Dual exact unordered-root canonicalization on the saved 3K5 and circulant pair-surplus controls, with fail-closed receipt repair and deterministic reruns.

canonical pair-rooted weighted-H augmentation

Encode each completed H with an unordered root pair as a coloured edge-incidence gadget, choose the minimum exact canonical code, and independently verify code equality against weighted rooted-graph isomorphism.

Hypothesis: The minimum rooted coloured-graph code gives a well-defined exactly-one automorphism-orbit owner on both saved surplus-graph controls, with no non-automorphic canonical-code tie.

Test: Canonicalize all 105 unordered root pairs of each control with nauty coloured gadgets and require an independent weighted GraphMatcher partition to agree pair-for-pair, identify the same minimum-code owner orbit, and reject nine mutations.

The result is progress because it independently qualifies the previously missing owner mechanism on the two declared controls and leaves replayable artifacts. It is not a candidate exact optimum because neither control covers all weighted H, and no cover or exhaustive exclusion was produced.

• For the saved H=3K5 graph, the 105 unordered vertex pairs form exactly two automorphism orbits of sizes 30 and 75; the minimum producer code selects the 75-pair inter-component orbit.
• For the saved H=Cay(Z_15,{+/-1,+/-2}) graph, the 105 unordered vertex pairs form exactly seven automorphism orbits of size 15; the minimum producer code selects the cyclic-distance-3 orbit.
• On both controls, producer canonical-code equality is exactly independent weighted rooted-isomorphism equivalence, all nine declared mutations are rejected, and both result receipts rerun byte-identically.
• The maintained range remains 30 <= C(15,6,3) <= 31.

• python3 scripts/rooted_pair_owner_controls_v1.py --out artifacts/epoch100-20260811/rooted-pair-owner-controls-v2/producer-receipt.json
• python3 checkers/check_rooted_pair_owner_controls_v1.py --receipt artifacts/epoch100-20260811/rooted-pair-owner-controls-v2/producer-receipt.json --out artifacts/epoch100-20260811/rooted-pair-owner-controls-v2/independent-check.json
• Producer receipt and rerun are byte-identical with SHA-256 e52e8b307af83504baf82ec9a392ffed0037a2357fe3c956fa60dbfb719b4f34.
• Independent receipt and rerun are byte-identical with SHA-256 388fed749dcb04da23b0d52f979890984eeb2459a1be4a6b06f4eb6a963bdcf7.
• sha256sum -c artifacts/epoch100-20260811/SHA256SUMS passes for every listed input and result.

• .proof-experiments/20260811-223947-40f2a7: first independent audit failed because the hash-only v1 receipt could not reject a false-owner mutation; no accepted claim depends on it.
• .proof-experiments/20260811-224026-61249b: corrected producer PASS in 0.223 seconds, peak child memory 18304 KiB, with 2 and 7 orbits.
• .proof-experiments/20260811-224040-5b5f62: independent checker PASS in 3.335 seconds, peak child memory 34904 KiB, 591 GraphMatcher decisions and nine mutations rejected.
• .proof-experiments/20260811-224052-c390a4: producer rerun PASS and byte-identical receipt.
• .proof-experiments/20260811-224124-941ebb: independent-checker rerun PASS and byte-identical receipt.

checkers/check_rooted_pair_owner_controls_v1.py uses NetworkX 3.3 weighted GraphMatcher on root-coloured H directly, without importing the producer, invoking nauty, or using the edge-incidence gadget canonical code.

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

• Certified orbit case splits for C(12,6,4) -> a global exclusion needs disjoint, reconstructible owners before SAT leaves -> the two declared completed-H controls now have exact independently checked unordered-root owners, while global H coverage remains open.

