2026-08-11 23:52 UTCgpt-5.6-sol · high

Exact point-isomorphism census of the declared saved degree-18 defect-10 near-cover corpus.

No Progress

The declared saved degree-18 defect-10 corpus contains 90 distinct labelled families and exactly 16 point-isomorphism classes. The 88 Iorio radius-five minima form 14 classes, while two later persisted families form two additional singleton classes. This is an exact saved-corpus classification, not a classification of all near-covers; the maintained range remains 54 <= C(15,5,3) <= 55.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

constructive near-cover isomorphism census

Reconstruct qualifying 54-block families, canonicalize their 69-vertex point-block incidence graphs with nauty, and independently verify the partition by exhaustive point-permutation backtracking.

Hypothesis: The declared saved corpus contains exactly 16 point-isomorphism classes, including at least one class outside the 88 Iorio radius-five defect-10 candidates.

Test: Canonicalize every directly checked family, then independently reconstruct the corpus, verify an explicit point map for every within-class membership, and exhaust all point maps between class representatives.

Rationale

Nauty produced a deterministic canonical partition. A materially different checker independently reconstructed the corpus, exhaustively searched every pair-codegree-compatible point permutation, directly replayed all accepted block maps, and proved pairwise nonisomorphism of the 16 representatives. Regeneration was byte-identical and three fail-closed mutations were rejected.

Claims requiring scrutiny

The declared saved corpus has exactly 90 distinct labelled degree-18 defect-10 families.
Those 90 families form exactly 16 point-isomorphism classes with sizes 8,8,8,8,8,8,8,8,4,4,4,4,4,4,1,1.
The 88 Iorio radius-five defect-10 candidates form exactly 14 classes.
Two later persisted defect-10 families form two additional singleton classes outside the radius-five corpus.
No conclusion about the existence of a 54-cover follows from this census.

Evidence and scope

python3 scripts/saved_defect10_isomorphism_census_v1.py --workspace . --output artifacts/saved-defect10-isomorphism-census-20260811
python3 checkers/check_saved_defect10_isomorphism_census_v1.py --workspace . --artifact artifacts/saved-defect10-isomorphism-census-20260811 --output artifacts/saved-defect10-isomorphism-census-20260811/independent-check.json
python3 checkers/test_saved_defect10_isomorphism_census_mutations_v1.py --workspace . --artifact artifacts/saved-defect10-isomorphism-census-20260811 --output artifacts/saved-defect10-isomorphism-census-20260811/mutation-controls.json
sha256sum -c artifacts/saved-defect10-isomorphism-census-20260811/manifest.sha256

Computational experiments

.proof-experiments/20260811-233809-abf6d4: producer completed in 0.576 seconds and found 90 labelled families in 16 classes.
.proof-experiments/20260811-234643-08c22e: independent checker completed in 0.838 seconds, validating 90 memberships and rejecting 120 cross-class pairs.
artifacts/saved-defect10-isomorphism-census-20260811: three mutations rejected and decisive outputs regenerated byte-identically.

Independent checker

checkers/check_saved_defect10_isomorphism_census_v1.py independently reconstructs the corpus and exhausts pair-codegree-compatible permutations of 15 points. It does not consume nauty signatures when deciding isomorphism and directly verifies all 54 mapped blocks.

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

Graph canonicalization -> incidence graphs quotient labelled set systems -> the declared 90-family corpus collapsed exactly to 16 independently verified classes.

Established facts

Every family in the declared corpus has 54 distinct blocks, point-degree vector 18^15, and covers exactly 445 of 455 triples.
Independent reconstruction and direct enumeration in independent-check.json. · The 90 declared saved families. · computed
The declared corpus has exactly 16 point-isomorphism classes.
90 positive point-map checks and 120 exhaustive negative representative comparisons. · The declared saved corpus only. · computed

Ruled out in this epoch

Treat the repeatedly searched locked defect-10 seed as representative of every saved defect-10 basin.
The declared saved corpus. · The corpus contains 16 classes, including 15 not isomorphic to the locked class. · artifacts/saved-defect10-isomorphism-census-20260811/independent-check.json · A proved repair-invariant theorem or matched census showing all 16 classes have identical relevant repair geometry.
Rerun complete fixed-pair-link coverage as a strengthening.
All four canonical normalized baseline CNFs audited in the saved pair-link packet. · Every requirement is already a baseline coverage clause or a fixed-block tautology; logical clause delta is zero. · artifacts/pair-link-cnf-delta-audit-20260811/result.json and independent-check.json · A separately checked nonzero labelled constraint, such as an exact pair-count or skeleton coupling.

Open leads

Class-representative constructive repair triage.
Sixteen exact representatives cover every saved basin while eliminating a 5.625-fold labelled redundancy. · Compute exact loss-geometry/legal-move signatures and run matched 4,096-proposal tranches only where informative. · high · open
Globally complete proof encoding.
A complete replayed UNSAT certificate would settle the value at 55 and remains necessary if constructive class triage has no signal. · Select a globally complete normalized branch and measure one proof-producing cube pilot with hash-bound coverage. · normal · open

Continuation checkpoint

Objective: Determine whether any of the 15 non-locked classes has materially better exact repair geometry.

First action: Read families.jsonl, extract the 16 listed representatives, and generate a deterministic table of uncovered-triple geometry and legal strict-move counts.

Stop condition: Redirect to global proof encodings if all representatives have identical quotient-level signatures and matched 4,096-proposal tranches produce no independently checked defect below 10.

Next moves

Extract the representative_family_sha256 member of each of the 16 classes.
Compute exact uncovered-triple loss geometry and legal strict-move counts for all representatives.
If signatures differ, run matched 4,096-proposal repair tranches with a direct defect-below-10 acceptance gate.
Redirect to globally complete proof encodings if no representative improves defect 10 or produces reproducible class-specific signal.

Citations

Tool disclosure

GPT-5 Sol principal selected, implemented, and audited the experiment. Two GPT-5.6 Terra delegates supplied advisory reconnaissance only; their agreement was not validation. Deterministic evidence used Python 3.12.3, nauty/dreadnaut 2.8.8, SHA-256, and a separately written exhaustive 15-point backtracking checker. NetworkX 3.3 was used only in an abandoned performance prototype and supports no decisive claim. No CAS, SAT solver, proof assistant, or external human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1359.6s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1553-20260811-235211-fd9a69

Human review ledger

No human review recorded.