diff --git a/research/p112-b5-caller-inventory/CHECKS.json b/research/p112-b5-caller-inventory/CHECKS.json new file mode 100644 index 0000000000..c4ffd6693b --- /dev/null +++ b/research/p112-b5-caller-inventory/CHECKS.json @@ -0,0 +1,13 @@ +{ + "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]", + "platform": "Linux-7.0.0-38-generic-x86_64-with-glibc2.39", + "command": "python3.12 -I -Werror -B scripts/research_package.py --package research/p112-b5-caller-inventory", + "status": "passed", + "UTC": "2026-10-19 07:30 UTC", + "evidence": [ + "PASS_P112_B5_CALLER_INVENTORY 38/38 76/77", + "PASS_P112_B5_INDEPENDENT 690 rule/row combinations; 462 basis subsets", + "PASS_P112_B5_CONTROLS weights/excess/cut/deletion; three optimized CLI mutations" + ], + "limits": "Only new composition replays; inherited geometric censuses, full decoder proof, human/formal review, selected cold replay, Lean and Docker unrun." +} diff --git a/research/p112-b5-caller-inventory/PREDECESSORS.json b/research/p112-b5-caller-inventory/PREDECESSORS.json new file mode 100644 index 0000000000..720a1a0367 --- /dev/null +++ b/research/p112-b5-caller-inventory/PREDECESSORS.json @@ -0,0 +1,61 @@ +{ + "sources": [ + { + "pr": 3154, + "author": "DreamingOfClouds", + "head": "708f0ad8928c383de8294aea3c126e9461d2066d", + "usage": "TWOSIDE filter and completed FINITE beta7p2; source bytes retained through canonical PR3282/3289", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3154" + }, + { + "pr": 3262, + "author": "Nick Petalas", + "head": "f7af207c5e8eabc4524448a0f7c6f77a03c059ba", + "usage": "rank-six three-endpoint shortening at29", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3262" + }, + { + "pr": 3283, + "author": "Nick Petalas", + "head": "089575ca9fdf03c734feecc2ae8a830fccb21812", + "usage": "rank-five three-endpoint shortening at47; scientific f8ec5ac6bbdb6c59b939cb3f4e0bd47a2987e21c", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3283" + }, + { + "pr": 3205, + "author": "Nick Petalas", + "head": "49d26a7604686aa77cf88d7280b2e313cb4882f6", + "usage": "six support20 endpoints and common support30", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3205" + }, + { + "pr": 3282, + "author": "Nick Petalas", + "head": "9607079de93907d87e6430d6de154f21a66c03e4", + "usage": "historical caller composition and retained original filter", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3282" + }, + { + "pr": 3289, + "author": "Nick Petalas", + "head": "e8570c50f9591c9ca653a527ed9626aaa703c3bc", + "usage": "source-bound original cover contracts and rational-kernel scalar extension", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3289" + }, + { + "pr": 3931, + "author": "Chris R / Clear1nsight with Codex", + "head": "33b6be488be1e9e38f2f3f9bcfc4a7db0e8a332d", + "usage": "common23 at most three projective directions; pending conditional input", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3931" + }, + { + "pr": 3960, + "author": "Chris R / Clear1nsight with Codex", + "head": "7e8d98e351ac153d81943218bf168dc8548b1cea", + "usage": "common24 at most two projective directions; pending conditional input", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3960" + } + ], + "evidence_status": "Exact-source conditional contracts; this package does not establish human or formal acceptance of predecessors." +} diff --git a/research/p112-b5-caller-inventory/PROOF.md b/research/p112-b5-caller-inventory/PROOF.md new file mode 100644 index 0000000000..39f161593b --- /dev/null +++ b/research/p112-b5-caller-inventory/PROOF.md @@ -0,0 +1,166 @@ +# A fixed conditional inventory for the historical b=5 cells + +Let K have characteristic zero, let C be the P112 root-evaluation code, +and let q_1,...,q_n be independent vectors in K^112. Their binary weights +are ranks of the leading-one E8 labels on their supports. Write T for their +span and D=T intersect C. The callers considered here have dim(D)>=5, +5<=n<=5+t, t in {5,6}, weights in {2,...,7}, and strict excess +sum(w_i-2)<30. These are the explicit historical TWOSIDE hypotheses. + +The result is a source-bound composition of six fixed contracts. Conditional +on the six stated contracts, all 38 original (5,5) survivors and 76 of the 77 +original (5,6) survivors are excluded. The latter cell contains the former; +there are 77 distinct survivor profiles, not 115. The sole row uncertified +by this inventory is 2^5,6,7^5. This is neither a claim that it is globally +open nor a claim that it is realizable. A concurrent investigation targets +its common30 geometry; that new theorem is outside this frozen inventory. + +## Sources, hypotheses and attribution + +We inherit the P112 distance53, injective root evaluation and support caps + +| binary weight | 2 | 3 | 4 | 5 | 6 | 7 | +|---|---:|---:|---:|---:|---:|---:| +| support cap | 2 | 4 | 8 | 12 | 20 | 36 | + +The low-rank caps follow from the leading-one labels; the rank-five and +rank-six capacities and geometric code facts are inherited, not recomputed +here. Their exact proof context is in the retained input contracts. Historical +filter capacities are those of DreamingOfClouds's PR3154, including its +conditional rank-seven cap32 in the low-support tests. The historical filter +count is a source reproduction, not an independent audit of that reduction. + +| Inventory key | Exact stated contract | Predecessor | +|---|---|---| +| rank6_29 | Three residual rank<=6 pieces outside one common cut<=29 intersect the restricted code in dimension<=1 | Nick Petalas, PR3262 | +| rank5_47 | Three residual rank<=5 pieces outside one common cut<=47 intersect the restricted code in dimension<=1 | Nick Petalas, PR3283 | +| six_support20_30 | Independent small pieces with support union<=30 and six independent endpoints each supported on<=20 coordinates have code intersection dimension<=4 | Nick Petalas, PR3205 | +| beta7p2 | Outside two fixed binary six-spaces and a common set<=2, qualifying residual-rank<=7 directions span<=4 | DreamingOfClouds, PR3154 FINITE, completed PROOF_MAP/full_b evidence; source-bound transfer in PR3289 | +| common23 | A common cut<=23 admits at most three projective residual-rank<=7 directions over characteristic zero | Chris R / Clear1nsight with Codex, PR3931 | +| common24 | A common cut<=24 admits at most two projective residual-rank<=7 directions over characteristic zero | Chris R / Clear1nsight with Codex, PR3960 | + +PR3283 is the rank-five cut47 source. An exploratory private script used +3277 as a rule label; that number names an unrelated result and is not an +accepted citation in this inventory here. PREDECESSORS.json records exact scientific/public +heads. SOURCES.json binds canonical-main input bytes and the two retained +pending proof texts. Pending contracts remain conditional. No heavy +predecessor census, human approval or proof-kernel validation is claimed. + +## Deletion and restriction transfer + +Delete d independent pieces and let T' be the span of those retained. Then +codim_T(T')=d and dim(T' intersect C)>=dim(D)-d>=5-d. For a selected collection +of small pieces let S be their actual support union. Its cardinality is at +most the sum of the