2026-08-11 06:46 UTCgpt-5.6-sol · high

Audited canonical lex ownership and constraint-subset dominance on the exact epoch-71--74 fixed-link pair-profile artifacts.

No Progress

Canonical ownership passed as arithmetic on the exact retained objects but failed its research hypothesis. The fixed-link group is order two; the only complete graph orbit was already known. Four certified partial cylinders generate six labelled images, overlap, and cover no declared complete frontier. Exact dominance leaves three maximal labelled cylinders in two orbits. No covering bound changed.

Research-policy redirect

Evidence receipt creation failed; durable progress is withheld.

Strategy and discriminator

canonical fixed-link ownership with predicate dominance

Reconstruct the complete fixed-link automorphism group, close retained profiles and certified cylinders under it, canonicalize images, and remove predicates dominated by weaker certified cylinders.

Hypothesis: Canonical ownership under the certified fixed-link group gives a new exactly-owned aggregation of the retained epoch-71--74 local exclusions.

Test: Independently reconstruct the group and every retained image, then determine whether the inputs form a complete disjoint full-profile frontier and whether ownership adds aggregation beyond the epoch-71 orbit lift.

Rationale

Both independent encodings reconstruct the same group, orbit sizes, overlap witness, and exact dominance relation, while the raw manifests explicitly state that the cylinders are partial and nonexhaustive. Therefore the local compression is valid but cannot be promoted to a cover exclusion or exactly-owned global frontier.

Claims requiring scrutiny

The fixed 12-block link used in epochs 71--74 has automorphism group of order two, generated by (4 5).
The four certified source cylinders generate six distinct labelled images, of which exactly three are maximal under constraint-subset dominance, representing two group orbits.
The retained selected 4-regular excess graph satisfies all four source cylinder predicates, so those predicates are not disjoint.
Canonical ownership of the retained objects does not supply a complete pair-profile frontier and does not change 30 <= C(15,6,3) <= 31.

Evidence and scope

Primary command: Python 3.12.3 producer under .proof-experiments/20260811-063801-d15a0f; returned PASS_REDIRECT in 0.123 seconds.
Independent command: NetworkX 3.3 checker under .proof-experiments/20260811-063807-c50b61; returned PASS in 0.574 seconds and rejected five mutations.
Primary receipt SHA-256 ad636bd2e16594c83fe2826c018741b72c25f73fb60cd9deb3521ba2d3cae059; checker SHA-256 1d85009d562c260d6ae2e7319685568b0e353ea92b951f51878ae86b0dd219a6; reruns byte-identical.

Computational experiments

.proof-experiments/20260811-063801-d15a0f: primary PASS_REDIRECT; group order 2; cylinders 6 to 3.
.proof-experiments/20260811-063807-c50b61: independent PASS; five mutations rejected; REDIRECT reproduced.

Independent checker

artifacts/epoch78-20260811/source-v1/check_canonical_pair_ownership_discriminator_v1.py uses NetworkX colored bipartite GraphMatcher rather than the producer's color-refinement/backtracking group reconstruction; it independently rebuilds images, overlap, and dominance and rejects five 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

Orbit-complete covering proofs -> predict local proof predicates need complete ownership -> observed that lex owners exist for the one retained orbit but cannot make partial overlapping cylinders exhaustive.
Compiler subsumption -> predict weaker certified predicates dominate stricter proof cases -> observed exact compression from six labelled cylinder descriptions to three.

Established facts

The retained fixed link has automorphism group {identity,(4 5)}.
Independent color-refinement/backtracking and NetworkX colored-bipartite GraphMatcher enumeration. · The exact 12 fixed link blocks in epoch-71 formula metadata. · computed
Four certified source cylinders close to six distinct labelled images, and subset dominance leaves three maximal labelled cylinders in two group orbits.
Primary receipt ad636bd2e16594c83fe2826c018741b72c25f73fb60cd9deb3521ba2d3cae059 and checker 1d85009d562c260d6ae2e7319685568b0e353ea92b951f51878ae86b0dd219a6. · Only epoch-72 leaves 0/1, epoch-73 child 1, epoch-74 child 1, and their fixed-link images. · computed
The four source cylinders overlap on the retained simple 4-regular excess graph.
Both programs evaluated every retained pair target on the explicit 30-edge graph. · The four source predicates in the retained fixed-link domain. · computed

Ruled out in this epoch

Use canonical ownership of the explicit epoch-71--74 objects to aggregate the local LRAT exclusions into a complete pair-profile frontier.
The one explicit complete graph orbit and four certified partial cylinders retained for the fixed link. · Only one complete orbit exists, the cylinders overlap, and the manifests declare no complete frontier coverage. · Primary and independent receipts plus raw manifest scope fields. · A hash-bound complete compatible full-profile catalogue or equivalent proved complete partition with independently checked exactly-once ownership and union coverage.

Open leads

Cross-artifact dominance audit on the exactly-owned fixed-first q>=5 profile frontier.
It is the cheapest way to learn whether any existing terminal predicate eliminates multiple legitimate live leaves before producing more proofs. · Join the epoch-44 249-profile manifest to retained terminal relaxed predicates and independently check every proposed containment. · high · open
Materially changed constructive degree-preserving search beyond support-three moves.
A direct 30-cover avoids exhaustive negative ownership, and moves supported on at most three blocks are locally closed only around recorded anchors. · Predeclare and calibrate a four-block or alternating-cycle move against the frozen support-two baseline on distinct exact-degree starts. · normal · open

Continuation checkpoint

Objective: Determine whether existing proof artifacts safely bulk-eliminate multiple leaves of the already exactly-owned fixed-first q>=5 frontier.

First action: Parse the epoch-44 manifest and retained terminal predicate manifests into one immutable cross-axis mapping, then run exact containment and coverage checks without a solver.

Stop condition: Redirect to a materially changed constructive route on axis-mapping failure, no multi-leaf dominance, or any ownership/coverage ambiguity.

Next moves

Build a hash-bound mapping from the exact fixed-first 249-profile manifest to all retained terminal relaxed predicates.
Test whether any terminal predicate safely contains more than one unresolved q>=5 profile leaf, with an independent subset/coverage checker.
If no cross-leaf bulk reuse exists, switch to a materially changed constructive route; do not extend the local cylinders or repeat unchanged incidence/profile-129 runs.

Citations

Tool disclosure

GPT-5.6 Sol principal; GPT-5.6 Terra advisory delegates supplied challenger/prior-art and experiment-verification memos, which Sol audited and did not treat as validation. Python 3.12.3, NetworkX 3.3, exact set/integer arithmetic, SHA-256, and the Proof Factory experiment harness were used. No SAT solver, CAS, proof assistant, cloud lab, external proof service, human validator, or publication action was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration: 1157.8s
Review state: evidence receipt failure; not durable progress
Attempt ID: covering-c1563-20260811-064650-fbc6b2

Human review ledger

No human review recorded.