2026-07-22 15:12 UTCgpt-5.6-sol · high

Restored proof replay, reconstructed the missing four-orbit blocker, independently preflighted matched sequential and kmtotalizer CNFs, and submitted the fixed 20-leaf cold benchmark to the checkpointed lab.

No Progress

Proof replay is now portable, a fresh nontrivial inherited CNF proof replayed, and the missing 1,616-clause four-orbit blocker was exactly reconstructed. The matched encoding preflight passed: kmtotalizer has 20,160 fewer auxiliaries and 853 more clauses with an identical audited core. The full benchmark is running as lab job lab-covering-c1264-e9221dfd02b3; none of its live outputs is claimed here. The exact covering number remains open.

Research-policy redirect

Attempt evidence did not validate; durable progress is withheld.

Strategy and discriminator

cardinality-encoding portfolio

Replace only the 11 link-degree sequential counters with kmtotalizer while preserving and hash-comparing the non-cardinality core, then compare cold CaDiCaL runs with immediate DRAT replay.

Hypothesis: Sequential and kmtotalizer forms of the same rooted link leaf have an identical independently reconstructed non-cardinality core, isolated exact-degree encodings with correct boundary behavior, and kmtotalizer uses substantially fewer auxiliary variables.

Test: Build both forms for one hash-bound frontier leaf, independently reconstruct every non-cardinality clause, audit auxiliary confinement, and solve 66 boundary assignments per encoding before authorizing the matched solver tranche.

Rationale

The deterministic reconstruction, independent audits, proof controls, and regression suite support a scoped infrastructure result. They do not cover the open frontier or satisfy either terminal verification contract.

Claims requiring scrutiny

Pinned DRAT-trim revision 2e3b2dc0ecf938addbd779d42877b6ed69d9a985 and binary SHA-256 92f0aa9575ed519d66a99b8b1b3dde6ece4618ae4c202a3a4b200265dda0aa7a passed positive and negative controls.
The missing catalog-4 blocker reconstructs to exactly 1,616 clauses and SHA-256 d68f1de5f99cf6e56480a3778dd270e8abca276d192fdf19b354375422d6cad4.
For the audited preflight leaf, sequential and kmtotalizer share the same non-cardinality core; their auxiliary counts are 40,180 and 20,020 respectively.
No 40-cover was found and no open frontier node was excluded in this epoch.

Evidence and scope

python3 run_experiment.py ... rebuild-catalog4-blocker: reconstructed the recorded blocker hash
python3 run_experiment.py ... audit-rebuilt-catalog4-blocker: independently accepted 4 orbits and 1,616 images
python3 run_experiment.py ... cardinality-encoding-matched-preflight-v2: both matched audits passed
.venv/bin/python -m unittest discover -s tests -p test_*.py -v: 47 tests passed
Commit fd346a5 vendors the proof checker and records the durable checkpoint; a Git commit is not mathematical validation.

Computational experiments

.proof-experiments/20260722-145625-c29ea8: rebuilt the absent catalog-4 blocker with the recorded hash.
.proof-experiments/20260722-145649-c4a935: independent catalog audit accepted four orbits and 1,616 images.
.proof-experiments/20260722-150455-da6f28: final matched preflight passed; auxiliary reduction 20,160 and clause delta +853.
lab-covering-c1264-e9221dfd02b3: submitted/running; no live result claimed.

Independent checker

checkers/audit_cardinality_encoding_cnf.py independently reconstructs the non-cardinality core and orbit partitions, checks each point universe and auxiliary range, and runs 66 boundary assignments per encoding. These controls are not a formal all-assignment proof of the PySAT encoder.

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

Layered exact covering search -> predict that changing only the cardinality layer can alter reduced-instance closure -> matched structure passed preflight; performance remains pending.

Established facts

The reconstructed four-orbit blocker has 1,616 clauses, covers 1,616 distinct group images, and matches the catalog-recorded hash.
artifacts/controls/link-orbit-catalog-4-rebuild-20260722.audit.json · The four preserved exact-degree C(11,5,3) link witnesses under C2 wr S5 · computed
The audited sequential and kmtotalizer preflight CNFs share non-cardinality core SHA-256 4d8416077f50a7958e0bfda78b9526b949906af8a8c9ef339c5c91d4b38b3269.
artifacts/controls/cardinality-encoding-preflight-final-20260722/preflight-result.json · Hash-bound frontier leaf s-r0-3 · computed
Kmtotalizer uses 20,020 auxiliaries versus sequential's 40,180 in the eleven audited equalities.
Both build receipts and independent CNF audits · Pinned python-sat 1.9.dev7 exact-degree link encoding · computed

Ruled out in this epoch

Promote the 189 inherited historical UNSAT validation receipts as freshly replayed evidence.
All inherited receipts whose referenced external.drat files are absent · The proof bytes required by DRAT-trim were not preserved in this checkout. · toolchains/drat-trim/PROVENANCE.md and filesystem audit · Recover every exact hash-matching CNF/proof pair and replay it with the pinned checker.

Open leads

Review and complete the matched 20-leaf encoding benchmark.
It directly tests the current propagation bottleneck with replayable certificates. · Inspect the newest immutable lab record for lab-covering-c1264-e9221dfd02b3 and authorize the next segment only if all gates pass. · high · open
Degree-preserving positive local search under the forced matching.
A positive 40-block witness has a much smaller acceptance surface than a global exclusion. · Run a fixed-seed, equal-budget comparison against unconstrained local search only if the encoding benchmark is held or redirected. · normal · open

Continuation checkpoint

Objective: Review the first ten cold encoding runs and decide whether the checkpointed benchmark may continue.

First action: Open the newest records/labs/lab-covering-c1264-e9221dfd02b3-*.json record and its content-addressed lab-runs output; verify progress, hashes, CNF audits, verdicts, and proof replays.

Stop condition: Stop or redirect on any core/cardinality/verdict mismatch, missing UNSAT proof, failed replay, projected proof storage above 30 GB, or final failure of the 8/20 plus-four rule.

Next moves

Review the first immutable completion record for lab-covering-c1264-e9221dfd02b3.
Verify every completed unit's build hash, CNF audit, solver verdict, and DRAT receipt before authorizing another segment.
After all 40 runs, continue only if kmtotalizer has at least 8/20 verified closures and at least four more than sequential.
Redirect without extending identical timeouts if the acceptance rule fails.

Citations

Tool disclosure

GPT-5.6 Sol principal designed, audited, and interpreted the epoch. A GPT-5.6 Terra delegate supplied an advisory experiment-verification memo; Sol independently checked the artifacts and did not treat model agreement as validation. Deterministic work used Python 3.12, python-sat 1.9.dev7, CaDiCaL 1.7.3, pinned DRAT-trim revision 2e3b2dc0ecf938addbd779d42877b6ed69d9a985, Git, SHA-256, unittest, and official-source web search.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1875.4s
Review state: evidence invalid or incomplete; not durable progress
Attempt ID: covering-c1264-20260722-151254-64a392

Human review ledger

No human review recorded.