displayed individual support caps, without any assumption +of disjointness. Whenever that cap is below53, coordinate deletion pi_S is +injective on C. The small pieces vanish under pi_S, and binary support ranks +of the remaining endpoints cannot increase. + +For either three-endpoint shortening theorem, select three endpoints and +n-6 small pieces, and delete the other three pieces. At least two code +dimensions remain. The common cap is respectively <=29 or <=47, hence +restriction preserves both. Their image lies in the span of the three +restricted endpoints, contradicting the stated dimension bound one. + +For the six-endpoint theorem, select six endpoints and n-6 small pieces. +Delete no pieces, retaining at least five code dimensions. Endpoints of +binary rank<=6 have support<=20. A small support union<=30 therefore +contradicts PR3205 directly. This rule does not use a three-endpoint theorem +at a larger cut, and retains the collective independence hypothesis. + +## Quotient transfer for the three direction contracts + +Choose n-5 small pieces X with total support cap below53. Their images in +Q=T/D are independent: a relation would give a nonzero codeword supported +on S, below distance53, and independence of the original pieces ensures +that this proposed codeword is nonzero. Since dim(Q)<=n-5, these images form +a basis, so dim(Q)=n-5 and dim(D)=5. + +Each of the five remaining pieces q_y has a unique combination a_y of X +such that c_y=q_y-a_y belongs to C. These five codewords are independent, +by their coefficients on the five distinct nonbasis pieces. Injective +root evaluation gives five independent directions h_y. Outside the ONE +common S, c_y agrees with q_y and thus has binary support rank<=7. +If the cap of S is<=23 or<=24, the respective common-cut contract admits +at most three or two projective directions. Each contradicts the required +five independent directions. There is no substitution of per-direction +small sets for one common set. + +For beta7p2, partition X into indexed groups A,B,P whose weight sums in A +and B are each at most6 and whose support-cap sum in P is at most2. +Their support labels fit into two fixed binary six-spaces V_A,V_B. Let +S_P be the actual support union of P; it is one common set of at most2. +Outside Lambda(V_A) union Lambda(V_B) union S_P, c_y agrees with q_y. +All five directions therefore satisfy the inherited span<=4 contract, +a contradiction. The rational-kernel transfer to every characteristic-zero +K is recorded in the exact PR3289 input proof; no embedding K into R is +assumed. The old FINITE notes' unfinished state is superseded by the +retained PROOF_MAP and labelled full_b completion, all separately pinned. + +## Exhaustive finite composition + +The primary enumerates every sorted weight multiset, including those rejected +before any theorem is applied: 7,798 for (5,5), 12,166 for (5,6). On every +multiset its filter agrees with unchanged PR3154 bk2b.py. A separate checker +uses multiplicity vectors in excess coordinates and subset-sum packing, +imports no predecessor or primary executable, and reconstructs both complete +accepted sets. This independently agrees on38 and77 survivors. + +For each of the six rules and each row, RESULT.json retains the number of +successful indexed assignments, the minimum capacity sum over the relevant +endpoint/basis class, and one complete literal witness when successful. +Equal-weight pieces have distinct indices. The primary shortening enumerator +chooses endpoints first; the separate implementation chooses small pieces +first. For beta7p2 the primary enumerates three-role strings, while the +separate checker chooses a cut subset and then splits its complement. +All690 rule/row combinations agree, including zero counts, minima and witness +membership. A minimum for beta7p2 is the unrestricted quotient-basis capacity +minimum; it is not a minimum under its packing constraints. The receipt's +unsuccessful beta count is the exhaustive packing result. + +Disjoint primary attribution follows the displayed rule order: + +| Cell | rank6_29 | rank5_47 | six_support20_30 | beta7p2 | common23 | common24 | Uncertified | +|---|---:|---:|---:|---:|---:|---:|---:| +| (5,5) | 34 | 1 | 0 | 2 | 1 | 0 | 0 | +| (5,6) | 61 | 6 | 2 | 2 | 3 | 2 | 1 | + +These are recovered applications of credited results. Neither primary +attribution nor the addition of a coherent inventory claims a newly proved +geometric theorem or first exclusion of a profile. Other rules and literal +exclusions are intentionally outside this fixed inventory. + +## Exact interface for the inventory gap + +For 2^5,6,7^5 there are eleven pieces, strict excess29 and required code +intersection dimension at least5. The first six pieces have support-cap sum +5*2+20=30<53. Hence their images force quotient dimension6 and code-intersection +dimension exactly5. The five remaining rank-seven pieces yield five independent +code directions with residual rank<=7 after that same support union S. + +All462 six-piece subsets have capacity sum at least30, with30 attained by +these first six pieces. This certifies the best sum of inherited individual +capacity bounds, not a lower bound on the actual union S. Actual support +overlap may reduce its size. The rank6_29, rank5_47 and six_support20_30 +endpoint-compatible minima are respectively78,96,180; none meets its cut. +The beta7p2 packing has no success. The stated common23/common24 contracts +therefore leave this exact caller uncertified. + +A uniform common30 theorem with span bound at most4 would exclude it, since +five independent directions are required. An arbitrary-cut witness admitting +five directions would only falsify that relaxation; it would not realize the +original independent pieces or their quotient coefficients. Conversely, a +separately verified common30 bound<=3 would complete the conditional77-row +inventory by this same quotient argument. The concurrent common30 work must +supply its own source pin, finite coverage and proof before that implication +can be promoted to a combined result. + +## Scope and remaining obligations + +This package authenticates sources and proves/replays the new composition. +The underlying geometric contracts, distance, capacities, characteristic-zero +normalization and original decoder reduction remain conditional mathematical +inputs with their published evidence status. The two cells are a historical +finite filter domain, not the entire current C5 frontier. Full C5, a global +P112 decoder floor, physical realization, supplier admission, multiplication +bounds and kappa are outside scope. Selected frontier remains unchanged. diff --git a/research/p112-b5-caller-inventory/README.md b/research/p112-b5-caller-inventory/README.md new file mode 100644 index 0000000000..946715bb17 --- /dev/null +++ b/research/p112-b5-caller-inventory/README.md @@ -0,0 +1,64 @@ +# Conditional reconciliation of the P112 b=5 caller cells + +Six fixed published contracts account for all38 historical TWOSIDE (5,5) +survivors and76 of77 historical (5,6) survivors. These are nested cells, +with77 distinct profiles. This package supplies exact