-variable component will not be enumerated. + +## Source and published theorem + +The exact source is #4994 head `ef2810fe43829960789f783e44ee6484d0368f09`, package `research/carried-warp-frame-intervals`, retaining #4971 at `0130b196145a43a7d305de41f49e56e8e8556378`. `SOURCE-MANIFEST.json` pins the eight Git-tree snapshots actually used. `inspect_graph.py` reuses only the source's authenticated swap constructor (AST-extracted function, no module-level native replay) and its frame-DAG implementation. This probe is not an independent verification of those source routines or physical phases. + +Rina Dechter, **Bucket elimination: A unifying framework for reasoning**, *Artificial Intelligence* 113(1–2), 41–85 (1999), DOI [10.1016/S0004-3702(99)00059-4](https://doi.org/10.1016/S0004-3702(99)00059-4). Publisher metadata and the [author's published PDF](https://ics.uci.edu/~dechter/publications/r76A.pdf) were inspected through the web reader. Section 8, Fig.25 and Theorem 11, journal pp.71–72, give min-sum variable elimination for finite-domain cost networks, with an exact optimum recoverable by stored minimizing choices. Cost factors must be evaluated and compared correctly; complexity is exponential in the induced width after prescribed variables are substituted. The paper does not justify dropping constraints, substituting dimension-only domains, floating-point optimality or physical frame admission. + +## Exact mathematical reduction + +For every contact v, retain its complete domain + + D_v = { U <= F2^9 : L_v <= U <= H_v }. + +The lattice interval is isomorphic to the full subspace lattice of H_v/L_v. Its cardinality is the sum of the Gaussian binomial coefficients for d=dim(H_v)-dim(L_v): for d=0,1,2,3,4,5 the counts are 1,2,5,16,67,374. A domain contains actual subspaces, including every orientation; it is not the integer interval of dimensions and is not limited to the old frame registry. + +For each original mapped multiedge e:a→b with its exact invertible binary map G_e, use the binary factor + + phi_e(U_a,U_b) = H_(dim(U_b)-dim(U_a)) if G_e(U_a) <= U_b, + M=5328 otherwise, + H_r = r^(1-C), H_0 = 0. + +The finite penalty makes the model meet Dechter's finite nonnegative cost hypothesis directly. For 0= 0, "Ascending edge rank") + if rank: + profile[rank] += 1 + else: + zero_edges += 1 + expected = Counter({int(k):v for k,v in published["directions"][direction]["schedules"][name]["paid"].items()}) + need(profile == expected, "Mapped-edge price differs from literal published price: " + name) + records[name] = {"paid":dict(sorted(profile.items())), "rank_mass":sum(r*n for r,n in profile.items()), + "zero_rank_edges":zero_edges, "counted_multiedges":sum(map(len,graph.parents))} + result["directions"][direction] = {"source_owned_centres":dict(centers), + "duplicate_operand_contacts":len(duplicated_operand_contacts), "profiles":records} + (HERE / "EDGE-PRICE-CHECK.json").write_text(json.dumps(result,indent=2)+"\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/small-coupled-frame-optimum/evidence/source/frozen/research/carried-warp-frame-intervals/PROOF.md b/research/small-coupled-frame-optimum/evidence/source/frozen/research/carried-warp-frame-intervals/PROOF.md new file mode 100644 index 0000000000..84a1a9213e --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/source/frozen/research/carried-warp-frame-intervals/PROOF.md @@ -0,0 +1,135 @@ +# Sharp marginal frame intervals and the extremal price test + +This is a written proof about the binary frame contract defined below. The +finite exact replays supplement it. No formal proof kernel, physical phase +admission or multiplication theorem is claimed. Prepared by 1337isnot1337 with +substantial OpenAI Codex assistance; Apache-2.0. + +## The graph and the quantified statement + +Let V be F₂^h for any finite positive h. Let D be a finite directed acyclic +multigraph whose vertices are topologically numbered. Each edge e:a→b carries +an invertible linear map G_e:V→V. A specified subset of vertices has prescribed +subspaces F_v. A feasible assignment consists of subspaces U_v≤V such that + + U_v = F_v at each prescribed vertex; + G_e(U_a) ≤ U_b for every edge e:a→b. + +Assume at least one feasible assignment exists. Define L in topological order: + + L_v = F_v at prescribed vertices; + L_v = sum_{e:a→v} G_e(L_a) otherwise. + +The empty sum is the zero subspace. Define H in reverse topological order: + + H_v = F_v at prescribed vertices; + H_v = intersection_{e:v→b} G_e^(-1)(H_b) otherwise. + +The empty intersection is V. Then: + +1. L and H are feasible, and every feasible U satisfies L_v≤U_v≤H_v. +2. For each single vertex v and each subspace S with L_v≤S≤H_v, there + exists a feasible assignment U with U_v=S. It is constructed by adding + the prescription U_v=S and recomputing the lower propagation. + +This is a standard order propagation argument applied to this caller. Choices +at different vertices remain coupled by the edges. The statement concerns +one prescribed marginal at a time, over all subspaces, not a registry search. + +## Proof of the bounds + +Compare against any feasible U. Forward induction gives L_v≤U_v: this is +immediate at prescribed vertices, and a sum of images of contained subspaces +is contained in U_v at an unprescribed vertex. Backward induction gives U_v≤H_v, +using inverse images and intersections. Thus L_v≤H_v. + +For an edge a→b, if b is unprescribed its recurrence contains G_e(L_a). +If b is prescribed, the existence of a feasible U gives +G_e(L_a)≤G_e(U_a)≤F_b=L_b. Hence L is feasible. For H, an unprescribed a +satisfies G_e(H_a)≤H_b by definition. At a prescribed a, use feasibility and +the already established backward bound to get G_e(F_a)≤H_b. Thus H is feasible. +The implementation checks these prescribed-vertex compatibility conditions +explicitly and rejects empty intervals. + +## Proof of complete marginal attainability + +Fix v and S between L_v and H_v. Keep L unchanged before v, prescribe S at v, +and propagate sums of images forward. Incoming edges at v remain valid because +their images are contained in L_v≤S. + +At each later vertex w, the extra contribution from S is the sum of G_path(S) +over paths from v to w whose internal vertices are unprescribed. This follows +inductively because linear isomorphisms preserve sums of subspaces. At the first +prescribed endpoint w on any such path, the reverse recurrence gives +H_v≤G_path^(-1)(F_w). Consequently G_path(S)≤F_w. The original lower contribution +was also contained in F_w, so prescribing F_w causes no conflict. That vertex +resets the downstream contribution to its fixed F_w. This proves compatibility +at every prescribed vertex and constructs the required feasible assignment. + +## Binding the graph to the native word + +The input is the exact frame-carrying program constructed by Dugongue's PR4971 +at head 0130b196145a43a7d305de41f49e56e8e8556378. It retains Cao Yifan's native +round-three source and the credited native/helper lineage. + +Each live field holds a pointer (v,A), meaning that its current frame, before +any next paid climb, is A(U_v). Initially v is its prescribed entrance and A=I. +A weighted whole-field swap exchanges the pointers. A native warp of signed +operator k changes A to G_k A, using the inverse map for negative k. + +A scalar contact between live fields creates one vertex u and an edge +(v,u,A) for each operand. Both pointers then become (u,I). A scalar SCALE +commutes with the frame and creates no constraint. A scalar contact with the +owned cell retains its supplied frame as a prescribed vertex. Every live +terminal frame is prescribed. Owned-center events and all scalar coefficients +are retained. The graph is acyclic because every new contact is later in the +word than the pointers feeding it. + +Every feasible graph assignment has a sufficient chronological realization: +before a contact u, climb each operand from A(U_v) to U_u. The edge constraint +makes this an ascending nested climb. At a warp carry the actual frame by G_k; +at a weighted swap carry it with the exchanged field. Restore each prescribed +terminal frame by its final edge. This realizes exactly the binary contract. + +Conversely, any