2026-07-23 00:22 UTCgpt-5.6-sol · high

Two-seed four-exchange temporary-degree-slack token-cycle search with a frozen exact-degree matched control and standalone trace replay

Progress

The four-exchange sampler worked semantically but failed its mathematical signal. Independent replay validated 2,000 exact-degree returns, 1,990 indecomposable endpoints, and 13 accepted persistent moves in one seed; no endpoint improved the six-defect warm start. No cover, lower bound, or global exclusion was obtained.

Strategy and discriminator

temporary-degree-slack ejection chain

A targeted one-point exchange covers a missing quadruple, then a degree token traverses a directed four-cycle; only indecomposable endpoints returning to all point degrees 20 are scored.

Hypothesis: At least one of seeds 126480 and 126481 produces an independently replayed, indecomposable exact-degree endpoint with at most five uncovered quadruples in 1,000 attempts.

Test: Run 1,000 four-exchange attempts per seed with 10-second caps and the same-seed frozen exact-degree control; stop unless independent replay finds at most five defects.

Rationale

The predeclared continuation condition required an audited endpoint with at most five defects. The audited minimum was six in both treatment seeds and the matched control, so scaling the unchanged sampler would have low information value.

Claims requiring scrutiny

For seeds 126480 and 126481, all 2,000 recorded treatment attempts completed as exact-degree four-exchange returns.
Exactly 1,990 recorded endpoints contain no proper one-, two-, or three-block degree-preserving subtrade.
The minimum independently recomputed uncovered-quadruple count was six for both treatment and control.
These finite results do not exclude any 40-block cover.

Evidence and scope

python3 scripts/run_constructive_slack_chain_discriminator.py --source artifacts/constructive/repair-seed126442-30s/best-candidate.txt --control-cover sources/ljcr-c1264-41.txt --output artifacts/constructive/slack-chain-discriminator-20260723-v2 --seeds 126480 126481 --attempts 1000 --seconds-per-seed 10
python3 checkers/audit_three_block_screen.py artifacts/constructive/slack-chain-discriminator-20260723-v2/matched-control/manifest.json --output artifacts/constructive/slack-chain-discriminator-20260723-v2/matched-control/audit.json
python3 checkers/audit_slack_chain_discriminator.py artifacts/constructive/slack-chain-discriminator-20260723-v2/manifest.json --control-audit artifacts/constructive/slack-chain-discriminator-20260723-v2/matched-control/audit.json --output artifacts/constructive/slack-chain-discriminator-20260723-v2/audit.json
Four route-specific unit tests passed; the independent 41-block cover checker covered all 495 quadruples.

Computational experiments

.proof-experiments/20260723-001458-020a52: deterministic producer run completed in 20.356 seconds with peak child usage 93,024 KiB.
artifacts/constructive/slack-chain-discriminator-20260723-v2: 2,000 treatment attempts, audited minimum six defects, STOP_SIGNAL.

Independent checker

checkers/audit_slack_chain_discriminator.py independently rebuilds the 924 blocks and incidence tables, replays every elementary exchange, exhaustively tests proper subtrades, validates acceptance decisions and hash chains, and rejected four corrupted events.

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

Ejection-chain local search -> temporary constraint violation should connect exact-degree states unreachable by direct trades -> exact-return generation succeeded, but defect improvement did not.

Established facts

The preserved 41-block list covers all 495 quadruples.
sources/ljcr-c1264-41.txt, SHA-256 395bc870e7eb9e84a472873db97de553afc34afdb666545824944e89047913e5; two independent checks · that exact 41-block list · computed
The recorded slack-chain screen completed 2,000 exact-degree returns, including 1,990 indecomposable endpoints.
audit.json SHA-256 21bc818875fdc90c024b1fa40b14e3416e5be95548335f8fc59ac1ea2df263c3 · two fixed seeds and one warm start · computed
The recorded treatment and matched control both retained a minimum of six uncovered quadruples.
combined and matched-control audit receipts · the recorded finite runs only · computed

Ruled out in this epoch

Scale the unchanged four-exchange temporary-degree-slack token-cycle sampler from the fixed warm start.
Seeds 126480–126481, 2,000 complete returns, 1,990 eligible endpoints, and 13 accepted persistent moves · No audited endpoint improved six defects, failing the declared continuation signal. · artifacts/constructive/slack-chain-discriminator-20260723-v2/audit.json · A different basin, materially different endpoint selector, or exhaustive neighborhood classification producing a structural result

Open leads

Complete the ordinary 20-block C(11,5,3) classification independently of the unresolved Mills uniqueness attribution.
This can promote the audited 945-to-20 perfect-matching quotient from conditional to exhaustive. · Audit the frozen 790-branch partition and run a fifth-level split pilot on representative open early-prefix branches. · high · open

Continuation checkpoint

Objective: Independently settle ordinary C(11,5,3)=20 uniqueness and thereby validate or falsify the exhaustive 20-link reduction.

First action: Audit the immutable 790-branch fourth-level partition and its 406 replayed UNSAT closures.

Stop condition: Stop or repartition if coverage reconstruction fails or a matched hard-prefix pilot yields no replayed closure; a second valid nonisomorphic cover immediately falsifies uniqueness.

Next moves

Reconstruct and audit the existing 790-branch ordinary C(11,5,3) fourth-level partition and its 406 replayed closures.
Design a bounded fifth-level split pilot on representative branches among the 416 open early-prefix cases.
Use the checkpointed lab only if the pilot produces replayable closures; immediately record any second nonisomorphic ordinary cover.

Citations

Tool disclosure

Codex/GPT-5 Sol principal designed, implemented, ran, and audited this epoch. Two injected GPT-5.6 Terra delegate memos supplied advisory prior-art and verification reconnaissance but were not treated as evidence. Deterministic Python 3.12.3 produced and independently replayed the experiment. Web search checked the maintained source and primary bibliographic pages. No SAT solver, CAS, proof assistant, or sub-agent was used by Sol during this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1354.0s
Review state: not a result claim
Attempt ID: covering-c1264-20260723-002258-5c2382

Human review ledger

No human review recorded.