caller composition, +source authentication and independently reconstructed coverage; predecessor +exclusions retain their credit. + +The only row uncertified **by this inventory** is `2^5,6,7^5`. Its eleven +independent pieces require code-intersection dimension5. The six small +pieces force quotient dimension6 and have common support cap30; all462 +six-piece subsets have individual-capacity sum at least30. Five independent +rank-seven residual directions are therefore required after that ONE common +support. This is a precise interface, not a global-open or realizability +claim. A separate concurrent investigation owns its common30 geometry. + +[PROOF.md](PROOF.md) proves deletion and quotient transfers and states every +conditional input. [RESULT.json](RESULT.json) retains all six rule attempts +for every row, including failed assignments, minima and indexed witnesses. +The original PR3154 filter and an independently written filter agree across +both complete domains (7,798 and12,166 multisets). A separate implementation +checks all690 rule/row combinations using different enumeration order and +packing logic. Controls reject source/metadata/receipt mutations under +optimized Python and exercise strict excess, deletion and common-cut limits. + +## Reproduce + +Python3.12 or later, standard library only, from the repository root: + +```sh +python3.12 -I -Werror -B scripts/research_package.py --package research/p112-b5-caller-inventory +``` + +The three direct scripts are `verify.py`, `independent.py` and +`test_controls.py`, with `-I -O -Werror -B`. All compare committed receipts; +none regenerates frozen inputs. The package and declared canonical-main +inputs suffice for a Git-free direct replay. Pending PR3931/3960 proof texts +are retained locally with exact public heads and hashes; no pending Git +objects or network are needed. Registered metadata additionally checks +historical provenance against canonical main. + +## Open next questions + +Bind the separately established common30 result to the literal +`2^5,6,7^5` interface, after its finite coverage and characteristic-zero +argument are reviewed. A span bound below5 would close the final row of +this fixed inventory. If a relaxation fails, retain actual common-support +and quotient-coefficient obligations rather than treating it as a literal +counterexample. This package stops before that separate geometric theorem. + +## Credit and limits + +DreamingOfClouds/PR3154 supplies TWOSIDE, the exact original filter and +completed beta7p2 geometry. Nick Petalas supplies PR3262, PR3283 and PR3205, +and the earlier PR3282/3289 caller-composition framework. Chris R / +Clear1nsight with substantial OpenAI Codex assistance supplies PR3931/3960. +The retained E8/P112 lineage includes joaqcoo. [PREDECESSORS.json](PREDECESSORS.json) +and [SOURCES.json](SOURCES.json) preserve exact sources and usages. + +The new conditional inventory was produced by Chris R / Clear1nsight with +substantial OpenAI Codex assistance, Apache-2.0. Separate implementations +and same-session review are not independent human or formal-kernel approval. +Predecessor heavy scientific replays and complete decoder reduction remain +unrun here. No full C5, global decoder floor, supplier or new kappa is claimed. diff --git a/research/p112-b5-caller-inventory/RESULT.json b/research/p112-b5-caller-inventory/RESULT.json new file mode 100644 index 0000000000..712dfd8304 --- /dev/null +++ b/research/p112-b5-caller-inventory/RESULT.json @@ -0,0 +1,128 @@ +{ + "schema": "p112-b5-caller-inventory/v1", + "source_manifest_sha256": "16c1e48186e42951b1ec39a79b51b637a9b5c064bb446e318807e3c695d57815", + "conditional_contracts": ["rank6_29","rank5_47","six_support20_30","beta7p2","common23","common24"], + "scope": "Fixed conditional inventory; uncertified does not mean globally open or realizable. Cells are nested, not 115 distinct rows.", + "cells": [ + {"cell":[5,5],"domain_multisets":7798,"historical_survivors":38,"certified":38,"primary_counts":{"rank6_29":34,"rank5_47":1,"six_support20_30":0,"beta7p2":2,"common23":1,"common24":0},"uncertified":[],"rows":[ + 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{"weights":[2,2,2,2,2,6,7,7,7,7,7],"piece_dimension":11,"required_code_dimension":5,"forced_code_dimension":5,"forced_quotient_dimension":6,"preferred_basis_indices":[0,1,2,3,4,5],"preferred_basis_cap":30,"all_six_piece_subsets":462,"minimum_six_piece_capacity_sum":30,"required_independent_rank7_directions":5,"actual_union_minimum_claimed":false} +} diff --git a/research/p112-b5-caller-inventory/SOURCES.json b/research/p112-b5-caller-inventory/SOURCES.json new file mode 100644 index 0000000000..8d75d15abb --- /dev/null +++ b/research/p112-b5-caller-inventory/SOURCES.json @@ -0,0 +1,92 @@ +{ + "schema_version": 1, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + 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a/research/p112-b5-caller-inventory/TASK.json b/research/p112-b5-caller-inventory/TASK.json new file mode 100644 index 0000000000..bfd757fba2 --- /dev/null +++ b/research/p112-b5-caller-inventory/TASK.json @@ -0,0 +1,83 @@ +{ + "schema_version": 1, + "task_id": "complex-rank-shape-decoder", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "complex-rank-shape-decoder", + "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)?", + "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" + ], + "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." + ], + "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.", + "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." + }, + "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).", + "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.", + "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." + ], + "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." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ] + }, + "scope_status": "changed", + "actual_scope": "Conditional exact caller reconciliation of historical TWOSIDE (5,5) and (5,6) cells using six fixed published contracts; identify the actual quotient and support-cap gap.", + "scope_change_reason": "Explicit donor assignment to parallel C5 follow-up; this worker owns caller/filter composition, while separate workers audit PR3960 and investigate common30 geometry.", + "bottleneck_link": "Replace an exploratory six-profile list with a source-bound conditional inventory and an exact remaining caller interface.", + "budget_minutes": 60, + "stop_rule": "Stop at these two nested cells, exact six-contract composition, independent finite replay and focused publication. No extension to other cells or geometric census.", + "outcome": "completed", + "evidence": "RESULT.json and PROOF.md; original and independently written full-domain filters, two application enumerators and failure controls.", + "author": "Chris R / Clear1nsight with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; same donor/assistant as PR3931/3951, no independent human or formal-kernel review.", + "open_questions": [ + { + "question": "Can the literal 2^5,6,7^5 caller be excluded using its common-support structure and coefficient