schedule in this contract with the same scalar contacts, swaps, +warp maps and fixed boundaries defines such a graph assignment. Between two +contacts, invertible maps preserve containment, so any ascending climbs can be +deferred through the intervening warps to the next contact. The composed map +on that edge therefore sends the earlier contact frame into the later one. +This is the precise schedule class to which the sharp bounds apply. + +These statements concern subspaces and normalized linear actions. They do not +prove that every new canonical frame transition has the required physical +absolute phase or uniform implementation. The separate replay checks all +632 independent-input normalized rows, actual G-image warp conditions, frame +chronology, paid ranks and owned-cell clearing for each emitted candidate. + +## Paid rank and the two extremal profiles + +The sum of the dimensions of the 632 live frames changes only at paid climbs. +Swaps permute its terms and the invertible warp maps preserve each dimension. +Consequently every ascending realization with these fixed entrances and exits +has the same total live paid rank. The eight retained rank-eight owned-center +jobs add a fixed 64. The complete source and each realized schedule have total +paid rank 5,327. + +For a paid profile n_r, define C_k(n)=sum_r n_r min(r,k). For any concave rank +price f on {0,...,9} with f(0)=0, put d_j=f(j)-f(j-1). Direct summation gives + + f(r) = r d_9 + sum_{k=1}^8 min(r,k) (d_k-d_(k+1)). + +Every curvature coefficient d_k-d_(k+1) is nonnegative. Equal total rank cancels +the linear term when comparing profiles. Therefore C_k(source)≤C_k(candidate) +for every k implies that the source price is no greater for every such f. +A positive cut difference yields strict inequality for every strictly concave f, +including f(r)=r^t for 0> vector & 1 and not generated >> vector & 1: + result.append(vector) + generated = space(result) + need(generated == subspace, "Not a binary subspace") + return tuple(result) + + +def dimension(subspace): + return subspace.bit_count().bit_length() - 1 + + +@lru_cache(None) +def join(left, right): + if left & right == left: + return right + if left & right == right: + return left + return space(basis(left) + basis(right)) + + +def linear(columns, vector): + result = 0 + for bit, column in enumerate(columns): + if vector >> bit & 1: + result ^= column + return result + + +@lru_cache(None) +def compose(left, right): + return tuple(linear(left, column) for column in right) + + +@lru_cache(None) +def inverse(columns): + size = 1 << len(columns) + need(all(type(x) is int and 0 <= x < size for x in columns), "Binary map range") + values = [linear(columns, x) for x in range(size)] + need(len(set(values)) == size, "Singular binary map") + back = [0] * size + for source, target in enumerate(values): + back[target] = source + return tuple(back[1 << bit] for bit in range(len(columns))) + + +@lru_cache(None) +def image(columns, subspace): + return space(tuple(linear(columns, vector) for vector in basis(subspace))) + + +class FrameDAG: + """Edges (a,b,G) impose G(U_a) <= U_b, with a < b and G invertible.""" + + def __init__(self, h): + need(type(h) is int and 1 <= h <= 9, "Ambient dimension between one and nine") + self.h = h + self.identity = tuple(1 << bit for bit in range(h)) + self.full = (1 << (1 << h)) - 1 + self.fixed = [] + self.parents = [] + self.children = [] + + def node(self, fixed=None): + if fixed is not None: + basis(fixed) + need(fixed & self.full == fixed, "Frame outside ambient space") + index = len(self.fixed) + self.fixed.append(fixed) + self.parents.append([]) + self.children.append([]) + return index + + def edge(self, source, target, columns=None): + columns = self.identity if columns is None else tuple(columns) + need(0 <= source < target < len(self.fixed), "Edges require topological order") + need(len(columns) == self.h, "Map dimension") + inverse(columns) + self.parents[target].append((source, columns)) + self.children[source].append((target, columns)) + + def bounds(self, extra=None): + fixed = self.fixed[:] + for node, subspace in (extra or {}).items(): + need(type(node) is int and 0 <= node < len(fixed), "Unknown pinned node") + basis(subspace) + need(subspace & self.full == subspace, "Pinned frame outside ambient space") + need(fixed[node] is None or fixed[node] == subspace, "Changed fixed node") + fixed[node] = subspace + lower = [] + for node, value in enumerate(fixed): + bound = 1 + for parent, columns in self.parents[node]: + bound = join(bound, image(columns, lower[parent])) + if value is not None: + need(bound & value == bound, "Infeasible lower bound") + bound = value + lower.append(bound) + upper = [None] * len(fixed) + for node in reversed(range(len(fixed))): + bound = self.full + for child, columns in self.children[node]: + bound &= image(inverse(columns), upper[child]) + if fixed[node] is not None: + need(fixed[node] & bound == fixed[node], "Infeasible upper bound") + bound = fixed[node] + need(lower[node] & bound == lower[node], "Empty frame interval") + upper[node] = bound + self.check(lower, fixed) + self.check(upper, fixed) + return lower, upper + + def check(self, values, fixed=None): + fixed = self.fixed if fixed is None else fixed + need(len(values) == len(fixed), "Node inventory") + for node, value in enumerate(values): + basis(value) + need(value & self.full == value, "Node outside ambient space") + need(fixed[node] is None or fixed[node] == value, "Fixed node mismatch") + for parent, columns in self.parents[node]: + moved = image(columns, values[parent]) + need(moved & value == moved, "Mapped containment failed") + + def extend(self, node, subspace): + return self.bounds({node: subspace})[0] + + +class NativeSchedule: + """Remove paid climbs; carry each demand pointer through swaps and warps. + + Owned-cell contacts retain their supplied frames. All main/helper entrances + and exits remain fixed. Scalar coefficients and normalized words stay fixed. + """ + + def __init__(self, canonical, program): + self.canonical = canonical + need(canonical["h"] == 9, "Retained nine-bit caller") + self.spaces = list(map(space, canonical["frames"])) + self.maps = {} + for warp in canonical["warps"]: + op, columns = warp["op"], tuple(warp["G_columns"]) + need(type(op) is int and op > 0 and op not in self.maps, "Warp IDs") + self.maps[op], self.maps[-op] = columns, inverse(columns) + self.program = [deepcopy(event) for event in program if event[0] != "climb"] + graph = self.graph = FrameDAG(9) + self.contacts = {} + values = [] + + def node(label=None): + value = None if label is None else self.spaces[label] + result = graph.node(value) + values.append(value) + return result + + current = [(node(label), graph.identity) for label in canonical["start"]] + for index, event in enumerate(self.program): + if event[0] == "weighted_swap": + left, right = event[1:3] + current[left], current[right] = current[right], current[left] + elif event[0] == "warp": + _, role, op, _, _ = event + need(role[0] == "L" and op in self.maps, "Known live warp") + parent, columns = current[role[1]] + current[role[1]] = parent, compose(self.maps[op], columns) + elif event[0] == "scalar": + gate, label = event[1:] + roles = gate[1:3] if gate[0] in ("add", "copy") else gate[1:2] + live = [role[1] for role in roles if role[0] == "L"] + if not live or gate[0] == "scale": + continue + contact = node(label if len(live) < len(roles) else None) + values[contact] = self.spaces[label] + for role in live: + parent, columns = current[role] + graph.edge(parent, contact, columns) + current[role] = contact, graph.identity + self.contacts[index] = contact + for role, label in enumerate(canonical["final"]): + final = node(label) + parent, columns = current[role] + graph.edge(parent, final, columns) + graph.check(values) + self.original_values = values + + def realize(self, values): + self.graph.check(values) + canonical = deepcopy(self.canonical) + frames = list(self.spaces) + labels = {subspace: label for label, subspace in enumerate(frames)} + current = [frames[label] for label in canonical["start"]] + result = [] + + def label(subspace): + if subspace not in labels: + labels[subspace] = len(frames) + frames.append(subspace) + canonical["frames"].append(list(basis(subspace))) + return labels[subspace] + + def climb(role, target): + old = current[role] + if old != target: + need(old & target == old, "Non-nested realized climb") + result.append(["climb", "carried", role, label(old), label(target), + dimension(target) - dimension(old)]) + current[role] = target + + for index, original in enumerate(self.program): + event = deepcopy(original) + if event[0] == "weighted_swap": + left, right = event[1:3] + event[5] = [label(current[left]), label(current[right])] + current[left], current[right] = current[right], current[left] + event[6] = [label(current[left]), label(current[right])] + elif event[0] == "warp": + role, op = event[1][1], event[2] + old = current[role] + current[role] = image(self.maps[op], old) + event[3:] = [label(old), label(current[role])] + elif event[0] == "scalar": + gate = event[1] + roles = gate[1:3] if gate[0] in ("add", "copy") else gate[1:2] + live = [role[1] for role in roles if role[0] == "L"] + if live: + target = current[live[0]] if gate[0] == "scale" else values[self.contacts[index]] + for role in live: + climb(role, target) + event[2] = label(target) + result.append(event) + for role, final in enumerate(canonical["final"]): + climb(role, frames[final]) + return canonical, result diff --git a/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/LICENSE b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/NOTICE b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/NOTICE new file mode 100644 index 0000000000..faa0f8ce7f --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/NOTICE @@ -0,0 +1,7 @@ +Cao Yifan / intqwq: authenticated joint-helper/native-map round-three word, canonical research/kappa-round3-warp-20261022, commit 624de9dc66858af0945e5f8a0942488d62280d43; PR4610 lineage. +Cinna Davis: PR4694 center-free/cache kernel and arbitrary-input raw dual, PR4698 cold-helper basis/conditional consumer; PR4440/4441/4447/4470 lineage. +Dugongue: present ground-chart helper pre-compensation and explicit invertible coded offer, with substantial OpenAI Codex assistance. +Retains native, E8, scalar, Clifford, compiler, precision, outer and contributor notices in the cited upstream sources; zxv, Jacob Alan Sussman, DaysSky, Nick Petalas and Ryanson Jonathan retain predecessor credit. +Apache-2.0. No independent human or formal proof-kernel review is claimed. + +Rohan Arun: PR1931 involutive source reflection and source-restored shear; Ali Romman: PR1862 broader source-code/repair family. Current 632-owner port and dyadic completion prepared by Dugongue with substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/SOURCE-WORD.json.gz b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/SOURCE-WORD.json.gz new file mode 100644 index 0000000000..46d929df83 Binary files /dev/null and b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/SOURCE-WORD.json.gz differ diff --git a/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/verify.py b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/verify.py new file mode 100644 index 0000000000..88aa08b7d5 --- /dev/null +++ b/research/small-coupled-frame-optimum/evidence/source/frozen/research/native-frame-carrying-swaps/verify.py @@ -0,0 +1,95 @@ +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import sys,json,gzip,hashlib,copy +P=Path(__file__).resolve().parent +S=P +if hashlib.sha256((S/'native_core.py').read_bytes()).hexdigest() != 'c510b8c171a57a92b2cfe2ad516cde00fa8a1148b457bb8de2197635e37f3296': raise ValueError('Retained core hash') +sys.path.insert(0,str(S));import native_core as V +raw=gzip.decompress((S/'SOURCE-WORD.json.gz').read_bytes()) +V.need(hashlib.sha256(raw).hexdigest()==V.SOURCE_SHA,'Frozen source payload') +a=json.loads(raw);c=a['canonical'] +def space(b): + s={0} + for v in b:s|={x^v for x in tuple(s)} + return s +spaces=list(map(space,c['frames'])) + +def construct(program): + p=[copy.deepcopy(e)for e in program if e[0]!='climb'];cur=c['start'][:];out=[];count=0;i=0;unequal=0 + def climb(r,f): + old=cur[r] + if old!