2026-07-22 20:26 UTCgpt-5.6-sol · high

Twenty-seed targeted annealing with indecomposable, exact-point-degree-preserving three-block trades from the six-defect 40-block near-cover

Progress

The bounded three-block discriminator completed in 90.77 seconds and its independent audit completed in 9.72 seconds. Twenty fixed seeds scored 200,000 proposals and accepted 17,999 valid indecomposable degree-preserving trades. No run improved the six-defect warm start, so no cover or bound was obtained. The exact-value problem remains open.

Research-policy redirect

Automated lab review may recommend validate/promote, but only an operator may apply it with an independent validation receipt.

Strategy and discriminator

degree-preserving positive local search

Each proposal targets an uncovered quadruple, removes three selected blocks, and adds three previously unselected blocks with identical aggregate point incidence. Pair-signature buckets derive the final two additions, and moves decomposable into a legal two-block trade are rejected.

Hypothesis: Twenty fixed seeds with 10,000 scored genuine three-block proposals each improve the six-defect exact-degree warm start to at most five uncovered quadruples or find a 40-block cover.

Test: Replay every accepted move independently and directly recompute each best candidate; retain the route only if the audited minimum is at most five uncovered quadruples, with zero requiring the all-495 cover verifier.

Rationale

The predeclared at-most-five signal failed uniformly, and the independent checker confirmed that this was not caused by broken incidence updates, duplicate blocks, disguised two-block moves, corrupted traces, or incorrect candidate scoring. The evidence therefore supports redirecting this particular heuristic route, but its stochastic and single-basin scope cannot support a lower bound.

Claims requiring scrutiny

For the frozen 20-seed screen, the independently audited best value was exactly six uncovered quadruples.
All 17,999 recorded accepted moves preserved aggregate point incidence and were indecomposable into a legal two-block subtrade.
The pinned 41-block control covered all 495 quadruples, while deleting its first block left 10 uncovered quadruples.

Evidence and scope

python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... run_constructive_three_block_screen.py; experiment 20260722-201455-25d88d returned 0 in 91.244 seconds
python3 checkers/audit_three_block_screen.py artifacts/constructive/three-block-screen-20260722-v1/manifest.json --output artifacts/constructive/three-block-screen-20260722-v1/audit.json; audit reported status=valid, seeds_audited=20, accepted_moves_replayed=17999, best_uncovered_quadruples=6
python3 -m unittest tests.test_constructive_three_block_screen -v; both route-specific tests passed

Computational experiments

.proof-experiments/20260722-201455-25d88d: producer completed 20 seeds and 200,000 proposals; best remained six
.proof-experiments/20260722-201739-aaf35b: independent audit replayed 17,999 accepted moves and returned valid

Independent checker

checkers/audit_three_block_screen.py uses separately written incidence counting to replay every accepted move, verify distinctness, exact aggregate point incidence, absence of a two-block subtrade, target coverage, hash chains, and final metrics. It also checks the 41-block positive control and a deletion negative control.

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 -> allowing larger exact-degree moves should cross the two-block barrier -> 17,999 such moves crossed barriers but never improved the six-defect incumbent, so the transfer failed in this basin and suggests testing temporary constraint slack instead.

Established facts

The preserved 41-block list covers every one of the 495 four-subsets.
Independent control in audit.json; source SHA-256 395bc870e7eb9e84a472873db97de553afc34afdb666545824944e89047913e5 · sources/ljcr-c1264-41.txt · computed
The frozen three-block screen's minimum uncovered count is six.
audit.json reports 20 audited seeds and best_uncovered_quadruples=6 · Seeds 126460 through 126479, 10,000 scored proposals each, one fixed warm start · computed
All 17,999 recorded accepted moves preserve exact point degrees and are not legal two-block trades in disguise.
Independent accepted-trace replay with signature and subtrade checks · Recorded accepted moves in three-block-screen-20260722-v1 · computed

Ruled out in this epoch

Repeat or scale the unchanged exact-point-degree targeted indecomposable three-block annealer from the six-defect warm start.
Twenty fixed seeds, 200,000 scored proposals, and 17,999 independently replayed accepted moves · Every seed retained six uncovered quadruples, failing the predeclared continuation signal. · artifacts/constructive/three-block-screen-20260722-v1/manifest.json and audit.json · A materially different state generator, such as bounded temporary point-degree slack, or an exhaustive direct-neighborhood classification producing a structural result

Open leads

Temporary-degree-slack ejection chain with exact-degree endpoints
It changes the state graph responsible for the observed failure while retaining compact positive certificates. · Implement L1 point-degree slack at most two, exact endpoint projection, independent delta replay, and a short two-seed semantic gate before the frozen 20-seed screen. · high · open
Exhaustive direct three-block-neighborhood classification
A complete classifier could convert the observed basin resistance into a precise local-minimality fact and validate proposal coverage. · Enumerate all C(40,3) removals, derive all addition pairs through exact signatures, canonicalize resulting families, and independently recompute the minimum defect count. · normal · open
Certified exclusion work on genuinely open link-frontier leaves
Unlike another unchanged local-search tranche, each replay-verified unique UNSAT closure reduces the maintained global frontier. · Select only hash-bound leaves absent from the durable certificate portfolio and run the smallest matched proof-producing sequential tranche. · normal · open

Continuation checkpoint

Objective: Test whether bounded temporary point-degree slack can escape the six-defect basin and return an improved exact-degree endpoint.

First action: Implement and unit-audit the slack-chain proposal and independent endpoint/trace checker before any multi-seed run.

Stop condition: Stop unless an audited exact-degree endpoint reaches at most five uncovered quadruples or a separately checked structural classification is obtained.

Next moves

Do not repeat or scale the unchanged exact-degree three-block annealer.
Implement a bounded temporary-degree-slack ejection chain with mandatory exact-degree endpoints and a separate trace checker.
As a lower-priority structural control, exhaustively classify the direct indecomposable three-block neighborhood of the fixed warm start.
Keep the certified exclusion route active and allocate compute only to genuinely open, unmeasured frontier leaves.

Citations

Tool disclosure

GPT-5.6 Sol served as principal investigator, audited the Terra memo, corrected the initial temperature and verification design, executed the experiments, and interpreted the result. A GPT-5.6 Terra delegate supplied advisory experiment-verification reconnaissance; its memo was not treated as evidence. Deterministic Python 3.12.3 generated and independently checked the screen. No SAT solver, CAS, proof assistant, or independent human validator was used in this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1583.1s
Review state: not a result claim
Attempt ID: covering-c1264-20260722-202640-1e718a

Human review ledger

No human review recorded.