relations?", + "why_it_matters": "It is the only row uncertified by this fixed inventory in (5,6).", + "first_step": "Use dim(T)=11, dim(D)=5, quotient dimension6 and the six-small-piece common cap30; distinguish an arbitrary-cut obstruction from a literal piece realization.", + "blocked_by": "The admitted common23/common24 contracts do not apply at30; a separate concurrent investigation owns that geometry." + } + ], + "freshness": { + "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "priority_revision": 6, + "open_PR_bodies": 671, + "entry_UTC": "2026-10-19 07:22 UTC", + "Discussion_coverage": "Parent coordinator read rendered C5, start-here, active board and latest loaded handoff; partial, not all Discussion pages.", + "selected_frontier_unchanged": true, + "final_open_PR_bodies": 673, + "final_PR_snapshot_UTC": "2026-10-19 07:30:28 UTC", + "parent_proof_review": "Read-only review of full PROOF.md and primary code: no objection found to deletion/restriction, six-endpoint transfer, quotient and beta7p2 packing. Same-session automated review, not independent human acceptance." + } +} diff --git a/research/p112-b5-caller-inventory/VERIFY.json b/research/p112-b5-caller-inventory/VERIFY.json new file mode 100644 index 0000000000..06d298783f --- /dev/null +++ b/research/p112-b5-caller-inventory/VERIFY.json @@ -0,0 +1,55 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p112-b6-t4-reconciliation/vendor/bk2b.py", + "research/p112-b6-t4-reconciliation/vendor/PR3154-TWOSIDE.md", + "research/p112-a2-rank6-sharp-shortening/PROOF.md", + "research/p112-rank5-sharp47/PROOF.md", + "research/p112-support30-shortening/PROOF.md", + "research/p112-b6-t4-original-covers/PROOF.md", + "research/p112-b6-t4-original-covers/vendor/PR3154-FINITE.md", + "research/p112-b6-t4-original-covers/vendor/PR3154-PROOF-MAP.md", + "research/p112-b6-t4-original-covers/vendor/PR3154-full_b.txt" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Source authentication, original and own filters on every multiset, six exact contract assignments and quotient-cap interface." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/independent.py" + ], + "timeout_seconds": 180, + "checks": "Independent excess-count filter and small-subset-first application enumeration, every assignment count/minimum/witness checked." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/test_controls.py" + ], + "timeout_seconds": 180, + "checks": "Strict excess and deletion boundaries, common versus separate cuts, invalid ranks and optimized CLI source/receipt/metadata corruptions." + } + ] +} diff --git a/research/p112-b5-caller-inventory/independent.py b/research/p112-b5-caller-inventory/independent.py new file mode 100644 index 0000000000..0703150453 --- /dev/null +++ b/research/p112-b5-caller-inventory/independent.py @@ -0,0 +1,140 @@ +"""Separate count-vector/filter and small-first assignment reconstruction. + +Imports no primary or predecessor executable. Apache-2.0; Codex assistance. +""" +from pathlib import Path +from itertools import combinations, product +import hashlib +import json + +HERE = Path(__file__).resolve().parent +CAP = (2, 4, 8, 12, 20, 36) +TIGHT = (2, 4, 8, 12, 20, 32) + + +def check(condition, message): + if not condition: + raise ValueError(message) + + +def subsets(items, k): + return combinations(items, k) + + +def vectors(n, k=6): + if k == 1: + yield (n,) + else: + for first in range(n + 1): + for tail in vectors(n - first, k - 1): + yield (first,) + tail + + +def accepts(xs): + n = len(xs) + if sum(xs) >= 30: + return False + for d, threshold in enumerate((53, 78, 92, 100, 106), 1): + ys = xs[:n - 5 + d] + total = sum(CAP[x] for x in ys) + special = sum(TIGHT[x] for x in ys) + if d <= 2: + if special < threshold and total < (73 if d == 1 else 82): + return False + elif total < threshold: + return False + small = xs[:n - 5] + if sum(CAP[x] for x in small) >= 53: + return True + weights = [x + 2 for x in small] + if sum(weights) <= 7: + return False + sums = {0} + for w in weights: + sums |= {s + w for s in tuple(sums)} + return not any(s <= 6 and sum(weights) - s <= 6 for s in sums) + + +def applications(xs, name): + n = len(xs) + indices = set(range(n)) + results = [] + minima = [] + if name in ('rank6_29', 'rank5_47', 'six_support20_30'): + endpoint_n = 6 if name.startswith('six') else 3 + maximum = 3 if name == 'rank5_47' else 4 + cut = {'rank6_29': 29, 'rank5_47': 47, 'six_support20_30': 30}[name] + for small in subsets(range(n), n - 6): + cost = sum(CAP[xs[i]] for i in small) + available = sorted(indices.difference(small)) + for endpoints in subsets(available, endpoint_n): + if max(xs[i] for i in endpoints) > maximum: + continue + minima.append(cost) + if cost <= cut: + results.append(dict(small=list(small), endpoints=list(endpoints), deleted=sorted(indices.difference(small).difference(endpoints)), common_cap=cost, surviving_code_dimension=5 - (6 - endpoint_n))) + else: + for basis in subsets(range(n), n - 5): + cost = sum(CAP[xs[i]] for i in basis) + minima.append(cost) + if cost >= 53: + continue + if name.startswith('common'): + if cost <= {'common23': 23, 'common24': 24}[name]: + results.append(dict(basis=list(basis), common_cap=cost, quotient_dimension=n - 5, required_directions=5)) + else: + for cut_n in range(len(basis) + 1): + for cut_set in subsets(basis, cut_n): + cut_cost = sum(CAP[xs[i]] for i in cut_set) + if cut_cost > 2: + continue + rest = sorted(set(basis).difference(cut_set)) + for a_n in range(len(rest) + 1): + for a in subsets(rest, a_n): + b = set(rest).difference(a) + if sum(xs[i] + 2 for i in a) > 6 or sum(xs[i] + 2 for i in b) > 6: + continue + roles = [2 if i in cut_set else 0 if i in a else 1 for i in basis] + results.append(dict(basis=list(basis), roles=roles, basis_cap=cost, cut_cap=cut_cost, required_directions=5, span_bound=4)) + return results, min(minima, default=None) + + +def main(): + receipt = json.loads((HERE / 'RESULT.json').read_text()) + source = (HERE / 'SOURCES.json').read_bytes() + check(hashlib.sha256(source).hexdigest() == receipt['source_manifest_sha256'], 'source binding differs') + attempts = 0 + for cell in receipt['cells']: + t = cell['cell'][1] + candidates = [] + for n in range(5, 6 + t): + for counts in vectors(n): + candidates.append(tuple(x for x, count in enumerate(counts) for _ in range(count))) + survivors = sorted(xs for xs in candidates if accepts(xs)) + recorded = sorted(tuple(w - 2 for w in row['weights']) for row in cell['rows']) + check(survivors == recorded, 'full historical domain mismatch') + check(len(candidates) == cell['domain_multisets'], 'domain count differs') + for row in cell['rows']: + xs = tuple(w - 2 for w in row['weights']) + check(row['strict_excess_deficit'] == 30 - sum(xs), 'strict deficit differs') + found = [] + for name, expected in row['attempts'].items(): + results, minimum = applications(xs, name) + check(len(results) == expected['successful_assignments'], 'assignment count: ' + name) + check(minimum == expected['minimum_capacity_sum'], 'capacity minimum: ' + name) + check(expected['witness'] in results if results else expected['witness'] is None, 'literal witness: ' + name) + if results: + found.append(name) + attempts += 1 + check(row['primary'] == (found[0] if found else None), 'primary attribution differs') + check(cell['certified'] == sum(row['primary'] is not None for row in cell['rows']), 'coverage count differs') + interface = receipt['remaining_interface'] + costs = sorted(sum(CAP[interface['weights'][i] - 2] for i in B) for B in combinations(range(11), 6)) + check(len(costs) == 462 and costs[0] == 30, 'remaining caller basis minimum') + check(30 < 53 and 11 - 6 == 5, 'remaining caller quotient') + check(receipt['cells'][0]['uncertified'] == [] and receipt['cells'][1]['uncertified'] == [interface['weights']], 'remaining rows differ') + print('PASS_P112_B5_INDEPENDENT', attempts, 'rule/row combinations; 462 basis subsets') + + +if __name__ == '__main__': + main() diff --git a/research/p112-b5-caller-inventory/test_controls.py b/research/p112-b5-caller-inventory/test_controls.py new file mode 100644 index 0000000000..0a4c6ce243 --- /dev/null +++ b/research/p112-b5-caller-inventory/test_controls.py @@ -0,0 +1,72 @@ +"""Behavioral boundary checks and actual optimized-CLI corruptions.""" +from pathlib import Path +import json +import os +import runpy +import shutil +import subprocess +import sys +import tempfile + +P = Path(__file__).resolve().parent +R = P.parent.parent +v = runpy.run_path(str(P / 'verify.py')) +need = v['require'] + + +def rejected(fn, text): + try: + fn() + except ValueError: + return + raise ValueError('accepted invalid control: ' + text) + + +def main(): + v['authenticate']() + for w in [(1,) * 5, (8,) * 5, (2, 3, 2, 7, 7), (True, 2, 3, 6, 7)]: + rejected(lambda: v['historical'](w), 'weight bounds') + need(not v['historical']((2,) * 5 + (7,) * 6), 'strict excess30 accepted') + actual = (2,) * 4 + (4,) * 2 + (7,) * 5 + need(v['historical'](actual), 'literal caller absent') + need(v['attempt'](actual, 'common23')['successful_assignments'] == 0, 'cut23 extended') + need(v['attempt'](actual, 'common24')['successful_assignments'] > 0, 'cut24 caller lost') + need(5 - 3 == 2 and 5 - 3 != 5, 'deletion did not charge dimensions') + # Individually small supports do not supply a common small support. + cuts = [set(range(24)), set(range(1, 25))] + need(all(len(c) <= 24 for c in cuts) and len(set.union(*cuts)) > 24, 'common-cut quantifier') + manifest = json.loads((P / 'VERIFY.json').read_text()) + for mutation in ('receipt', 'input', 'manifest'): + with tempfile.TemporaryDirectory(prefix='p112-b5-control-') as td: + root = Path(td) + package = root / 'research' / P.name + shutil.copytree(P, package) + for name in manifest['inputs']: + target = root / name + target.parent.mkdir(parents=True, exist_ok=True) + shutil.copyfile(R / name, target) + if mutation == 'receipt': + target = package / 'RESULT.json' + target.chmod(target.stat().st_mode | 0o200) + result = json.loads(target.read_text()) + result['cells'][0]['rows'][0]['attempts']['rank6_29']['witness']['surviving_code_dimension'] = 5 + target.write_text(json.dumps(result)) + elif mutation == 'input': + target = root / manifest['inputs'][0] + target.chmod(target.stat().st_mode | 0o200) + target.write_bytes(target.read_bytes() + b'\n# changed source\n') + else: + target = package / 'SOURCES.json' + target.chmod(target.stat().st_mode | 0o200) + source = json.loads(target.read_text()) + source['files'][2]['usage'] = 'provenance' + target.write_text(json.dumps(source)) + env = dict(os.environ, PYTHONPYCACHEPREFIX=str(root / 'private-bytecode')) + run = subprocess.run([sys.executable, '-I', '-O', '-Werror', '-B', str(package / 'verify.py')], capture_output=True, text=True, env=env, check=False, timeout=60) + need(run.returncode != 0, 'CLI accepted ' + mutation) + need('ValueError' in run.stderr, 'unexpected rejection ' + mutation) + print('PASS_P112_B5_CONTROLS weights/excess/cut/deletion; three optimized CLI mutations') + + +if __name__ == '__main__': + main() diff --git a/research/p112-b5-caller-inventory/vendor/PR3931-PROOF.md b/research/p112-b5-caller-inventory/vendor/PR3931-PROOF.md new file mode 100644 index 0000000000..95a1eb2060 --- /dev/null +++ b/research/p112-b5-caller-inventory/vendor/PR3931-PROOF.md @@ -0,0 +1,187 @@ +# A common cut of 23 sites admits at most three rank-seven directions + +## Model and statement + +Let P be the 112 E8 root lines left after deleting the eight frame lines +in the pinned PR3163 fixture. Use the doubled integral representatives r_t +and their simple-root parity labels ell(t) in F2^9, with affine bit one. +The replay checks every root row against the canonical +`research/one-sided-six-multisets/data/data.txt`. Its label convention moves +the affine bit from bit 0 to bit 8; the invertible bit permutation is checked +on all 112 labels. This changes no binary support rank. + +For a characteristic-zero field K, put + + c_h(t) = r_t dot h, + C = {c_h : h in K^8}, + w(q) = rank_F2 {ell(t) : q(t) != 0}, + Off(h) = {t : c_h(t) != 0}. + +The pairing is bilinear, including over C. The live-row Gram matrix is +112 I_8, checked exactly, so evaluation is injective over K. + +**Common-cut theorem.** Fix ONE subset S of P with |S| <= 23. The nonzero +directions h satisfying + + rank_F2 ell(Off(h) outside S) <= 7 + +belong to at most three distinct projective lines. In particular, their +K-linear span has dimension at most three. The bound three is an upper +bound: attainment by three directions and sharpness of 23 are unclaimed. +A literal two-independent-direction fixture at 22 cuts is checked. + +The proof uses the standard finite E8 Weyl-chamber theorem and exact finite +checks described below. It is not proof-kernel verification. The new result +is the combination of the root-restricted flat cap and fourfold overlap +with one common deletion set, and its named caller application. The E8 model, +Weyl reduction and earlier flat-cap lineage retain predecessor credit. + +## 1. Completeness: qualifying directions are root normals + +There are exactly 43,435 binary seven-spaces. Their live traces have maximum +size 36. The primary enumerates all two-dimensional annihilators by their +three nonzero functionals a,b,a XOR b, using a= 21. + +The 32 cap is a fresh exhaustive check of an earlier type of local capacity +bound, not a newly claimed root/label model. Both implementations reproduce +it using their separate geometry and seven-space enumeration. + +## 3. Four distinct root normals share at most 14 live off-sites + +The exact finite identity needed is + + max |Off(alpha_1) intersect ... intersect Off(alpha_4)| = 14, + +over every four DISTINCT projective E8 root normals. No independence +restriction is needed. The primary checks all C(120,4)=8,214,570 quadruples. +The second reconstructs roots from the doubled E8 lattice shell, and joins +ordered pairs with a=21 and every A_i is contained in that SAME S, + + |A_1 intersect A_2 intersect A_3 intersect A_4| + >= sum_i |A_i| - 3|S| + >= 84 - 3*23 = 15. + +This contradicts the exact upper bound 14. Hence at most three projective +directions qualify. At the actual caller's budget 22, the lower bound is 18. +Per-direction cuts would not imply this inequality. The controls explicitly +exhibit four independent normals with individual 21-site cuts whose common +union has 66 sites; pooling them is rejected. + +## 4. Excluding the named historical caller 2,3,4,4,7,7,7,7,7,7 + +Suppose ten K-linearly independent pieces span T, have these binary weight +bounds, and dim(T intersect C)>=6. Their first four supports have union S +with + + |S| <= 2+4+8+8 = 22. + +These low-rank cardinality bounds follow directly from the distinct labels' +affine bit: a d-dimensional binary linear space meets that affine +hyperplane in at most 2^(d-1) points. No rank-five or rank-six census is used. + +Write D=T intersect C. The quotient T/D has dimension at most four. The +four small pieces have independent quotient images. Otherwise a nonzero +linear combination would be a nonzero codeword supported on S, contradicting +distance 53. They are therefore a quotient basis; dim D=6. + +Each of the six other pieces q_i has a unique combination a_i of the four +small pieces with c_i=q_i-a_i in C. These six c_i are independent, by their +coefficients on the six distinct q_i in the original independent-piece +basis. Evaluation supplies six independent directions h_i. Outside the ONE +common S, c_i agrees with q_i, so its residual binary support rank is at +most seven. The common-cut theorem permits at most three projective +directions. This contradiction excludes the named caller. + +This result concerns the explicit independent-piece/code-intersection +hypotheses. Applying the historical TWOSIDE reduction to a physical decoder +continues to inherit that reduction's other premises. + +## 5. Application audit and decision about normal planes + +The source-bound PR3289 inventory conditionally covers 65 of its 69 +historical (6,4) rows and lists four inventory-uncertified rows. The explicit +PR3322 contract excludes 2^3,7^7; the PR3405 contract excludes 2,5,6^8. +Those two theorems remain inherited conditional premises in this tally; +their heavy scientific replays are not claimed here. The new theorem +excludes 2,3,4^2,7^6. This NAMED contract inventory therefore accounts for +68/69 rows, leaving 4,5^3,6^6 uncertified BY THIS INVENTORY. This is neither +a current global unresolved count nor a proof that the last row is possible. + +The PR3163 global two-six-flat/rank-seven/common-four question has different +hypotheses from this theorem. It is not settled here. For the named caller, +the actual small footprint already excludes normal planes before section 2. +For the other inventory row, its four-small-piece budget 8+12+12+12=44 and +rank-six endpoint cap 20 similarly give support<=64<70, hence root normals, +under those inherited capacities. Uniform normal-plane exclusion would not +close either of these caller gaps by itself. No all-first-space or global +normal-plane census is launched or claimed. + +## Evidence boundaries and credit + +The generic metadata/pin checks authenticate sources; they are not theorem +acceptance. The primary and separate mathematical implementations establish +the stated finite facts. The written arguments discharge the finite-to- +characteristic-zero implication and the caller composition, using the +explicit standard Weyl-chamber theorem. Same-session computational +corroboration is not independent human review or formal-kernel verification. + +Credit DreamingOfClouds/PR3154 for C5, TWOSIDE and the FINITE lineage; Nick +Petalas/PR3160/3161/3163 for geometry, quantifier controls and the completed +slice; PR3282/3289 for the historical caller inventory and exact cover +contracts; PR3253/3322 and PR3397/3405 for the separate inherited exclusions; +and joaqcoo and the retained E8/P112/root-code lineage. All exact live pins +are at canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90 in SOURCES.json. +New work is by Chris R / Clear1nsight with substantial OpenAI Codex +assistance, Apache-2.0. No complete C5, global decoder floor, physical +supplier, new kappa or selected-frontier change is claimed. diff --git a/research/p112-b5-caller-inventory/vendor/PR3960-PROOF.md b/research/p112-b5-caller-inventory/vendor/PR3960-PROOF.md new file mode 100644 index 0000000000..264d263dfd --- /dev/null +++ b/research/p112-b5-caller-inventory/vendor/PR3960-PROOF.md @@ -0,0 +1,201 @@ +# A common24 rank-seven bound and two literal C5 callers + +Fix the 120 doubled E8 root lines R, oriented by first nonzero coordinate, +the eight frame lines F = {2e_0 +/- 2e_1,...,2e_6 +/- 2e_7}, and P=R\F. +The original caller table orders P lexicographically. Its labels are +ell(r)=(1,c(r) mod2) in F2^9, where c(r) are the integral simple coordinates +in the pinned simple system. Binary weight means the rank of the actual +support labels, not the number of support sites. + +For a characteristic-zero field K put C={c_h : h in K^8}, where +c_h(r)=r dot h for r in P. Let Off(h) be its nonzero support. + +**Theorem.** For every ONE fixed S subset P of size at most 24, the nonzero +directions h with + + rank_F2 ell(Off(h)\S) <= 7 + +occupy at most TWO projective lines over K. Their K-linear span has +dimension at most two. A literal independent pair at a cut of size 24 +attains two. Sharpness of the cut allowance 24 is not claimed. + +**Caller corollary.** Eleven collectively independent pieces with binary +weight bounds either + + 2,2,2,2,3,5,7,7,7,7,7 + 2,2,2,2,4,4,7,7,7,7,7 + +cannot have dim(span(pieces) intersect C)>=5. These are two actual historical +TWOSIDE (b,t)=(5,6) profiles, each with strict excess deficit one. This is a +scoped exclusion, not the full cell, C5, a decoder floor, supplier admission +or a new kappa. + +## 1. Complete finite spaces and the root-normal reduction + +The primary reconstructs the 112 original table rows and adds exactly F. +It checks the elementary 56 two-coordinate and 64 all-odd E8 line patterns, +the nonsingular simple system, every exact coordinate reconstruction, uniform +simple-coordinate signs and the original 112 label bindings. The live Gram +matrix is 112 I_8. Evaluation is therefore injective over every characteristic- +zero K. The binary labels all have leading bit one. + +Every seven-space is the kernel of a unique two-dimensional annihilator +in reduced row-echelon form. The reversed-column enumeration chooses its +highest pivots and all free nonpivot entries below each pivot. Uniqueness of +RREF proves coverage and nonduplication. All 43,435 spaces are enumerated; +their full-root trace maximum is 36. Smaller residual spans extend to a +seven-space. Consequently a qualifying direction has + + |Off(h)| <= |S|+36 <= 60 < 70. + +Here is the needed chamber statement, including the field step. The checked +eight simple reflections permute all 240 signed roots (1,920 images). Since +these roots span, their generated group acts faithfully on a finite set and +is finite. The checked rational rho satisfies rho dot alpha_i=1. For a real +normal v maximize rho dot g(v) over this finite group. If g(v) dot alpha_i<0, +reflecting in alpha_i strictly increases that functional, a contradiction. +Thus g(v) is in the closed chamber. Uniform signs of the simple coordinates +imply that a root is perpendicular exactly when its simple support lies in +the zero simple