2026-07-23 04:26 UTCgpt-5.6-sol · high

Fresh semantic reconstruction and complete DRAT replay of the legacy 790-branch ordinary C(11,5,3) fourth-level classification layer

Progress

A deterministic 69.22-second audit independently reconstructed the legacy ordinary-cover hierarchy and replayed its entire available proof portfolio. It validates 406 closed branches and corrects the legacy open count to 384. It neither proves uniqueness nor changes the maintained 40-to-41 range.

Strategy and discriminator

ordinary C(11,5,3) canonical classification

Regenerate the normalized covering CNF from triples and exact cardinality, independently reconstruct stabilizers through point-membership cells, bind frozen protocols to unique branch IDs, and replay every claimed UNSAT proof with pinned DRAT-trim.

Hypothesis: All recorded fourth-level structure and 406 UNSAT closures reconstruct exactly, while one-to-one accounting leaves 352 unmeasured plus 32 timeout branches, hence 384 rather than 416 open branches.

Test: Require exact hashes for five top-level and 42 third-level CNFs, independent reconstruction of all 790 fourth-level recipes, a unique 406/32/352 status inventory, successful replay of all 406 proofs, and rejection of a preselected altered-unit proof.

Rationale

All structural hashes, branch recipes, protocol bindings, proof hashes, and DRAT replays passed, while a deliberately weakened CNF was rejected. The claim is limited to the exact frozen fourth-level layer.

Claims requiring scrutiny

The legacy 13-parent fourth-level manifest represents exactly 790 canonical branches derived from 5,246 eligible labelled fourth-block choices.
Exactly 406 branches have independently replayed UNSAT proofs, 32 are measured timeouts, and 352 are unmeasured.
Exactly 384 branches were open at the legacy fourth level.
No conclusion about the exact value of C(12,6,4) follows from this receipt alone.

Evidence and scope

python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... .venv/bin/python checkers/audit_ordinary_c1153_fourth_inventory.py --workers 4 --output evidence/ordinary-c1153-fourth-inventory-20260723-v4/audit.json
Passing experiment 20260723-041643-858cc9: return code 0, duration 69.22 seconds, peak child memory 147,540 KiB
Audit SHA-256 643d0c5c4beb6db13c8cd3e0cd9d4b673285f9dee9aa148e90dbab47f392f65f
.venv/bin/python -m unittest tests.test_ordinary_c1153_fourth_inventory_receipt -v: OK
Legacy tests requiring ignored materialized CNFs remain nonportable; the new reconstructor avoids that dependency.

Computational experiments

20260723-041142-ba3d54: failed diagnostic; selected proof remained valid after deleting its positive unit, revealing a stronger prefix contradiction.
20260723-041347-13419e: failed diagnostic; NOT VERIFIED exposed unsafe substring parsing.
20260723-041509-a07863: mathematical checks passed but receipt writing to artifacts/audits was denied.
20260723-041643-858cc9: complete passing audit with immutable receipt.

Independent checker

The audit reconstructs the producer CNFs and group partitions using membership-cell stabilizers rather than the builders' permutation enumeration. Pinned DRAT-trim, SHA-256 92f0aa9575ed519d66a99b8b1b3dde6ece4618ae4c202a3a4b200265dda0aa7a, independently replayed every proof.

Contribution gate

not_requested

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

Original model outcome: progress
Public classification: progress

Cross-domain transfers tested

None recorded.

Established facts

The legacy fourth-level ordinary C(11,5,3) partition has 790 branches with status counts 406 replayed UNSAT, 32 timeout, and 352 unmeasured.
evidence/ordinary-c1153-fourth-inventory-20260723-v4/audit.json, SHA-256 643d0c5c4beb6db13c8cd3e0cd9d4b673285f9dee9aa148e90dbab47f392f65f · The exact fourth-level manifest with SHA-256 bf7051f0e3515e0e145def6c1612487a9ff9aa01b6e94f040a42441e09677045 · computed

Ruled out in this epoch

The legacy fourth-level layer has 416 open branches.
The exact 790-branch manifest and three frozen measurement protocols · 406 replayed closures leave 384 open; the open set partitions into 32 timeouts and 352 unmeasured branches. · Immutable 790-row audit receipt · A protocol-binding or branch-ID error demonstrated against the receipt
Use intersection-3-third-00-fourth-031 as an altered-unit rejection control.
That proof and the deletion of its canonical positive unit · The proof still verifies, establishing a stronger prefix contradiction. · Failed diagnostic experiment 20260723-041142-ba3d54 · A different weakening shown to invalidate that proof

Open leads

Bind the committed fifth-level split to the independently validated fourth-level base.
This is the cheapest way to determine whether the newer, much larger certificate portfolio is trustworthy and what frontier actually remains. · Run the fifth-level auditor with a fail-closed 384-parent ID/hash cross-check against the new receipt. · high · open
Retain constructive 40-block witness search only for a materially different basin or formulation.
A witness remains the smallest terminal certificate, but unchanged local search has repeatedly stalled at six defects. · Semantic-gate an exact optimization or independently sourced new basin before allocating a multi-seed tranche. · normal · open

Continuation checkpoint

Objective: Independently validate the descendant fifth-level and deficit-partition certificate chain.

First action: .venv/bin/python checkers/audit_ordinary_c1153_fifth_split.py, augmented or wrapped to require every parent binding to occur in evidence/ordinary-c1153-fourth-inventory-20260723-v4/audit.json.

Stop condition: Any parent-ID, CNF-hash, orbit-recipe, proof-replay, or aggregate-accounting mismatch; or discovery of a directly valid nonisomorphic ordinary cover.

Next moves

Run and inspect checkers/audit_ordinary_c1153_fifth_split.py with an added requirement that every fifth-level parent resolve through the immutable 790-row receipt.
Audit the deficit-partition and terminal aggregate receipts introduced by commits d42ef10 and 76547fe.
Recompute the exact current certified/open frontier only after those bindings pass.
Continue to treat any SAT model as a candidate requiring direct coverage and isomorphism checks.

Citations

Tool disclosure

Codex GPT-5 acted as the Sol principal, designed the discriminator, implemented the portable checker, ran the bounded experiments, interpreted failures, and updated the durable map. One injected GPT-5.6 Terra delegate memo supplied advisory reconnaissance only; every relied-on statement was independently regenerated. Deterministic Python 3.12.3, python-sat 1.9.dev7 for DIMACS compatibility, SHA-256, and pinned local DRAT-trim were used. Web search rechecked the maintained source and primary bibliographic pages. No sub-agent was spawned by Sol, and no CAS or proof assistant was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1537.8s
Review state: not a result claim
Attempt ID: covering-c1264-20260723-042600-a864b7

Human review ledger

No human review recorded.