[commdata2338]

Change and mathematical scope

Add research/connector-capacity-parity-audit/, a scoped proof and independent implementation audit of Engine::capacity, the parity-capacity filter in conorholds' retained connector-covering-code source (its simple length-22 exclusion).

The predicate is necessary for simple restored universal words in its four-low/three-high projection, including repeated low vertices: the pair counts include pairs between different blocks at the same low vertex. Direct position-pair enumeration agrees with the actual compiled predicate on 791,827 declared gap inputs; 53,379 pass the capacity relaxation, with no claim that these are realizable words. The proof also identifies sixteen low-linear parity changes that preserve the verdict; full-word time parity is one of them.

A concrete scope control matters: the credited universal word 010201030102010345464546 has 24 steps and 23 distinct prefixes. The predicate rejects it because nine positions at low zero represent only eight distinct high states. This disproves extending the predicate to arbitrary restored words; it is not a predecessor bug or a counterexample to the length-22 exclusion. The predecessor excludes repeated-prefix length-22 candidates by separate arguments (sections 2 and 3 of its README) and applies this filter only to simple cycles.

The package reconstructs #2973's 01021323 as credited calibration and pins the affected #2542/#2634/#2691 call sites. Their old bit-0-filter receipts remain invalid exclusion evidence; #2973/#3005 supply separate corrected evidence already on main. This audit neither reruns those complete censuses nor establishes the successor's complete f(7)=24 claim. No supplier, tariff, selected frontier or kappa change.

Task and overlap

Base and refresh checkpoint: 463113d, priority revision 6. Canonical main was fetched again at 2026-10-17 17:44 UTC and was unchanged, including the guidance, selected record and relevant scientific sources. Contribution commit: 69567e40e8d92542248eda0d6a400d83adc1d3a3.

The claim is in discussion #1317, comment 19001874, following #2973's released length-22 question and its newer main successor. Full structured task metadata is in TASK.json.

Task-card field	Scope
Task / track / scope key	census-pruning-audit / adversarial-audit / f4a1c1da9a553967d3c6/connector-covering-code-capacity-slot-pairs
Selection	Handoff-first read of #1166/#1317; specific-card lookup nonce 9002c0620e3b764139af9b103bec4b66.
Scope status	Refined: the tiny counterexample and full independent length-20 replay already exist; audit one successor predicate instead of reconstructing them.
Exact object and question	Does the actual capacity predicate implement necessary high-parity pair counts, including pairs across equal-low blocks, and where is its simple-word premise essential?
Method and bounded domain	Written necessity/gauge proof; independent literal slot pairs versus the actual native method. Five A templates with eight gaps in 0..3 summing to 14; 77 B templates with ten gaps in 0..2 summing to 12; all boundary vectors with at most two nonzero gaps, each in 1..8; explicit universal controls.
Milestone / cost decision	Audit. No physical construction or cost gain; unknown consumer/restoration/hosting costs stay outside scope. Narrow and stop, with no family expansion.
Success / falsification / stop	Require exact source-oracle agreement and nonvacuous positive/failure controls. Stop at this predicate; no complete word search, template-completeness proof or classification replay.
Artifact / reproduction	Package above; python3 -I -B scripts/research_package.py --package research/connector-capacity-parity-audit.

Exact predecessor heads (the audited input bytes were compared with these heads):

Contribution	Head
conorholds' connector-covering-code main introduction	e67ca5f26351e09c5bb314821633e511212f88ec
#2542, Aaron Wang	3b6011d2400f50ab0ad9e105c7c55a18f3cef4cf
#2634, Aaron Wang	e2f30d93efbef5658334072aa855aa95e795e394
#2691, Nicholas Stone	88dda3534071442773106e9c0b941b9d39a3cea8
#2973, Nicholas Stone	d48f3945dbb1ef5d06835744c4082b3bd04181c0
#3005, Nick Petalas	68e67922294d96a42f479f80fdc352eb04a9b550

SOURCES.json records Git blobs and SHA256 pins. The native source SHA256 is 597844fc32cde19c1d4104633fa6d3eb0d28c1ca140f8f3d2ba2cb632ecd30d1. Frozen packages are unchanged.

Overlap queries were --task census-pruning-audit and connector-covering-code / parity capacity. The final offline snapshot covered 251 open PRs at 2026-10-17T17:37:12.534077+00:00 and 2,015 Discussions records at 2026-10-17T17:39:04.580509+00:00, both with complete pagination. Offline coverage can miss later changes. Main was checked as well.

