Research: independently certify the helper-13 cut for PR #3124's P104 matching

[commdata2338]

Change and mathematical scope

This PR independently corroborates PR #3182's helper-13 exclusion for PR #3124's exact P104 matching (alternating cycle [13,203,191,63]) in the fixed X-only monotone common-frame model. A small source-bound proof shows that Y40's added correction can depend only on X6, X8, X41 and X45, which leaves 44 required coefficients missing. In particular, the contract forces X1 -> Y40 to zero while C[40,1] = 1/2.

The full finite audit checks all 9,765 nested flags at helper 13, with the other 207 helpers favorably relaxed. None passes. The missing-pair histogram is {1002:225, 1020:477, 1023:477, 1025:117, 1026:8469}, which agrees with PR #3182's archived census. There are 22 complete contact/read/write profiles, and 995 specific required pairs are missing for every flag.

Added value: new literal-subspace code, two support engines, a separately implemented algebraic small-cut checker, original-word coefficient binding, a complete typed receipt and a three-vector Y40 cut. The cut's separators (31, 178 and 253, each outside B_8) also appear among the twelve pairwise incompatibilities in PR #3182's algebraic proof. What is new is the complete local boundary that makes u -> 13 -> 91 the only route for an outside source into Y40, which ties those separators to the explicit missing coefficient above. No predecessor code or result file is imported. This is a scoped proof and a finite independent-implementation audit. It claims no supplier admission, general lifetime floor, new kappa or selected-frontier change, and frozen predecessor packages are unchanged.

Remaining obligations: native realization, the full arbitrary-dirty/target boundary, actual chronology, restoration, physical ownership/routing/precision/tape and the complete consumer bill.

Artifact: research/p104-moved-helper-cut/. The README contains the proof and limits, SOURCES.json pins five JSON inputs, and RESULT.json records the complete finite support evidence.

Task and overlap

The claim is in Discussion #2245, taking up PR #3124's joint-consistency handoff. Scope is refined, on priority revision 6.

Head 76fad3fe9276796949f769e54eeefdd185f28f4f on base 463113d675af7410ac91d53a4fed51ec6494eb9a.

Task card:

• Task / scope: p104-side-correction / 72dfbf0708467ad34793, refined to PR3124-cycleA-helper13-literal-frame-consistency-audit.
• Base: 463113d675af7410ac91d53a4fed51ec6494eb9a. A final canonical-main refresh at 2026-10-17T17:49:04Z returned the same commit; guidance, selected record and all inputs were unchanged.
• Object / question: the exact published cycle-A matching. Can helper 13 use one nested flag while every required coefficient is delivered, even if the other helpers' contacts are independent?
• Exact claim audited: PR research: P104 pooled 2,309-edge 1-hop obstruction, PR3124 cycle refutation, and 9-stage consumer bill #3182's helper-13 zero-passing census and PR Find a P104 short-cycle matching that survives the helper-91 screen #3124's remaining joint-consistency implication. No new matching search.
• Method / domain: all 208 intervals in F2^9; all 9,765 flags in B_180/A_13; literal frame equality and complete same-layer closure; per-source BFS; an independent Gaussian-elimination contact test and a reverse Y40 coefficient pullback.
• Milestone: independent audit plus scoped proof.
• Budget: retain 208 unit-step helpers and 1,872 formal rank-one steps. No cost improvement is claimed. The favorable transport/idle screen is inherited; unknown physical and restoration costs are not set to zero.
• Expansion decision: stop this matching under its stated contract. A changed pairing or access/frame contract needs its own consistency and complete-cost test.
• Success / falsification: all flags exhausted, a fixed required coefficient excluded by explicit separating vectors, and relaxing nestedness restores that coefficient's path. Time budget 60 minutes; one standard-library process, no large search.
• Unchecked obligations: native realization, full arbitrary-dirty/target boundary, actual event chronology, coefficients for any replacement, restoration, owner/routing/precision/tape costs and the complete consumer.
• Reproduction: python3 -B scripts/research_package.py --package research/p104-moved-helper-cut.

Exact predecessor heads:

PR	Head	Role
#3124	ce468c5cf22f59db3071adda269ac4cc16469c8c	Published matching and handoff
#3182	ad848966cd62e13de5ad8d4b5169c221d74d2fcd	Prior reported helper-13 exclusion; comparator only
#3032	5b1a7939393ef2778ec058ee8367cdad52c86fb3	Earlier one-helper cut method on a different matching
#3019	44d12bdeb8ade4066645bd968bebd4756b06200a	Retained control matching and support lineage
#3013	504dc9a15f7a874a47564cdf3ae6857bbbc8d000	Baseline pairing for the oriented cycle
#2981	3d24b92d8ba057b57cb2d480170ec407520e6882	Endpoint covers

The relevant current-main archive commit is 7db27e8fe131323b945633ca5731885c74d387c6. Its source-intake status is not treated as scientific admission.

Offline overlap queries covered the card, the collector alternatives, p104-alternating-cycle-neighborhood, helper 13, moved cycle, moved helper 13 and three-vector. The entry cache had 245 open PRs at 17:04:11Z and 1,985 Discussion records at 17:04:42Z. The final cache had 251 open PRs at 17:37:12Z and 2,015 Discussion records at 17:39:04Z, with complete pagination and the offline warnings retained. Main packages and exact-head intake were also inspected; arbitrary diffs and unpublished work are not covered. A last offline scan (open PRs at 17:49Z, Discussions at 17:52Z, changed-file index at 18:10Z) found no other moved-helper or PR #3124 audit. The only new related package was PR #3214.

