Audit and independently classify all 61 depth-four pair-surplus ownership chunk volumes before approving the saved full-ledger lab shape; also preflight fail-closed full-union checker semantics.

checkpointed canonical pair-surplus augmentation

Count each internal-edge-orbit chunk by stabilizer Burnside DP, reproduce the complete vector by explicit residual-table enumeration and minimum-image canonicalization, and reject unsafe materialization caps before scale-up.

Hypothesis: Every one of the 61 internal-orbit chunks fits the saved 5000-record cap and can therefore use the epoch-108 full-job shape.

Test: Compute exact per-orbit canonical profile counts, reconcile their sum to 62437, and independently reproduce all 61 raw and canonical counts by explicit enumeration.

The cap claim is finite and exactly decidable without materialization. Two distinct exact mechanisms agree entrywise, and mutation controls reject aggregate or ordering errors. One verified oversized chunk is sufficient to invalidate the old job; the full vector identifies the exact repair target. None of this is a cover or UNSAT certificate.

• The 61 canonical internal-edge-orbit chunks have the ordered counts recorded in all-orbit-cap-result.json, summing to 62437.
• Exactly chunks 0, 1, and 5 exceed 5000 records, with counts 18316, 21182, and 7798; chunk 1 is the exact maximum.
• The epoch-108 job shape with max_records_per_chunk=5000 cannot complete all 61 chunks.
• The generalized full-mode checker rejects incomplete or overlapping union metadata and preserves independent validation of chunks 16 and 38; it does not establish a complete ledger.

• all-orbit Burnside gate: REDIRECT_CAP_TOO_LOW, total 62437, maximum index 1 count 21182
• standalone C++17 explicit enumerator: PASS_ALL_ORBIT_ENUMERATIVE_CROSS_CHECK
• entrywise comparator: PASS_EXACT_61_ORBIT_AGREEMENT with three mutations rejected
• generalized selected checker: PASS_INDEPENDENT for 2550 retained profiles
• real two-chunk manifest in full mode: exit 1 and no false promotion artifact
• pure-Python explicit orbit-0 enumeration: timed out at 120.011 seconds; no count claim relies on it

• .proof-experiments/20260812-051920-080f42: full-checker preflight passed seven controls in 0.121 seconds.
• .proof-experiments/20260812-051928-220291: selected checker revalidated 2550 profiles in 17.901 seconds.
• .proof-experiments/20260812-051954-2c33ab: incomplete manifest was rejected in full mode.
• .proof-experiments/20260812-052059-1333e6: orbit-0 Burnside gate found 18316 profiles.
• .proof-experiments/20260812-052136-526011: pure-Python enumerator timed out without a result.
• .proof-experiments/20260812-052433-c85105: orbit-0 C++ enumeration independently found 383542 raw and 18316 canonical profiles.
• .proof-experiments/20260812-052516-42e110: all-orbit Burnside gate returned the complete vector in 9.357 seconds.
• .proof-experiments/20260812-052639-198d0c: all-orbit C++ enumeration independently returned the vector in 1.278 seconds.
• .proof-experiments/20260812-052710-d759c3: exact comparator passed and rejected three mutations.

checkers/check_pair_surplus_depth4_all_orbit_counts_v1.cpp independently rebuilds all internal representatives and explicitly enumerates and minimum-image canonicalizes residual tables without Burnside fixed points. compare_pair_surplus_depth4_all_orbit_counts_v1.py verifies ordered entrywise agreement and mutations.

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

• Checkpointed exhaustive classification -> aggregate frontier size may hide severe bucket skew -> exact per-bucket audit found a 4.2364x cap violation.
• Compiled canonical-enumeration kernels -> repetitive minimum-image testing should accelerate without semantic change -> C++ reproduced the full vector in 1.278 seconds after Python orbit-0 enumeration exceeded 120 seconds.

• The depth-four quotient contains 62437 profiles partitioned among 61 internal-edge orbits with the recorded ordered counts.
  Entrywise agreement of Python Burnside DP and standalone C++ enumeration; comparison receipt SHA-256 92581cab912fc181f56a516d76e3ee2e684ad838feb1c6ef837e32df79a6676b. · All degree-feasible four-row prefixes of loopless weighted 4-regular multigraphs on 15 vertices modulo S4 x S11; not complete graphs or covers. · computed
• The largest chunk is index 1 with 21182 profiles; exactly indices 0, 1, and 5 exceed 5000.
  artifacts/epoch109-20260812/all-orbit-count-agreement.json · The exact 61-chunk partition. · computed
• The generalized checker preserves validation of chunks 16 and 38 and rejects declared incomplete or duplicate union controls.
  selected-checker-regression-result.json and full-checker-preflight-result.json · Checker implementation and the retained 2550-profile baseline only. · computed

• Submit the epoch-108 one-file-per-internal-orbit job with max_records_per_chunk=5000.
  Complete 61-orbit depth-four ownership materialization. · Exact independent counts show chunks 0, 1, and 5 exceed the cap. · artifacts/epoch109-20260812/all-orbit-count-agreement.json · Use exact subchunking or a cap at least 21182, remeasure resources, and obtain human approval.
• Use the current Python explicit canonicalization kernel with a 60-second cap for orbit 0.
  Orbit-0 count-only enumeration on the epoch host before parent reconstruction. · The no-parent enumeration timed out at 120.011 seconds. · .proof-experiments/20260812-052136-526011/experiment.json · An optimized kernel or checkpoint subdivision terminating within the declared cap with identical exact output.

• Canonical two-level subchunks for oversized internal orbits
  Only three chunks exceed 5000; a proved table-prefix owner rule can preserve small artifacts and restart granularity. · Define index-1 prefix buckets and independently verify an exact disjoint union of 21182 canonical tables. · high · open
• C++ record producer for the depth-four ledger
  The C++ count kernel classified all orbits in 1.278 seconds while Python orbit-0 count-only enumeration exceeded 120 seconds. · Add sparse-table serialization and deletion-parent reconstruction for index 1 and compare every record with Python. · high · open
• Constructive 30-cover search
  A directly checked 30-block list would settle the problem without ownership-ledger completion. · Run only after specifying a materially new witness-generating mechanism. · normal · open

Objective: Repair ownership materialization on the exact largest chunk without launching full compute.

First action: Implement a canonical second-level bucket key for internal-orbit index 1 and run a count-only exact-union checker against target 21182.

Stop condition: Stop on overlap, gap, total other than 21182, noncanonical ownership, parent mismatch, checkpoint drift, or projection above 900 seconds/1 GiB.

• Design a canonical second-level partition for oversized chunks 0, 1, and 5 with exact owner rules.
• Run the smallest stress pilot on all 21182 index-1 profiles using the C++ kernel or equivalent optimized producer and independently reconstruct deletion parents.
• After the pilot passes, request human approval for a revised full-lab scope; do not submit the old scope.
• Keep SAT/PB proof leaves blocked until the complete 62437-profile ownership union has an independently checked receipt.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory reconnaissance; their agreement was not evidence and relied-on claims were independently reproduced. Deterministic tools were Python 3.12.3, g++ 13.3.0 with C++17, exact integer arithmetic, SHA-256, Burnside DP, explicit enumeration, and the computational-researcher harness. Web search supported the source and bounded novelty audit. No SAT/PB solver, CAS, proof assistant, cloud lab, external proof service, or human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1348.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-053518-652154

No human review recorded.