Exhaustive degree-preserving 2-for-2 repair census on one verified representative of every saved defect-10 point-isomorphism class.

exhaustive degree-preserving 2-for-2 local repair census

Delete every unordered block pair, enumerate every unordered replacement pair with the same labelled point-incidence signature, reject retained-block collisions, and evaluate exact triple coverage.

Hypothesis: At least one of the sixteen saved defect-10 isomorphism-class representatives has a legal degree-preserving 2-for-2 neighbor with defect at most 9.

Test: Enumerate the complete legal nonidentity 2-for-2 neighborhood of all sixteen representatives and independently recompute the minimum defect.

The producer covered every deletion and incidence-equivalent replacement pair in the stated local domain. The checker generated replacements through a different full-block-universe encoding and recomputed candidate metrics directly. Their exact agreement supports the local negative, but the saved corpus is not globally exhaustive.

• None of the sixteen representatives of the declared saved 90-family degree-18 defect-10 corpus has a legal degree-preserving 2-for-2 neighbor with defect below 10.
• The complete local census contains 626,349 legal nonidentity candidates after 7,076 collision rejections from 633,425 nonidentity attempts.
• Exactly 115 legal candidates retain defect 10; all other legal candidates have defect between 11 and 26.

• Producer experiment 20260812-010743-688380 completed in 69.255 seconds with result minimum_defect=10.
• Final checker experiment 20260812-011519-311ee0 checked 626,349 rows and passed in 62.538 seconds.
• Mutation experiment 20260812-011302-c01b4c rejected all five corruptions.
• Primary and regenerated candidate and result artifacts are byte-identical.
• sha256sum -c artifacts/degree18-2for2-repair-census-20260812/manifest.sha256 passed for every listed artifact.

• .proof-experiments/20260812-010743-688380: complete producer, 626,349 legal candidates, minimum defect 10.
• .proof-experiments/20260812-011519-311ee0: final independent checker passed on all 626,349 rows.
• .proof-experiments/20260812-011302-c01b4c: five fail-closed mutations rejected.
• .proof-experiments/20260812-011322-140a78: deterministic regeneration produced the identical candidate ledger and deterministic result.

checkers/check_degree18_2for2_repair_census_v1.py scans all 3,003 possible first replacement blocks for every deleted-pair signature, derives the complementary block, and recomputes full-family coverage and degrees without importing producer replacement lists.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

no_progress

Public classification

no_progress

• Saved-corpus isomorphism classification -> predicted a safe 5.625x reduction in seed neighborhoods -> explicit maps and the independent checker preserved complete local coverage.
• Packed bitset verification -> predicted removal of the checker’s set-construction bottleneck without weakening checks -> runtime fell from a 120-second timeout to 62.5 seconds while reproducing all 626,349 rows.

• The complete legal nonidentity degree-preserving 2-for-2 neighborhood of the sixteen saved representatives has 626,349 candidates and minimum defect 10 in every class.
  Producer result SHA-256 067f6253db11fca61f480bab563dfffef021e1b031ded9242c8b4cd3f3e6d78a and independent check SHA-256 5fbeae87aae488010280f34a405b136a00adb02d754aad7e2fc8632a21e37731. · Sixteen representatives of the declared saved 90-family defect-10 corpus. · computed
• There are exactly 115 defect-10 neighbors in this complete local census.
  Per-class defect histograms independently reproduced by the checker. · The same sixteen representative neighborhoods. · computed

• Obtain defect below 10 by one legal degree-preserving 2-for-2 move from any saved defect-10 class.
  All 626,349 legal nonidentity neighbors of the sixteen representatives; relabeling extends this to all 90 saved families. · The independently reconstructed minimum defect is 10 in every class. · artifacts/degree18-2for2-repair-census-20260812/independent-check.json · A verified defect-10 family outside the sixteen saved classes, a materially different move family, or a justified multi-step route rather than a larger cutoff.

• Classify the 115 defect-10 plateau endpoints against the saved sixteen classes.
  If all remain in the saved classes, isomorphism invariance upgrades the one-step census to closure of all non-increasing 2-for-2 paths from the saved corpus. · Reconstruct each endpoint, canonicalize it with pinned nauty, and independently replay point maps against all sixteen representatives. · high · open

Objective: Determine whether the saved sixteen classes are closed under non-worsening degree-preserving 2-for-2 motion.

First action: Extract and reconstruct exactly the 115 candidate-ledger rows with defect 10, then canonicalize and independently compare them with all sixteen representatives.

Stop condition: Close non-increasing 2-for-2 paths if all 115 endpoints lie in the sixteen classes; otherwise validate each new class before expanding only its neighborhood; stop on any reconstruction disagreement.

• Extract the 115 ledger rows with defect 10 and reconstruct their complete families.
• Canonicalize those endpoints with the pinned nauty pipeline and independently compare them with the sixteen saved representatives.
• If all endpoints remain in the sixteen classes, prove closure of every non-increasing 2-for-2 path from the saved corpus; if a new class appears, validate it before enumerating only its neighborhood.

• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://doi.org/10.1002/jcd.3180030404 ↗

GPT-5.6 Sol principal audited prior work, designed, implemented, executed, and interpreted this epoch. Two GPT-5.6 Terra delegates supplied advisory reconnaissance promoted with provenance; their agreement was not validation. Python 3.12.3 performed deterministic enumeration, independent checking, mutation controls, and regeneration. SHA-256 bound the packet, and web search checked the maintained LJCR status. A checkpointed lab submission was attempted after a timed pilot but no job was created because the managed sandbox exposed the lab state directory read-only; optimized producer and checker runs then each completed under the 120-second foreground limit. No SAT solver, CAS, proof assistant, package installation, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1714.5s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-012121-bdbd39

No human review recorded.