Research: audit PR #2542's set/word pruning and refute its minimum-length degree-filter justification

[commdata2338]

Change and mathematical scope

The retained PR2542 joint_covers documents weight-parity splits but actually enumerates coordinate-bit-0 classes. Its actual-size pruning survives the parity objection, as #2973's MATH.md section 4 already states and this package checks on the actual function; its separate assertion that minimum-length universal words justify a degree-two filter does not.

The concrete counterexample is the predecessor's Gray word 010122: its six steps restore, its prefix set {0,1,2,3,4} covers all eight masks, and vertex 4 has degree one. Six is minimal because every label must occur a positive even number of times. The actual (3,2) call returns 18 covers with the filter disabled and zero with it enabled. The sufficient simple-cycle hypothesis is |P|=L>=4. This is a counterexample to the interface claim, not a new construction or bound.

The new package research/f7-set-word-pruning-boundary/ adds a written actual-size pruning argument and a direct subset oracle: all 32,906 zero-containing sets in dimensions 1–4, 200 exact split/filter comparisons, including asymmetric and empty domains. It reconstructs PR2973's known 01021323 counterexample and gives an explicit witness for #2973's remark that a general linear change of coordinates need not preserve cube adjacency: the linear map aligning weight parity with bit 0 isolates a vertex of that witness in the original cube graph.

A source-bound inventory isolates six Python calls and PR2691's native rule that repeat the invalid word budget. Four retained set-search callers leave the optional degree flag disabled. PR2773's separate set modules import only standard-library code; its row arithmetic is reproduced without the word engine, conditional on separately recorded Sidon floors. Those large floor censuses and the corrected n=7 word censuses were not rerun. Frozen predecessors and the selected frontier are unchanged.

Task and overlap

Task: census-pruning-audit; priority revision 6; scope refined from 641feda6be471c89abb9 to pr2542-joint-covers-actual-bit0-all-subsets-n1-4. The full task card is in TASK.json. The claim is in discussion #1317.

• Base and final refreshed main: 463113d675af7410ac91d53a4fed51ec6494eb9a. Contribution commit: 00b4f73cd0ea0ea7639288d3bdb59010fa66c299. Refresh found no upstream changes.
• Object/question: the actual set-enumerator contract, optional adjacency restriction, and boundary to invalid word-exclusion evidence.
• Method/domain: every zero-containing subset of F2^n, n=1..4, every actual bit-0 split, both degree settings; forced-word and linear-map controls; six named Python caller files plus the native rule.
• Milestone/stop rule: scoped audit and finite certificate. Stop after the dependency boundary; no large census, supplier implementation, cost saving or kappa claim.
• Success/falsification: exact returned-set equality to an unpruned oracle, positive witnesses, semantic mutants and explicit source/cap failures. No physical consumer or restoration-cost contract is proposed.

Exact predecessor heads, whose named engine bytes match the retained base:

PR	Head
#2542	3b6011d2400f50ab0ad9e105c7c55a18f3cef4cf
#2634	e2f30d93efbef5658334072aa855aa95e795e394
#2691	88dda3534071442773106e9c0b941b9d39a3cea8
#2773	6739c799799621878a9249c93e2b12cc799c1482
#2973	d48f3945dbb1ef5d06835744c4082b3bd04181c0
#3005	68e67922294d96a42f479f80fdc352eb04a9b550

Nearest coverage: #2973 already derives the parity correction, states that bit 0 is valid for a set-level census at actual class sizes, and lists the affected word-census files in prose; James Reed's #3096 (research/f7-bit0-false-prune) already audits small words; #3005 already supplies the independent full n=7 implementation. This package audits the actual set API and degree implication. The concurrent connector-covering-code investigation concerns a different projected length-22 capacity rule.

Overlap queries: --task census-pruning-audit; joint_covers, set-level boundary, bit-0 split; 010122, require_min_degree, minimal length walks. Final complete snapshots: open PRs 2026-10-17T17:26:19.594925+00:00 (249 records); Discussions 2026-10-17T17:27:03.117721+00:00 (2,001 records). Offline freshness warnings apply; local main was also inspected. Searches do not cover every diff or establish novelty.

Validation

Python 3.12 standard library:

python3 -B scripts/research_package.py --package research/f7-set-word-pruning-boundary
python3 -I -O -B research/f7-set-word-pruning-boundary/verify.py
python3 -B scripts/check_research_commit.py --package research/f7-set-word-pruning-boundary

All pass. The registered replay runs the audit and all six failure-control tests. Expected marker:

PASS_F7_SET_WORD_BOUNDARY sets=32906 comparisons=200 degree_counterexample=010122 no_new_kappa

Cover counts for n=1,2,3,4 are 1,4,64,23552; degree-two subcounts are 0,1,20,5074. Comparisons use complete returned witness sets and deterministic digests. Source hashes are checked before loading original bytes, and the set census runs with the old word entry point replaced by a raising function.

Controls detect a balanced-size budget mutant, cap completion misuse, source corruption, wrong partitions, duplicate results, a newly enabled degree-filter caller, and changed/missing receipt fields. The staged whitespace check passed. Committed-byte preflight covers seven package files plus fourteen live inputs.

Not checked: full n=5 controls, large Sidon floor censuses, full corrected n=7 word replay, all repository call paths, formal-kernel proof, hosted CI, selected supplier cold replay, physical supplier admission or a multiplication theorem.

Credit

Ross Richardson: PR943 model. Aaron Wang: PR2542/2634 engines, Gray construction and PR2773 set-level work. Nicholas Stone: PR2691 and PR2973's correction, its set-level scoping and 01021323. Nick Petalas: PR3005 independent word census. James Reed (@jwr404): PR3096's prior tiny false-prune audit. Douglas Colkitt: retained project and contribution framework. The new result is the degree-contract counterexample, actual set-interface comparison and dependency audit; no priority over the credited constructions or corrected f(7) claim is asserted.

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

The README and TASK.json give two bounded follow-ups: define a maintained actual-size set API separately from a |P|=L>=4 simple-cycle API; and route historical exclusion requests through corrected evidence while preserving old counter-reproduction paths. The named caller inventory is the first step. Scientific review of full n=7 receipts and large Sidon floors remains separate. No new length-22 search is proposed.

Workflow feedback (optional)

Handoff-first reading prevented duplicating PR3005. The catalogue's empty existing_checks should link PR2973, PR3005 and PR3096's tiny audit, distinguishing completed implementation coverage from remaining contract/source-impact questions.

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