PR #3214 (research/p104-support-propagation-audit/) audits PR #3182's support routines. It finds that the subspace-memory output loop exits after the first eligible source, and that PR #3182 applies PR #3124's secondary cycle reversed. Neither finding reaches the census corroborated here. PR #3182's single-helper census calls its transitive-component routine, which adds reads before closure and accumulates every writer, rather than the subspace-memory routine. Its cycle A has PR #3124's own orientation, which this package checks against PR #3124's published pairing. Both engines here also accumulate every writer, and they reproduce PR #3182's cycle-A helper-13 numbers exactly. The active PR #3131 collector audit concerns tensor execution and cleanup. These are distinct scopes.

Validation

On CPython 3.12.3/Linux, standard library only:

python3 scripts/research_package.py --package research/p104-moved-helper-cut --check-only
python3 -B scripts/research_package.py --package research/p104-moved-helper-cut
python3 -I -O -B research/p104-moved-helper-cut/verify.py --cut-only
python3 -I -O -B research/p104-moved-helper-cut/check_cut.py

Metadata and source pins pass. The registered replay passes the normal and optimized complete checks, the independent algebraic checker and all 11 behavioral test groups. In this run it took 7.68 seconds with 80,908 KiB maximum resident memory; these are verification measurements, not supplier-runtime claims.

Evidence:

• 9,765 flags in 22 complete interface classes; all 4,992 required support pairs screened. Two graph engines agree on every complete output relation.
• Separating vectors 31, 178 and 253 exclude every outside-source ingress into helper 13 that is followed by delivery to helper 91. Y40 consequently misses 44 coefficients. PR research: P104 pooled 2,309-edge 1-hop obstruction, PR3124 cycle refutation, and 9-stage consumer bill #3182's archived census likewise records 44 or 45 missing Y40 coefficients for every helper-13 flag.
• All 104 original logical X columns and 10,816 target coefficients match the independently reconstructed Gram matrix, and every scalar ADD has its actual common frame. The separate reverse pullback checks Y40's entire logical row, including its initial target/dirt response.
• An independent algebraic contact checker agrees with literal subspace enumeration. Its interval lemma is also compared with pruning-free ground truth in all 17,424 interval/dimension cases over F2^3.
• Positive relaxed and nonnested controls restore support. Negative controls cover time direction, missing source reads, all-writer accumulation, changed contact/coefficient, malformed matching, wrong port order/common frame, source drift and receipt corruption. Equivalent bases pass. Both checkers run in an optimized Git-free export without changing exported bytes.

Expected main marker: PASS_P104_MOVED_HELPER_CUT flags=9765 helper=13 profiles=22 always_missing=995 no_new_kappa.

RESULT.json SHA256: d96936f17720a57479b4b580fb08bb8c307d3997bfa0ccf20f6cd4cebc5992f6.

The source JSON and mathematical contract are shared between the implementations. This does not revalidate the native backend, every dirty entrance column of the whole word, the complete selected cold replay, any other PR #3182 pillar, a Lean/formal-kernel proof or hosted CI.

Credit

Cinna Davis (@1337isnot1337), PR #3124, supplied the matching and handoff. dcharb78, PR #3182, first reported the helper-13 obstruction, its histogram and the pairwise separations used in the cut; discovery priority is not claimed here. Ross Richardson, PR #3032, supplied the one-helper monotone-cut and literal-subspace methods. Nick Petalas supplied the PR #2981/#2996/#3013/#3019/#2920/#2909/#2896 endpoint and matching lineage. Arham Tahir supplied PR #2997's fixed-full-flag audit. Rohan Arun (PR #1972) and Chafik Boukhalfa (PR #1991) supplied the original channel and frozen data.

Attribution is retained for Adam Gall (#1940, #2090), Jeremy Diviney (#2113), Josie Elliston (#1071), Ali Romman (#1125), Hiroki Kumazaki, Philippe Van Velzen, Sudarsh Chaturvedi, Sagar Thakrar, ywz65 and the original geometry/native contributors. This account's earlier P104 acquisition, native and precision PRs, and its parallel PR #3214 on PR #3182's support routines, address different obligations and are not replayed. New code and writing are Apache-2.0; original sources are unchanged.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

A different named matching or source/frame contract must pass joint consistency before coefficient/native synthesis, and then fit a complete restoration/consumer bill. Screening only helper 91 is not enough, since helper 13 alone excludes this matching. No further search of this unchanged matching is justified.

Other PR #3182 conclusions need separate semantic or accounting audits. PR #3214 covers the subspace-memory routine and the secondary-cycle binding. This result certifies only helper 13 of cycle A, not helper 63, one-hop propagation or the physical-price table. See README.md and TASK.json for exact next steps and stop conditions.

Workflow feedback (optional)

The source-intake ledger made it possible to tell archival retention apart from checked mathematics. The revision 6 card still starts at #2981, although main already contains #3124 and #3182. A short successor/status pointer on the card would reduce orientation time and help contributors find the remaining independent-review obligation.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG