2026-08-11 00:13 UTCgpt-5.6-sol · high

Four-type CNF-delta audit of complete pair-link coverage

No Progress

The complete pair-link proposal was audited across all four canonical CNFs. Every labelled requirement was already present, so the logical clause delta is zero. This rules out only link-only strengthening and leaves 54 <= C(15,5,3) <= 55 unchanged.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

complete fixed-pair link relaxation

Classify every labelled pair-link requirement as fixed-block true, an exact existing coverage clause, or genuinely non-subsumed.

Hypothesis: At least one labelled complete-pair-link requirement adds a non-subsumed clause to a canonical degree-18 baseline CNF.

Test: Compare all 4*105*13 labelled requirements against fixed-block coverage and the actual hash-bound DIMACS coverage prefixes.

Rationale

Each requirement has a direct certificate: either a fixed common block contains its triple or its incident-variable clause occurs exactly in the baseline coverage prefix. Independent reconstruction confirmed the exhaustive classification.

Claims requiring scrutiny

Across the four canonical CNFs, all 5,460 labelled pair-link requirements are already present: 570 as fixed-block tautologies and 4,890 as exact coverage clauses.
Complete pair-link coverage alone cannot strengthen these formulas.
The maintained 55-cover fixture covers all 455 triples and has pair-degree histogram {5:83,6:21,9:1}.

Evidence and scope

sha256sum -c artifacts/pair-link-cnf-delta-audit-20260811/manifest.sha256 passed
Byte-identical regeneration produced SHA-256 2d9a800be480a78480728bc2b9b496913cc999c44b93d860a3dec8592cbce408
Independent checker reconstructed 1,630 clauses and 5,460 requirements and rejected nine mutations

Computational experiments

.proof-experiments/20260811-000808-a32219 — producer returned REDIRECT with zero non-subsumed requirements
.proof-experiments/20260811-000821-9affc5 — independent checker returned valid=true

Independent checker

checkers/check_pair_link_cnf_delta_audit_v1.py independently reconstructs coverage clause sets using frozenset semantics, checks all link maps, and rejects claim and literal-incidence mutations.

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

None recorded.

Established facts

Every complete pair-link requirement in the four canonical formulas is already enforced.
Exact exhaustive producer and independent checker · 5,460 labelled requirements across the four hash-bound canonical CNFs · computed

Ruled out in this epoch

Add complete pair-link coverage alone as a strengthening of any canonical CNF.
All 105 pairs, 13 third points, and four canonical types · Logical clause delta is exactly zero. · result.json and independent-check.json · Provide a separately justified pair-count or skeleton constraint with an explicit non-subsumption witness.

Open leads

Certificate-first semantic 16-cube pilot on the complete type-4 branch
It preserves exhaustive labelled coverage and can produce independently replayable branch evidence. · Bind four audited primary literals, verify all 16 leaves, then run proof-emitting capped solves. · high · open

Continuation checkpoint

Objective: Obtain the first replayable SAT/UNSAT signal from a disjoint labelled partition of a complete canonical branch.

First action: Create protocols/type4-semantic-16-cube-pilot-v1.json and independently audit its four literals and 16-leaf map.

Stop condition: Stop or redirect on any map mismatch, or if all 16 leaves merely hit their cap without a checked model or replayed proof.

Next moves

Create protocols/type4-semantic-16-cube-pilot-v1.json binding the type-4 CNF hash and four audited primary literals.
Independently verify that the 16 leaves are disjoint and exhaustive.
Run every leaf with proof emission and advance only on a checked SAT model or replayed UNSAT leaf.

Citations

Tool disclosure

GPT-5.6 Sol principal selected, implemented, ran, audited, and interpreted the epoch. GPT-5.6 Terra delegates supplied advisory prior-art and route-selection reconnaissance only; their agreement was not validation. Python 3.12.3, exact standard-library enumeration, DIMACS parsing, SHA-256, the computational-researcher experiment harness, and the configured web reader were used. No SAT solver, CAS, proof assistant, cloud lab, subagent spawned by Sol, system installation, or external write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 996.0s
Review state: not a result claim
Attempt ID: covering-c1553-20260811-001343-f54f29

Human review ledger

No human review recorded.