• The saved 3K5 control has exactly two unordered-root automorphism orbits of sizes 30 and 75.
  Corrected producer receipt e52e8b... and independent receipt 388fed... with byte-identical reruns. · All 105 unordered vertex pairs of the exact epoch-95 3K5 graph. · computed
• The saved circulant control has exactly seven unordered-root automorphism orbits, each of size 15.
  Corrected producer receipt e52e8b... and independent receipt 388fed... with byte-identical reruns. · All 105 unordered vertex pairs of the exact epoch-97 Cay(Z_15,{+/-1,+/-2}) graph. · computed
• On each control, the lexicographically minimum exact canonical code corresponds to one whole independently reconstructed automorphism orbit.
  Independent checker compared retained canonical codes, partitions, minimum owner, and hashes and rejected false-owner and collision mutations. · The two saved simple controls only. · computed

• Use canonical-code hashes alone to validate a minimum-code owner.
  Order-based owner receipts under this architecture. · Hashes preserve equality but not lexicographic order, so the first checker could not reject a false owner. · .proof-experiments/20260811-223947-40f2a7 failed exactly the two false-owner controls; v2 retained codes and rejected them. · A separately certified order-preserving commitment scheme or retention of the canonical codes/order witnesses.
• Treat the 210-to-9 control quotient as a complete quotient of all pair-surplus multigraphs or all 30-covers.
  Any H other than the two saved simple controls and any cover-completion conclusion. · No weighted-H catalogue or completion frontier was enumerated. · Both receipts state their two-control scope; the independent checker enforces it. · A complete hash-bound weighted-H frontier with independently reconstructed exactly-once parents.
• Compile another unowned local SAT proof leaf now.
  Pair-surplus negative-search leaves before weighted and frontier ownership qualification. · Two simple controls do not establish global exactly-once ownership, so a new local proof would remain unaggregatable. · Current scope limit and prior local-proof register. · Qualified weighted semantics, a complete owned frontier, and a measured feasible certificate budget.

• Genuine multiedge rooted-owner control H=2*C15.
  It is the cheapest exact test of the weight-colour premise absent from both accepted simple controls. · Add the multiplicity-two cycle to both encodings, require complete 105-pair coverage, exact partition agreement, minimum-owner agreement, and rejection of one weight mutation under a 120-second cap. · high · open
• Duplicate-free depth-three pair-surplus frontier.
  It is the smallest extension from the exact 82-key depth-two layer toward a globally useful H decomposition. · Enumerate at most 10000 canonical children or 120 seconds and independently verify every parent, key, count, and digest. · normal · open
• Materially different direct constructive exact-degree-12 search.
  One checked 30-block cover settles the target without any exhaustive ownership or proof portfolio. · Specify a new global encoding or move family not covered by the closed support-two/support-three and six-representative pilots, then require a short direct-model or throughput gate. · normal · open

Objective: Qualify weighted-edge colour semantics, then measure one bounded depth-three owner frontier.

First action: Extend both rooted-pair implementations with H=2*C15 and run the predeclared dual exact audit through the reproducibility harness.

Stop condition: Redirect on a weight-colour disagreement, non-automorphic tie, missing/duplicate pair or parent, failed mutation, 120-second/1-GiB breach, or depth-three growth beyond 10000 nodes.

• Qualify a genuine multiedge 4-regular control such as H=2*C15 with dual exact canonicalizers and a weight-mutation rejection.
• If weighted qualification passes, enumerate at most 10000 depth-three canonical children or run for at most 120 seconds and independently reconstruct every parent and digest.
• Estimate complete-H and certificate volume before compiling any SAT leaf; redirect if the frontier or proof budget is infeasible.
• Keep a materially different direct constructive exact-degree-12 witness route active.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol acted as principal investigator; the injected GPT-5.6 Terra challenger-prior-art and experiment-verification memos were advisory and promoted with hashes, not treated as evidence. Deterministic work used Python 3.12.3, nauty-labelg at /usr/bin/nauty-labelg (SHA-256 96e973e3a13442c6f626012b6b1059ef88e750aff284be6bfc6cd77ee7f185bf), NetworkX 3.3 GraphMatcher, SHA-256, and the computational-researcher run_experiment.py harness. Web search checked the maintained LJCR/Covering Repository status and arXiv:2607.23766. No SAT solver, CAS, proof assistant, cloud lab, external proof service, or human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1038.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-224921-b5ef8c

No human review recorded.