2026-08-11 11:35 UTCgpt-5.6-sol · high

Proof-capable CNF feasibility test for defect at most nine over the complete strict 5-for-5 exact-degree neighborhood of one verified defect-10 seed.

No Progress

The complete strict 5-for-5 defect-at-most-nine local question was compiled and independently reconstructed, but CaDiCaL returned UNKNOWN at the fixed cap. No candidate, local exclusion, global bound, or exact covering value was obtained. The incomplete partial DRAT from the initial proof-producing control was removed by the runner because it was non-evidence.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

strict 5-for-5 local threshold CNF

One-hot bounded counters encode five deletions, five additions, fifteen point-balance equalities, 455 coverage-or-uncovered clauses, and at most nine uncovered triples.

Hypothesis: The hash-bound defect-10 seed has a strict five-deletion/five-addition point-degree-preserving neighbor with at most nine uncovered triples.

Test: Run the independently reconstructed threshold CNF once with CaDiCaL seed 0, 100000 conflicts, and 90 wall seconds; accept SAT only after direct family checking and UNSAT only after LRAT replay.

Rationale

UNKNOWN has no mathematical content beyond the recorded resource-bounded solver behavior. Exact reconstruction validates the formula, not satisfiability or unsatisfiability.

Claims requiring scrutiny

The recorded CNF exactly represents every strict point-degree-preserving 5-for-5 neighbor of the frozen seed having at most nine uncovered triples.
CaDiCaL 1.7.3 returned UNKNOWN at exactly 100000 conflicts on that CNF.
No local move or global covering-design branch was excluded.

Evidence and scope

sha256sum -c artifacts/degree18-strict5-defect9-cnf-20260811/manifest.sha256
python3 scripts/check_degree18_strict5_defect9_v1.py --protocol protocols/degree18-strict5-defect9-cnf-v1.json --cnf artifacts/degree18-strict5-defect9-cnf-20260811/threshold.cnf --manifest artifacts/degree18-strict5-defect9-cnf-20260811/manifest.json --result artifacts/degree18-strict5-defect9-cnf-20260811/run/result.json --output /tmp/c1553-strict5-defect9-check.json
100000 conflicts; 921802 decisions; 222436564 propagations; status UNKNOWN

Computational experiments

.proof-experiments/20260811-112333-41b142: deterministic build produced 116318 variables, 535762 clauses, and CNF SHA-256 9f3c42f5713c34013597375a23d5a2186ae28c2da91ef96b9a61ea96bc306c1a.
.proof-experiments/20260811-112524-848091: proof-free decision returned UNKNOWN at 100000 conflicts.
.proof-experiments/20260811-112732-157a5f: independent reconstruction and mutation controls passed.

Independent checker

scripts/check_degree18_strict5_defect9_v1.py uses a separately written builder, reconstructed all 535762 clauses and 116318 variables, checked 4350 bounded-counter cases, rejected dropped/duplicated/flipped clauses, and confirmed that the recorded result claims only UNKNOWN.

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

Integer optimization to proof-producing SAT -> replacing the MILP objective by a defect<=9 feasibility threshold should make either outcome certifiable -> the formula was certifiable in principle but remained solver-UNKNOWN.
Prior Wallace/carry-save compiler benchmark to local threshold encoding -> compact binary arithmetic may improve propagation over one-hot rows -> not yet tested on this formula.

Established facts

The strict-5 defect-at-most-nine CNF has 116318 variables, 535762 clauses, and SHA-256 9f3c42f5713c34013597375a23d5a2186ae28c2da91ef96b9a61ea96bc306c1a.
Producer manifest, independent reconstruction, byte-identical regeneration, and hash-manifest replay. · Frozen seed SHA-256 3e83de2272aaf5fa18b6167ba384ac6722bd4f03d49c6b1ca3979e98c3f80462. · computed
CaDiCaL returned UNKNOWN at 100000 conflicts with 921802 decisions and 222436564 propagations.
run/result.json, solver.log, and experiment 20260811-112524-848091. · The recorded CNF, CaDiCaL 1.7.3, seed 0, and fixed limits. · computed

Ruled out in this epoch

Repeat the complete fixed-pair-link relaxation as a strengthening.
All four canonical degree-18 CNFs and 5460 labelled link requirements. · The independent audit found zero non-subsumed CNF-clause delta. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A separately proved nonredundant constraint with audited nonzero semantic or propagation delta.
Scale this one-hot strict-5 threshold encoding solely by increasing the cutoff.
The recorded frozen seed, encoding, solver, and seed-0 protocol. · The predeclared 100000-conflict discriminator returned UNKNOWN without a candidate or proof. · artifacts/degree18-strict5-defect9-cnf-20260811/run/result.json · A materially different propagation/decomposition mechanism with independent equivalence checking and matched improvement.

Open leads

Binary/carry-save strict-5 threshold compiler.
It changes the inference mechanism while preserving the exact local question; prior target-specific Wallace arithmetic showed substantial size and wall improvements on a different leaf. · Compile the identical semantic rows and run a 5000-conflict matched comparison. · high · open
Hash-bound 3072-cell selector map.
It offers deletion-cell proof-throughput calibration with an independently validated map. · Obtain explicit owner approval of map SHA-256 7fcfd2d9b429c02d3c968921155f1384343ba5bde865d7f0d9c59aab0f59a403 before dispatching any selector compute. · normal · open

Continuation checkpoint

Objective: Determine whether binary/carry-save arithmetic materially improves the exact strict-5 threshold decision.

First action: Freeze a 5000-conflict matched protocol and independently reconstruct a binary point-balance plus defect-cardinality compiler.

Stop condition: Stop on semantic disagreement, SAT/UNSAT verification failure, or less than 20 percent improvement in both decisions and propagations.

Next moves

Build a semantically identical carry-save/binary point-balance and cardinality-network compiler.
Independently reconstruct both encodings and reject any semantic mismatch.
Run a matched seed-0 5000-conflict pilot; stop unless both decisions and propagations improve by at least 20 percent.
Require direct checking for SAT and complete LRAT replay for UNSAT before any local claim.

Citations

Tool disclosure

Sol acted as principal investigator. GPT-5.6 Terra delegates supplied advisory prior-art and experiment-verification memos; Sol audited their zero-delta fixed-link warning and did not count model agreement as validation. Python 3.12.3 generated and independently reconstructed CNF; CaDiCaL 1.7.3 performed the bounded decision; pinned drat-trim and lrat-check were wired for UNSAT but not invoked because the status was UNKNOWN. SHA-256, mutation testing, byte-identical regeneration, the computational-researcher experiment harness, and a bounded browser check were used. The browser returned no rendered payload. No lab job, package installation, system change, external write, CAS, proof assistant, publication, or sub-agent execution occurred.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1144.7s
Review state: not a result claim
Attempt ID: covering-c1553-20260811-113500-713bb3

Human review ledger

No human review recorded.