pairings. The perpendicular roots are therefore a checked +simple face. This argument classifies full-root zero systems; no move is +assumed to preserve the removed frame or live support labels. + +The largest face on at most six simple nodes has 36 full root lines. The +seven-node face counts are 42,28,22,14,16,23,37,63. The last face has a single +normal root line. If the rational span Z of the live roots perpendicular to +a qualifying K-normal had rank at most six, choose a generic real normal +to Z avoiding all other root hyperplanes. Such a choice exists because a +finite union of proper hyperplanes cannot cover a real vector space. Its +perpendicular roots span Z, so its chamber face has rank at most six. +But it has at least 112-60=52 perpendicular live roots, contradicting 36. + +Thus Z has rational rank seven. Rational minors and Gaussian elimination +preserve this rank over any characteristic-zero K; its one-dimensional +rational kernel extends to the kernel over K and contains h. A rational +generator is real and has at least 52 perpendicular roots. Of the listed +seven-node faces only the 63-line face can occur. Its normal is a root, +and inverse reflection transport preserves the signed root set. Therefore +h is a K-scalar multiple of one of the 120 rational root normals. No embedding +of K into R or C is assumed. Direct evaluation gives support 53 for each +of the 112 live normals and 56 for each of the eight frame normals. + +## 2. Exact completion cuts, including frame normals + +For each root normal a and every binary seven-space V define + + C(a,V) = Off(a)\Lambda(V), + +where Lambda(V) is the live root trace of V. A normal qualifies under S +exactly when C(a,V) subset S for some V. This includes arbitrary partial +supports: extend their residual binary span to a seven-space. The primary +tests all 120*43,435=5,212,200 normal/space pairs. The root-word trace maximum +is 32. The complete records with |C(a,V)|<=24 are: + +| Normal type | Cut size | Records | +|---|---:|---:| +| Live | 21 | 336 | +| Live | 23 | 5,376 | +| Frame | 24 | 504 | + +There are 6,216 records and 6,188 distinct cuts. There are no other cut +sizes at most 24. Each of the 336 size-21 cuts has exactly one record, +hence one normal owner. Retaining frame normals is necessary at size 24. +Complete sorted record and flat-multiplicity digests, not just maxima, are +reconstructed and compared in RESULT.json. + +## 3. Why the finite common-cut test covers every S + +Make a graph on the 336 size-21 cuts, joining two distinct cuts when their +union has size at most 24. Exact comparison of every pair gives 168 edges, +each vertex of degree one: the graph is a perfect matching. Therefore no +set S of size at most 24 can contain three distinct size-21 cuts. Since +these cuts have single owners, they admit at most two normal directions. + +To cover any remaining possibility, enumerate all size-23 and size-24 cuts, +and all unions of one size-23 cut with any completion cut whenever the union +has size at most 24. These give exactly 8,540 candidate sets: + +| Size | Admitted normal directions | Candidate sets | +|---:|---:|---:| +| 23 | 1 | 5,376 | +| 24 | 1 | 448 | +| 24 | 2 | 2,716 | + +Suppose S admitted at least three distinct normals. Select one contained +completion cut for each. They cannot all have size 21 by the matching. +If a selected cut has size 24, it equals S and is a candidate. Otherwise +a selected cut B has size 23. If all selected cuts lie in B, B already +admits the normals and is a candidate. If some selected cut T does not +lie in B, then B union T has size 24, equals S, and is an enumerated +candidate. All cases contradict the table's maximum two. Arbitrary unused +sites in S do not invalidate this argument. It does not replace one common +cut by separately chosen cuts for different directions. + +The theorem follows over every characteristic-zero K because section 1 +reduces all directions to rational root lines. The pair witness lists the +actual live labels, root normals, seven-space trace masks and a positive +Gram determinant. Direct residual-label ranks verify its attainment. + +## 4. Two different literal caller bindings + +Let T be the span of either eleven-piece list in the corollary, with +D=T intersect C and dim D>=5. The quotient T/D has dimension at most six. +The first six pieces have support-cap sums + + 4*2+4+12=24, 4*2+8+8=24. + +Ranks two, three and four permit at most 2,4,8 leading-one points. The +rank-five capacity 12 is Nick Petalas's prior bound and is independently +rechecked on all 3,309,747 binary five-spaces here. Since 24<53, every +nonzero combination of these six independent pieces has support below +the code distance and cannot be a codeword. Their quotient images are +independent, so the quotient dimension is exactly six and dim D is exactly +five. Let S be their ONE actual support union, of size at most 24. + +For each of the five remaining weight-seven pieces q_y there is a unique +a_y in the six-piece span with c_y=q_y-a_y in C. These five codewords are +independent: their coefficients on the five distinct nonbasis pieces are +the identity matrix in the original independent piece basis. Injective +evaluation gives five independent h_y. Outside S their supports are subsets +of support(q_y), of binary rank at most seven. The theorem allows at most +two projective directions, contradicting five independent directions. +Coefficients, overlaps and cancellations are unrestricted over K. + +The pinned PR3154 filter is retained in canonical main by PR3282. Both +literal lists satisfy its necessary conditions and have +sum(w-2)=29<30. No failed sufficient filter is interpreted as a construction. +This proof does not assert that the two lists were the only publicly open +profiles or that (5,6) is closed. + +## 5. Independent implementation, predecessor credit and limits + +The primary uses the table model adapted from this donor's PR3951 and a +reversed-column annihilator enumeration. The separate checker imports no +primary or predecessor executable. It constructs the E8 shell, uses Cramer's +rule with integer Bareiss determinants for the labels, and enumerates all +10,795 binary six-spaces in F2^8 and their four affine cosets. These 43,180 +affine sections, plus 255 leading-zero seven-spaces, reproduce the entire +flat-multiplicity inventory and every critical record. + +Its common-cut composition uses different joins: size-23 cuts sharing a +22-subset, and size-23/21 pairs sharing a 20-subset. Admission is checked by +looking up the candidate's 21-,23- and24-subsets. Complete candidate/admission +digests agree with the primary union and per-normal containment loops. +This is computational corroboration in the same author/assistant context, +not independent human or formal-kernel acceptance. + +Credit Nick Petalas for the retained global capacities, root geometry, +root-shortening and shared-cut predecessors, including PR3163/3282/3289; +DreamingOfClouds/PR3154 for TWOSIDE and C5, David Arias for the quadratic model, +joaqcoo and the retained E8/P112 lineage. PR3931 already supplies a common23 +bound of three and a different