=f: + V.need(spaces[old]= 1, "Four feasible ascending pair choices require positive lower gap") + multiplicity = sum(child == b for child, _ in graph.children[a]) + return {"a": a, "b": b, "lower_dimensions": [frame.dimension(lower[a]),frame.dimension(lower[b])], + "upper_dimensions": [frame.dimension(upper[a]),frame.dimension(upper[b])], + "edge_multiplicity": multiplicity, "all_other_contacts": "fixed at source original values", + "four_assignments_feasible": True, + "submodular_difference": f"{multiplicity}*(f({gap-1})+f({gap+1})-2*f({gap})) < 0 for strictly concave f", + "selected_subspaces_decimal": [[str(av), str(bv)] for av,bv in choices]} + return None + + +def main(): + data, construct, frame = load() + published = json.loads((FROZEN / "research/carried-warp-frame-intervals/RESULT.json").read_text()) + cardinality = domains_by_gap(9) + result = {"status": "SOURCE_BOUND_GRAPH_STRUCTURE_ONLY", "pin": "ef2810fe43829960789f783e44ee6484d0368f09", + "domain_cardinality_by_gap": cardinality, "directions": {}, "new_candidate_emitted": False} + for direction, source_program in data["programs"].items(): + program, swaps, unequal = construct(source_program) + need((swaps, unequal) == (534, 43), "Retained swap construction census") + schedule = frame.NativeSchedule(data["canonical"], program) + graph = schedule.graph + lower, upper = graph.bounds() + record = published["directions"][direction] + need(len(graph.fixed) == record["graph_nodes"] and sum(map(len, graph.parents)) == record["graph_edges"], + "Published graph census") + variable = {i for i, (a,b) in enumerate(zip(lower, upper)) if a != b} + gaps = {i: frame.dimension(upper[i])-frame.dimension(lower[i]) for i in variable} + sizes = {i: cardinality[gaps[i]] for i in variable} + adjacency = {v: set() for v in variable} + for v in variable: + for p, _ in graph.parents[v]: + if p in variable: + adjacency[v].add(p) + adjacency[p].add(v) + comps = components(adjacency) + bounds = [elimination_bound(adjacency, c, sizes) for c in comps] + report = {"all_nodes": len(graph.fixed), "variable_nodes": len(variable), + "variable_edges_simple": sum(map(len,adjacency.values()))//2, + "gap_histogram": dict(sorted(Counter(gaps.values()).items())), + "domain_size_histogram": dict(sorted(Counter(sizes.values()).items())), + "components": len(comps), "component_size_histogram": dict(sorted(Counter(map(len, comps)).items())), + "maximum_bucket_assignments": max(x["maximum_bucket_assignments"] for x in bounds), + "sum_bucket_assignments": sum(x["sum_bucket_assignments"] for x in bounds), + "max_induced_width_upper": max(x["induced_width_upper"] for x in bounds), + "submodularity_counterexample": pair_submodularity_counterexample(graph, lower, upper, schedule.original_values, frame), + "elimination_components": bounds} + result["directions"][direction] = report + print(direction, json.dumps({k:v for k,v in report.items() if k not in ('elimination_components','submodularity_counterexample')}, sort_keys=True), flush=True) + print("actual_four_assignment_submodularity_counterexample", report["submodularity_counterexample"] is not None, flush=True) + (HERE / "GRAPH-STRUCTURE.json").write_text(json.dumps(result,indent=2)+"\n") + + +if __name__ == "__main__": + main() diff --git a/research/small-coupled-frame-optimum/verify.py b/research/small-coupled-frame-optimum/verify.py new file mode 100644 index 0000000000..a9a640c070 --- /dev/null +++ b/research/small-coupled-frame-optimum/verify.py @@ -0,0 +1,101 @@ +#!