Falsified the predeclared 120-class capacity premise for the q=6 special-star point-link bin by producing and independently classifying 121 valid links.

certified point-link frontier census

Fix the unique perfect-matching star, generate valid residual links, and compare exhaustive fixed-matching group canonicalization with independently replayed nauty forms.

Hypothesis: The 6,6,5^12 point-link bin with q=6 has at most 120 isomorphism classes and is small enough for the proposed frontier route.

Test: Either complete the bin within 120 classes or exhibit 121 valid pairwise nonisomorphic links under both exhaustive matching-group classification and independent nauty replay.

Each witness satisfies the exact residual degree and pair constraints. Exhaustive action of the full 46,080-element fixed-matching group proves pairwise inequivalence, and independent nauty replay agrees on classes and automorphism orders. The 121st class triggers the predeclared redirect condition.

• Every q=6 link has six common special blocks whose ordinary pairs form a perfect matching; the 10,395 labelled matchings form one orbit.
• The q=6, 6,6,5^12 link bin contains at least 121 isomorphism classes.
• The predeclared at-most-120 frontier capacity hypothesis is false.

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 scripts/run_q6_frontier_capacity_v1.py --output-dir artifacts/q6-frontier-capacity-20260809-v3 --dreadnaut /usr/bin/dreadnaut --seconds 75
• artifacts/q6-frontier-capacity-20260809-v3/independent-check.json reports 121 classes, 5,575,680 group actions, and 121 independent dreadnaut replays.
• sha256sum -c artifacts/q6-frontier-capacity-20260809-v3/manifest.sha256 returned OK for every entry.

• .proof-experiments/20260809-082251-cf2aa1: PASS in 32.04 seconds; 121 checked classes. Failed controls: 20260809-081344-de8f9f incomplete at 27 classes, and 20260809-082057-bc020b superseded for missing independent nauty replay.

checkers/q6_matching_group_check_v1.cpp independently exhausts C2 wr S6; checkers/check_q6_frontier_capacity_v1.py separately reconstructs every constraint, recounts matchings, replays dreadnaut, and compares automorphism orders.

not_requested

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

Original model outcome

progress

Public classification

progress

• Certified link classification in covering designs -> measure the smallest orbit bin before building global extension leaves -> the q=6 bin already exceeds the saved 120-class capacity, so literal aggregate refinement has better immediate value.

• There are exactly 10,395 perfect matchings on twelve labelled ordinary points, forming one S12 orbit with fixed-matching stabilizer 46,080.
  Recursive enumeration, factorial formula, and independent-check.json · q=6 star normalization · proved
• At least 121 q=6 links are pairwise nonisomorphic.
  representatives.txt plus exhaustive group codes and independent nauty forms · 6,6,5^12 C(14,4,2) links with q=6 · computed

• Continue the q=6 special-star census under a 120-representative frontier budget.
  The saved link-frontier-census-v1 capacity plan only. · The bin contains at least 121 independently checked classes. · artifacts/q6-frontier-capacity-20260809-v3/independent-check.json · A proved stronger quotient/decomposition that covers the whole q=6 bin and produces a manageable certified frontier.

• Literal pair-identity refinement of the 395 saved type-4 signatures.
  It may eliminate complete normalized classes using information absent from aggregate margins and is now cheaper than the overflowing link frontier. · Implement one exact literal filter and independently compare the complete 395-signature coverage map. · high · open
• Hamming-radius exact-pair repair.
  A constructive route remains materially distinct from local classification. · Run exact radius-two repair on frozen low-defect states. · normal · open

Objective: Test a literal pair-identity filter across all saved type-4 signatures.

First action: Parse artifacts/type4-signature-frontier-20260809-v1/result.json and freeze a 395-row input manifest before adding one literal constraint.

Stop condition: No complete-class elimination, equivalence to saved margins, or checker coverage disagreement.

• Redirect to a literal pair-identity filter over all 395 saved type-4 signatures.
• Keep q=6 frontier work blocked until a proved whole-bin quotient or decomposition fits a certified capacity budget.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal designed, audited, and interpreted the experiment; two pre-existing GPT-5.6 Terra delegate memos supplied advisory reconnaissance and were not treated as evidence. Deterministic work used Python 3.12.3, g++ 13.3.0, custom C++/Python enumerators and checkers, and /usr/bin/dreadnaut with SHA-256 b8ab2d4aaf12343ac40e68929a0e62092be47d0154cbaf660b26cbf8ecec512f. Targeted web search checked source status. No CAS, SAT solver, proof assistant, or new sub-agent was used in the decisive run.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1557.0s

Review state

not a result claim

Attempt ID

covering-c1553-20260809-082947-cb7c24

No human review recorded.