caller; its adjacent 2^3,3,5,7^5 application +requires only cut22 and is not a new geometric theorem here. PR3951 supplies +the previous dependency audit and chamber/field argument. The new result is +the common24 bound and these two caller applications. The donor's adapted +model is credited, not presented as newly independent relative to PR3951. + +No full C5, complete decoder reduction, physical/supplier or multiplication +theorem, selected cold replay, new kappa, independent human review or formal +proof-kernel verification follows. Frozen predecessors and the selected +record remain unchanged. New work: Chris R / Clear1nsight, with substantial +OpenAI Codex assistance, Apache-2.0. diff --git a/research/p112-b5-caller-inventory/verify.py b/research/p112-b5-caller-inventory/verify.py new file mode 100644 index 0000000000..8828d3fa41 --- /dev/null +++ b/research/p112-b5-caller-inventory/verify.py @@ -0,0 +1,130 @@ +"""Source-bound conditional caller composition. Apache-2.0; Codex assistance.""" +from pathlib import Path +import contextlib +import hashlib +import io +import itertools as it +import json + +P = Path(__file__).resolve().parent +R = P.parent.parent +CAP = {2: 2, 3: 4, 4: 8, 5: 12, 6: 20, 7: 36} +RULES = ('rank6_29', 'rank5_47', 'six_support20_30', 'beta7p2', 'common23', 'common24') +SOURCE_DIGEST = '16c1e48186e42951b1ec39a79b51b637a9b5c064bb446e318807e3c695d57815' + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def authenticate(): + raw = (P / 'SOURCES.json').read_bytes() + require(hashlib.sha256(raw).hexdigest() == SOURCE_DIGEST, 'source inventory changed') + src = json.loads(raw) + for rec in src['files'] + src['retained_files']: + if rec['usage'] == 'provenance': + continue # Registered metadata verifies historical Git provenance. + path = (P if rec in src['retained_files'] else R) / rec['path'] + data = path.read_bytes() + require(hashlib.sha256(data).hexdigest() == rec['sha256'], 'changed input: ' + rec['path']) + blob = hashlib.sha1(b'blob ' + str(len(data)).encode() + b'\0' + data).hexdigest() + require(blob == rec['git_blob'], 'changed Git blob: ' + rec['path']) + return SOURCE_DIGEST + + +def domain(t): + return [w for n in range(5, 6 + t) for w in it.combinations_with_replacement(range(2, 8), n)] + + +def historical(w): + require(tuple(sorted(w)) == tuple(w) and all(type(x) is int and x in CAP for x in w), 'invalid weights') + if sum(x - 2 for x in w) >= 30: + return False + for k in range(1, 6): + keep = w[:len(w) - 5 + k] + g = sum(CAP[x] for x in keep) + t = sum(32 if x == 7 else CAP[x] for x in keep) + if k == 1 and g < 73 and t < 53 or k == 2 and g < 82 and t < 78: + return False + if k >= 3 and g < {3: 92, 4: 100, 5: 106}[k]: + return False + basis = w[:len(w) - 5] + if sum(CAP[x] for x in basis) < 53: + if sum(basis) <= 7: + return False + for bits in range(1 << len(basis)): + a = sum(x for j, x in enumerate(basis) if bits >> j & 1) + if a <= 6 and sum(basis) - a <= 6: + return False + return True + + +def attempt(w, rule): + n = len(w) + successes = [] + feasible_caps = [] + if rule in ('rank6_29', 'rank5_47', 'six_support20_30'): + m, rank, bound = {'rank6_29': (3, 6, 29), 'rank5_47': (3, 5, 47), 'six_support20_30': (6, 6, 30)}[rule] + for endpoints in it.combinations(range(n), m): + if any(w[i] > rank for i in endpoints): + continue + for small in it.combinations([i for i in range(n) if i not in endpoints], n - 6): + cap = sum(CAP[w[i]] for i in small) + feasible_caps.append(cap) + if cap <= bound: + successes.append({'endpoints': list(endpoints), 'small': list(small), 'deleted': [i for i in range(n) if i not in endpoints and i not in small], 'common_cap': cap, 'surviving_code_dimension': m - 1}) + else: + for basis in it.combinations(range(n), n - 5): + cap = sum(CAP[w[i]] for i in basis) + feasible_caps.append(cap) + if cap >= 53: + continue + if rule in ('common23', 'common24'): + if cap <= int(rule[-2:]): + successes.append({'basis': list(basis), 'common_cap': cap, 'quotient_dimension': n - 5, 'required_directions': 5}) + else: + for roles in it.product(range(3), repeat=len(basis)): + a = [i for i, role in zip(basis, roles) if role == 0] + b = [i for i, role in zip(basis, roles) if role == 1] + cut = [i for i, role in zip(basis, roles) if role == 2] + if sum(w[i] for i in a) <= 6 and sum(w[i] for i in b) <= 6 and sum(CAP[w[i]] for i in cut) <= 2: + successes.append({'basis': list(basis), 'roles': list(roles), 'basis_cap': cap, 'cut_cap': sum(CAP[w[i]] for i in cut), 'required_directions': 5, 'span_bound': 4}) + return {'successful_assignments': len(successes), 'minimum_capacity_sum': min(feasible_caps, default=None), 'witness': successes[0] if successes else None} + + +def compute(): + authenticate() + original = {} + source = R / 'research/p112-b6-t4-reconciliation/vendor/bk2b.py' + with contextlib.redirect_stdout(io.StringIO()): + exec(compile(source.read_bytes(), str(source), 'exec'), original) + cells = [] + for t in (5, 6): + candidates = domain(t) + accepted = [historical(w) for w in candidates] + old = [sum(x - 2 for x in w) < 30 and original['feasible'](w, 5) and not original['killed'](w, 5) for w in candidates] + require(accepted == old, 'historical filter disagreement') + rows = [] + for w, keep in zip(candidates, accepted): + if not keep: + continue + attempts = {rule: attempt(w, rule) for rule in RULES} + primary = next((r for r in RULES if attempts[r]['successful_assignments']), None) + rows.append({'weights': list(w), 'strict_excess_deficit': 30 - sum(x - 2 for x in w), 'required_code_dimension': 5, 'attempts': attempts, 'primary': primary}) + cells.append({'cell': [5, t], 'domain_multisets': len(candidates), 'historical_survivors': len(rows), 'certified': sum(row['primary'] is not None for row in rows), 'primary_counts': {rule: sum(row['primary'] == rule for row in rows) for rule in RULES}, 'uncertified': [row['weights'] for row in rows if row['primary'] is None], 'rows': rows}) + require([c['historical_survivors'] for c in cells] == [38, 77], 'historical cells changed') + require([c['certified'] for c in cells] == [38, 76], 'fixed inventory coverage changed') + gap = [2] * 5 + [6] + [7] * 5 + require(cells[1]['uncertified'] == [gap], 'wrong inventory gap') + caps = [sum(CAP[gap[i]] for i in B) for B in it.combinations(range(11), 6)] + return {'schema': 'p112-b5-caller-inventory/v1', 'source_manifest_sha256': SOURCE_DIGEST, 'conditional_contracts': list(RULES), 'scope': 'Fixed conditional inventory; uncertified does not mean globally open or realizable. Cells are nested, not 115 distinct rows.', 'cells': cells, 'remaining_interface': {'weights': gap, 'piece_dimension': 11, 'required_code_dimension': 5, 'forced_code_dimension': 5, 'forced_quotient_dimension': 6, 'preferred_basis_indices': list(range(6)), 'preferred_basis_cap': 30, 'all_six_piece_subsets': len(caps), 'minimum_six_piece_capacity_sum': min(caps), 'required_independent_rank7_directions': 5, 'actual_union_minimum_claimed': False}} + + +def main(): + require(compute() == json.loads((P / 'RESULT.json').read_text()), 'committed result disagrees') + print('PASS_P112_B5_CALLER_INVENTORY 38/38 76/77') + + +if __name__ == '__main__': + main()