/usr/bin/env python3 +"""Portable, read-only wrapper; no scientific expressions or source bytes changed. +Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance. +Apache-2.0. Retained authorship and notices are in evidence/ and NOTICE.md. +""" +from pathlib import Path +from hashlib import sha256 +import json +import os +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +EVIDENCE = HERE / 'evidence' +EXPECTED_MANIFEST = '2a54c76896586db9cd3562652531959bd524818d6e438baed39641911073079a' + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def authenticate(root, records): + for name, expected in records.items(): + path = root / name + need(path.is_file() and not path.is_symlink(), 'Missing regular input: ' + name) + need(sha256(path.read_bytes()).hexdigest() == expected, 'Input hash mismatch: ' + name) + + +def semantic(value, summary=False): + if isinstance(value, dict): + excluded = {'runtime_seconds', 'total_runtime_seconds'} + if summary: + excluded.add('receipt_sha256') + return {k: semantic(v, summary) for k, v in value.items() if k not in excluded} + if isinstance(value, list): + return [semantic(v, summary) for v in value] + return value + + +def same_receipt(actual, expected, summary=False): + a, b = json.loads(actual.read_bytes()), json.loads(expected.read_bytes()) + need(semantic(a, summary) == semantic(b, summary), 'Semantic receipt mismatch: ' + expected.name) + + +def run(script, arguments, temporary, name): + # Each child has a new cache namespace: -B alone does not disable cache reads. + cache = temporary / ('cache-' + name) + command = [sys.executable, '-I'] + if sys.flags.optimize: + command.append('-O') + command += ['-X', 'pycache_prefix=' + str(cache), '-W', 'error', '-B', str(script)] + arguments + env = dict(os.environ) + env.pop('PYTHONOPTIMIZE', None) + result = subprocess.run(command, cwd=temporary, env=env, stdout=subprocess.PIPE, + stderr=subprocess.PIPE, check=False, timeout=150) + need(result.returncode == 0, name + ' failed: ' + result.stderr.decode(errors='replace')[-3000:]) + need(not result.stderr, name + ' unexpected stderr: ' + result.stderr.decode(errors='replace')[-3000:]) + return result.stdout + + +def main(): + package_manifest = json.loads((HERE / 'PACKAGE-FILES.json').read_bytes()) + authenticate(HERE, package_manifest) + manifest_bytes = (EVIDENCE / 'FILES.json').read_bytes() + need(sha256(manifest_bytes).hexdigest() == EXPECTED_MANIFEST, 'Independent manifest changed') + records = json.loads(manifest_bytes) + authenticate(EVIDENCE, records) + # Original requests remain unchanged and bind local copies as well as Git provenance. + for row in json.loads((HERE / 'ORIGINS.json').read_bytes())['upstream_requests']: + local = HERE.parent.parent / row['retained_path'] + need(sha256(local.read_bytes()).hexdigest() == row['sha256'], 'Original source request mismatch') + with tempfile.TemporaryDirectory(prefix='small-frame-verify-') as directory: + temporary = Path(directory) + independent = run(EVIDENCE / 'check.py', [], temporary, 'independent') + need(independent == (EVIDENCE / 'REVIEW-RESULT.json').read_bytes(), 'Independent result changed') + result = json.loads(independent) + need(result['status'] == 'PASS_FIXED_C_AND_K3_DISTINCT_RESULTS', 'Independent status') + need(result['independent_message_states_verified'] == 8760, 'Independent complete bucket coverage') + need(not result['all_concave_ceiling'] and not result['cuts4_to8_executed'], 'Scope guard') + output = temporary / 'fixed.json' + source = EVIDENCE / 'source' + run(EVIDENCE / 'frozen/optimize.py', ['--source-root', str(source), '--output', str(output)], temporary, 'author-fixed') + same_receipt(output, EVIDENCE / 'frozen/RESULT.json') + cuts = temporary / 'cuts' + run(EVIDENCE / 'frozen/min_rank_cuts.py', ['--source-root', str(source), '--output-dir', str(cuts)], temporary, 'author-cuts') + need({x.name for x in cuts.iterdir()} == {'SUMMARY.json', 'CUT-1.json', 'CUT-2.json', 'CUT-3.json'}, 'Stop at cut3 exactly') + for k in (1, 2, 3): + same_receipt(cuts / f'CUT-{k}.json', EVIDENCE / f'frozen/cuts-normal/CUT-{k}.json') + same_receipt(cuts / 'SUMMARY.json', EVIDENCE / 'frozen/cuts-normal/SUMMARY.json', summary=True) + authenticate(HERE, package_manifest) + print(json.dumps({'status': 'PASS_SMALL_COUPLED_FRAME_OPTIMUM', 'fixed_C': '15108879/5000000000', + 'small_components': 18, 'small_variables': 68, 'big_variables_held_source': 1271, + 'independent_bucket_evaluations': 8760, 'author_fresh_receipts': 'fixed and cuts1..3 match frozen semantics', + 'source_histogram_is_fixed_C_optimum': True, 'all_concave_extension': False, + 'cuts4_to8_executed': False, 'new_kappa': None}, sort_keys=True)) + + +if __name__ == '__main__': + main()