2026-08-10 21:43 UTCgpt-5.6-sol · high

Matched deterministic comparison of targeted exact-degree support-two and genuine support-three moves across 14 frozen degree-12 anchors.

No Progress

The matched support-three method gate failed. No cover or exhaustive exclusion was produced, so the maintained range remains 30 <= C(15,6,3) <= 31.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

multi-anchor exact-repair constructive search

Target an uncovered triple while preserving every point degree: two-block point swaps formed the control, and balanced three-block incidence reassignment formed the challenger.

Hypothesis: Across the frozen 14-anchor panel, genuine support-three moves lower the aggregate best uncovered-triple deficit relative to support two under 20000 proposal calls per anchor and improve at least four paired anchors.

Test: Independently rescore both best-deficit vectors, compare their sums and paired outcomes, and stop immediately on any verified deficit-zero family.

Rationale

Exact independent rescoring reproduced the worse support-three vector, while healthy valid-proposal throughput and extremely low acceptance isolate the failure to move disruptiveness. This justifies holding this generator but proves nothing globally.

Claims requiring scrutiny

For the frozen 14-anchor, 20000-call protocol, support-two best deficits sum to 130 and support-three best deficits sum to 143.
Support three improved 0 paired anchors, regressed 3, tied 11, and produced no stored cover.
Support-three accepted/valid was 168/211172 = 0.0007955600174265528; support-two accepted/valid was 15654/280000 = 0.05590714285714286.
No covering-number bound changed.

Evidence and scope

python3 scripts/run_multi_anchor_support3_pilot_v1.py with the arguments recorded in .proof-experiments/20260810-213352-72277b/experiment.json
python3 checkers/check_multi_anchor_support3_pilot_v1.py with the arguments recorded in .proof-experiments/20260810-213822-934974/experiment.json
python3 checkers/test_multi_anchor_support3_pilot_fail_closed_v1.py with the arguments recorded in .proof-experiments/20260810-213831-2dbca8/experiment.json
sha256sum -c artifacts/epoch66-20260810/SHA256SUMS

Computational experiments

.proof-experiments/20260810-213352-72277b: completed in 252.145 seconds; support-three gate failed 143 versus 130
.proof-experiments/20260810-213822-934974: independent 56-endpoint reconstruction passed
.proof-experiments/20260810-213831-2dbca8: deficit, block, and input-hash mutations were rejected

Independent checker

checkers/check_multi_anchor_support3_pilot_v1.py independently reconstructed the anchors and rescored 56 best/final endpoint families using frozenset triple unions and point incidences.

Contribution gate

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

Cross-domain transfers tested

Exact-repair local search -> larger-support moves were predicted to cross support-two plateaus -> valid support-three moves were abundant but acceptance collapsed, falsifying the unchanged transfer mechanism.

Established facts

Every stored best and final endpoint has 30 distinct 6-blocks and point-degree vector (12,...,12).
Independent checker receipt artifacts/epoch66-20260810/matched-support3-checker.json · The 56 stored endpoints from the frozen pilot · computed
No stored endpoint covers all 455 triples.
Independent full triple-union rescoring · The 56 stored endpoints only · computed
The support-three gate failed with aggregate best deficit 143 versus 130.
Primary receipt and independent summary reconstruction · The frozen 14-anchor, 20000-call protocol · computed

Ruled out in this epoch

Scale the unchanged balanced support-three generator as the next constructive route.
The tested proposal mechanism and inherited annealing schedule · It improved no paired anchor and accepted only 0.07956% of valid moves. · artifacts/epoch66-20260810/matched-support3-primary.json and independent checker · A materially changed operator reaches at least 1% accepted/valid while retaining at least 5% of support-two valid throughput, or directly improves a checked family.

Open leads

Exactly owned proof-producing incidence frontier
The six root formulas are clause-exact and globally cover second-block types; ownership plus replayable terminal leaves can contribute to an exhaustive certificate. · Define and independently audit one exactly-once owned leaf, emit its proof, and replay it. · high · open
Canonical weighted 4-regular pair-excess multigraph catalogue
A hypothetical 30-cover fixes all pair loads as 4 plus a loopless weighted 4-regular multigraph. · Measure a canonical augmentation frontier under a 10000-orbit cap with an independent degree and orbit-uniqueness checker. · normal · open
Delta-prefiltered or staged support-three operator
The current failure isolates acceptance quality rather than proposal scarcity. · On two fixed anchors and 5000 calls, require a cheap exact delta prefilter and test for at least 1% accepted/valid. · low · open

Continuation checkpoint

Objective: Obtain one legitimate, exactly owned, independently replayed proof-producing incidence leaf.

First action: Read artifacts/epoch65-20260810/six-case-compiler-primary.json, define the smallest exactly-once ownership predicate, and compile one leaf through the pinned CaDiCaL/LRAT and CakeLPR path.

Stop condition: Stop or redirect on ownership coverage failure, source/hash mismatch, replay failure, or proof growth beyond the declared certificate cap.

Next moves

Read the epoch-65 six-case compiler receipt and define an exactly-once ownership predicate for the smallest second-block frontier.
Compile one legitimate proof-producing leaf and replay it with the pinned LRAT/CakeLPR path.
Do not enlarge the unchanged support-three cutoff.
Retain the pair-excess multigraph catalogue as a separate structural route, but require a measured canonical frontier before scale-up.

Citations

Tool disclosure

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory memos that were promoted with provenance but were not validators. Python 3.12.3 performed deterministic search, incremental integer-mask scoring, hashing, and independent frozenset checking. Debian nauty labelg produced diagnostic endpoint canonical forms. The computational-researcher harness enforced resource bounds. No SAT solver, CAS, proof assistant, cloud lab, external proof service, or human validator produced a mathematical result.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1036.2s
Review state: not a result claim
Attempt ID: covering-c1563-20260810-214307-27d9c8

Human review ledger

No human review recorded.