2026-08-10 14:58 UTCgpt-5.6-sol · high

Construct and independently audit H6, the fixed-first incidence CNF with q(F)>=6, then compare it against exact-q6 in a frozen two-seed proof-producing calibration.

No Progress

H6 was built and independently verified as the exact fixed-first q>=6 branch. It compresses seven exact-q cases into one CNF and passed the bounded H6/q6 rate and RSS gate. All four searches were UNKNOWN, and every partial proof was rejected twice. The exact range remains 30<=C(15,6,3)<=31.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

maximum-pair-excess anchored incidence SAT

Reuse the capped exact totalizer over 450 fixed-block pair-support variables and assert its threshold-66 output, representing q=6,...,12 with one proof-compatible formula.

Hypothesis: H6 preserves at least 95% of exact-q6 conflict throughput on each seed, at least 1.0 geometric mean, and at most 1.10 times matched RSS while compressing seven exact-q cases into one formula.

Test: Independently reconstruct H6, then run alternating H6/q6 five-second CaDiCaL trials at seeds 0 and 1 and replay every proof fail-closed.

Rationale

The independently reconstructed formula and hash-bound boundary checks establish the encoding and case compression. The solver runs establish only a bounded route-selection signal because none returned a witness or complete proof.

Claims requiring scrutiny

The immutable H6 CNF exactly encodes the fixed-first incidence model with q(F)>=6.
H6 has 36,330 variables and 217,367 clauses and represents q=6,...,12 in one formula.
The frozen H6/q6 geometric-mean conflict-rate ratio was 1.0474498396; this is a bounded calibration result, not a complexity theorem.
No covering bound changed.

Evidence and scope

sha256sum -c artifacts/epoch56-20260810/h6-threshold-calibration-v1/artifact-manifest.sha256: all entries OK
python3 checkers/check_h6_threshold_calibration_v1.py --receipt artifacts/epoch56-20260810/h6-threshold-calibration-v1/run/calibration-receipt.json --output artifacts/epoch56-20260810/h6-threshold-calibration-v1/independent-check.json: PASS
Independent checker reconstructed 60,899 suffix clauses, 3,152 auxiliary variables, and all 450 support equivalences.
All four UNKNOWN LRAT prefixes were explicitly rejected by fresh lrat-check and CakeLPR builds.

Computational experiments

.proof-experiments/20260810-145036-13e7b0 — four UNKNOWN H6/q6 runs; geometric ratio 1.0474498396; prechecker gate passed.
.proof-experiments/20260810-145123-38d1d9 — independent reconstruction and replay PASS; all incomplete proofs rejected.

Independent checker

checkers/check_h6_threshold_calibration_v1.py independently reconstructs the totalizer without importing the producer, checks all support clauses and boundaries, reparses logs, validates any SAT block list, and freshly builds both LRAT replayers.

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

Certified cube-and-conquer campaigns -> represent a disjoint family by one proof-compatible union threshold -> exact seven-case H6 compression passed reconstruction.
Fail-closed proof engineering -> require two fresh replayers and explicit rejection of incomplete prefixes -> all four UNKNOWN proofs were correctly classified as non-evidence.

Established facts

The H6 CNF enforces internal pair incidence at least 66, equivalently q(F)>=6.
Independent reconstruction of every suffix clause plus semantic tests at 65, 66, and 67 true supports. · The immutable fixed-first incidence CNF with SHA-256 b728643e0565ed3bedfac7624e34098f053f3028364b68552a42f83548511086. · computed
One H6 formula represents the union of the seven possible values q=6,...,12.
q=sum(y)-60, threshold sum(y)>=66, and the retained excess-degree bound q<=12. · Fixed-first non-equality anchor family. · proved
The frozen H6 route-selection gate passed.
Independently reparsed per-seed rate ratios 1.0900342130 and 1.0065291101 with RSS ratios approximately 1.0018. · CaDiCaL 1.7.3, seeds 0 and 1, five-second setting, recorded host. · computed

Ruled out in this epoch

Treat the epoch-56 UNKNOWN H6 runs as satisfiability or unsatisfiability evidence.
All four immutable calibration runs. · No model or empty clause was produced, and both fresh proof replayers explicitly rejected every LRAT prefix. · artifacts/epoch56-20260810/h6-threshold-calibration-v1/independent-check.json · A directly checked SAT block list or complete LRAT accepted by both fresh replayers.
Launch a long global H6 search solely from the short conflict-rate ratio.
Unconditioned H6 with the current calibration data. · Only 301 conflicts occurred per run and no certificate-budget projection or complete owned frontier exists. · Raw logs and checkpointed experiment result. · A hash-bound owned decomposition and a local proof-emitter calibration projecting within the declared certificate budget.

Open leads

Owned H6 intersect r=5 proof-emitter calibration
It combines the validated H6 union with the smallest uniquely owned second-block branch and tests certificate production before scale-up. · Append threshold 66 to the epoch-34 r=5 owner formula, independently reconstruct, and run one bounded LRAT calibration. · high · open
Canonical root-link catalogue
A complete exactly-once structural frontier addresses the unresolved ownership layer without relying on short CDCL throughput. · Run two independent canonical augmenters to 10,000 completed graphs and compare owner/parent receipts. · normal · open
Compressed E5 via inherited pair-totalizer outputs
Removing duplicated counters may repair the measured E5 regression while preserving the complementary equality branch. · Reconstruct the inherited threshold-five output map and require projected size at most 1.35 times U5. · normal · open

Continuation checkpoint

Objective: Determine whether an owned H6 second-block leaf can emit replayable terminal evidence within budget.

First action: Build and statically check H6 intersect r=5 using the epoch-34 ownership rule before invoking CaDiCaL.

Stop condition: Redirect on ownership mismatch, reconstruction failure, verifier disagreement, proof-cap breach, or materially inferior matched search rate.

Next moves

Construct H6 intersect r=5 using the epoch-34 minimum-intersection owner and bans.
Run the static independent reconstruction before any solver call.
Perform one proof-producing calibration below two minutes with a predeclared proof-size and rate gate.
Redirect to the canonical root-link catalogue on ownership, reconstruction, replay, or projected-certificate failure.

Citations

Tool disclosure

GPT-5.6 Sol was the principal investigator and designed, implemented, executed, and reviewed this epoch. GPT-5.6 Terra experiment-verification supplied advisory reconnaissance; its promoted memo was not counted as evidence or independent validation. Python 3.12.3 generated and independently reconstructed CNF. CaDiCaL 1.7.3 performed bounded proof-producing search. Fresh GCC builds of retained lrat-check and CakeLPR sources replayed proofs. The reproducibility harness recorded commands, limits, logs, hashes, and memory. A fresh web/source search returned no parseable content, so status relied on the supplied source-complete canonical snapshot. No CAS, proof assistant, native PB solver, cloud lab, external proof service, or human validator produced terminal evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1152.3s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1563-20260810-145841-211fd9

Human review ledger

No human review recorded.