Nearest work: #2973, #3005, and James Reed's #3096 (f7-bit0-false-prune) already cover the historical correction and small word counterexample. The concurrent actual-size set-enumerator audit (#3215, claimed in comment 19001818) concerns old joint_covers; this package concerns the newer projected-word capacity predicate. conorholds' existing tests and AI source audits are credited, including its repeated-origin control, which the path search's same-low disjointness rule rejects; this adds a separate direct slot-pair oracle, the parity-change lemma and an executable simple-only boundary for the capacity predicate itself. It is not a second complete B exclusion.

Validation

On CPython 3.12.3 and GCC C++ 13.3.0, the registered replay (ordinary and optimized verify.py, then check_failure_controls.py) passed in 14.703 seconds, and the metadata/pins and committed-byte checks pass:

python3 -I -B scripts/research_package.py --package research/connector-capacity-parity-audit --check-only
python3 -I -B scripts/research_package.py --package research/connector-capacity-parity-audit
python3 -B scripts/check_research_commit.py --package research/connector-capacity-parity-audit

Observed from the registered replay:

PASS_CONNECTOR_CAPACITY_PARITY cases=791827 accepted=53379 positive_projections=176 gauges=2816 python_queries=1282 repeated_prefix_control=1 no_full_census
PASS_CONNECTOR_CAPACITY_PARITY cases=791827 accepted=53379 positive_projections=176 gauges=2816 python_queries=1282 repeated_prefix_control=1 no_full_census
PASS_CAPACITY_FAILURE_CONTROLS source_pin=1 native_mutants=2 malformed_query=2 receipt=1
PASS_REGISTERED_RESEARCH_PACKAGE research/connector-capacity-parity-audit outcome=completed

Evidence:

• 791,827 native/source-oracle comparisons, no disagreement; exact domain sizes independently computed by generating-function coefficients or closed counts.
• 176 genuine universal simple 24-step projections pass, including 120 with repeated low vertices; 2,816 parity-bucket permutation checks.
• 1,282 separately specified Python/native queries; the universal repeated-prefix boundary is additionally checked against the actual predicate.
• Parity-reset and omitted-equal-low-pair mutants change 1,148 and 542 B-core verdicts. The two explicit fixtures change C(6,1) from 4 to 3 and C(0,0) from 6 to 2; these are gap fixtures, not word witnesses.
• Actual native parity-reset and relaxed-fiber-cap mutations discriminate in private copies. Source hash changes, a corrupted fresh receipt and truncated native queries reject. These checks also run with Python -O.
• All four native domain rows match under AddressSanitizer and UndefinedBehaviorSanitizer with no diagnostics (-O1 -g -fsanitize=address,undefined -fno-omit-frame-pointer).
• Eight exact predecessor-head byte comparisons, package metadata/pins, git diff --check, and committed-byte preflight for all 18 package/input files pass.

No hosted CI, complete n=7 word census, full successor proof, published classification proof, formal-kernel check or independent human review is claimed. The source template generator supplies the 82 tested low templates; this audit does not prove that generator complete. Remaining path tables, propagation, symmetry reductions, non-simple branch and physical/all-size obligations remain open to separate review.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. conorholds supplied the successor predicate, finite exclusion and simple 24-step fixture; Nicholas Stone supplied #2691/#2973 and the tiny counterexample; Nick Petalas supplied #3005; Aaron Wang supplied #2542/#2634 and later set-level work. Ross Richardson supplied the #943 model. Douglas Colkitt (@Mister-Meeseeks) supplied #1185 and the retained Gray upper witness. James Reed (jwr) supplied the earlier #3096 tiny audit; its calibration is not presented as new. Apache-2.0 and predecessor attribution are preserved.

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

Independently check the successor's remaining B path-domain propagation rules with explicit endpoint, same-low disjointness and conditional-coverage controls. Only after those pass should a separately budgeted complete B replay be proposed. The published covering/classification premises and non-simple branch remain distinct obligations; this predicate proof cannot discharge them.

Workflow feedback (optional)

The revision-6 card has empty existing_checks even though main contains #3005 and the tiny audit. Populate that field with their precise coverage and the newer successor's still-unchecked implications, so the next session starts at the remaining obligation instead of rediscovering the counterexample.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG