Dual exact rooted canonicalization of H=2*C15 and a one-edge weight mutation, with a deliberately weight-blind negative arm, 13 fail-closed receipt attacks, and deterministic reruns.

canonical pair-rooted weighted-H augmentation

Represent each positive-weight edge by a weight-coloured incidence vertex, mark an unordered root pair by two same-coloured leaves, compare exact nauty canonical-code classes with an independently reconstructed weighted rooted-isomorphism partition, and use a one-edge mutation to expose weight-blind behavior.

Hypothesis: Exact weight-coloured canonicalization and an independent weighted GraphMatcher give the same unordered-root equivalence relation on H=2*C15 and distinguish changing one cycle edge from weight two to weight one.

Test: Canonicalize all 105 unordered roots of each of the doubled cycle and its one-edge mutation; require exact partition and minimum-owner agreement, predicted 7- and 56-orbit profiles, a different weight-blind mutation partition, 13 rejected corruptions, and byte-identical reruns.

The result is progress because it falsifiably and independently closes the specific weight-colour gap blocking the next ownership experiment. It is not a candidate exact optimum: two controls do not cover all weighted surplus graphs, and no 30-block cover or complete UNSAT decomposition exists.

• For H=2*C15, all 105 unordered roots form seven exact automorphism orbits of size 15.
• After changing weight({0,1}) from two to one, the 105 unordered roots form seven singleton and 49 size-two orbits.
• On both controls, nauty canonical-code equality is exactly independent weighted rooted-isomorphism equivalence; the mutation is distinguishable from a weight-blind encoding; all 13 declared corruptions are rejected; and accepted receipts rerun byte-identically.
• The maintained covering range remains 30 <= C(15,6,3) <= 31.

• Harnessed producer command in .proof-experiments/20260811-231934-21f9dd/experiment.json returned 0 in 0.122 seconds.
• Harnessed independent checker in .proof-experiments/20260811-231942-cebfda/experiment.json returned 0 in 13.770 seconds and rejected 13 mutations.
• Producer receipt and rerun are byte-identical with SHA-256 8736b842d05d380868327524618627b9db8dfc05588b8c57410eef2fb94aa743.
• Independent receipt and rerun are byte-identical with SHA-256 721c2b346c8872b606274e05290e795f2c74bfb1dbdd77b108eb2ea210a10148.
• The checker records weighted mutation profile 7x1+49x2 and deliberately unweighted profile 7x15.

• .proof-experiments/20260811-231934-21f9dd: accepted producer PASS, 0.122 seconds, 18176 KiB peak child memory, orbit profiles 7x15 and 7x1+49x2.
• .proof-experiments/20260811-231942-cebfda: accepted independent PASS, 13.770 seconds, 36156 KiB, 3282 main GraphMatcher decisions, weight-blind contrast, 13 mutations rejected.
• .proof-experiments/20260811-232005-5146f8: producer rerun PASS; receipt byte-identical.
• .proof-experiments/20260811-232011-260f83: checker rerun PASS in 16.035 seconds; receipt byte-identical.
• Preliminary raw v1 commands had an unquoted ampersand-bearing source URL and were not captured by the harness; their outputs are excluded from evidence and were replaced by fresh v2 runs.

checkers/check_rooted_pair_weighted_control_v1.py uses NetworkX 3.3 weighted GraphMatcher directly on attributed 15-vertex graphs reconstructed from the cycle definition. It neither imports the producer nor invokes nauty nor uses the producer's incidence-gadget representation.

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

• Certificate-backed orbit decomposition for C(12,6,4) -> a negative covering proof needs independently reconstructible, disjoint owners before SAT leaves -> the proposed C(15,6,3) owner now respects multiplicity on decisive controls, but global parent coverage remains open.

• H=2*C15 has seven unordered-root automorphism orbits, each of size 15.
  Producer 8736b842..., checker 721c2b34..., byte-identical reruns, and dihedral-distance derivation. · All 105 unordered vertex pairs of the exact doubled 15-cycle. · computed
• The doubled 15-cycle with only edge {0,1} reduced to weight one has seven singleton and 49 size-two unordered-root orbits.
  Dual exact partitions plus Burnside count (105+7)/2=56 for the surviving reflection. · All 105 unordered vertex pairs of the declared one-edge mutation. · computed
• The accepted producer partition is weight-sensitive on the declared controls.
  The weighted mutation has 56 classes while the deliberately weight-blind independent arm has seven; exact partitions and hashes are retained. · The doubled-cycle mutation test only, not every weighted graph. · computed

• Use a uniform-multiplicity graph alone to validate weight-aware canonicalization.
  Controls where every positive edge has the same multiplicity. · Erasing a common weight preserves the graph automorphism action, so the root partition cannot expose a weight-blind implementation. · The predeclared one-edge mutation separates the weighted 56-orbit partition from the unweighted seven-orbit partition. · Add at least two edge-weight classes whose preservation changes an independently known orbit partition.
• Treat the 210-to-63 control quotient as a quotient of all pair-surplus multigraphs or all 30-covers.
  Any weighted H outside the two explicit controls and every cover-completion conclusion. · No complete weighted-H catalogue or later-row frontier was enumerated. · Both receipts enforce their exact two-control scope. · A complete hash-bound weighted-H frontier with independently reconstructed exactly-once parents.
• Compile isolated pair-surplus SAT proof leaves now.
  Negative-search leaves before depth-three and complete-H parent coverage are qualified. · Weighted semantics is necessary but not sufficient for aggregating local exclusions into a global theorem. · The current result contains no frontier ledger or all-H completeness certificate. · Independent exact frontier coverage and a measured feasible proof-certificate budget.

• Duplicate-free depth-three pair-surplus frontier.
  It is now the smallest missing step between the exact 82-key two-row prefix and a globally useful weighted-H owner decomposition. · Enumerate at most 10000 canonical third-row children or 120 seconds and independently verify every processed parent, child key, count, digest, and declared mutation. · high · open
• Materially different direct constructive exact-degree-12 search.
  One directly checked 30-block cover settles the target without any global negative frontier. · Specify a new global move or encoding outside the closed support-two/support-three and six-representative pilots, then require a five-second direct-model or throughput gate. · normal · open
• Canonical root-link catalogue fallback.
  Fixing a 12-block root link remains structurally distinct from the pair-surplus row frontier. · If depth-three growth breaches its cap, run a 10000-orbit or 120-second root-link catalogue pilot with independent parent coverage. · normal · open

Objective: Measure a duplicate-free, independently checkable depth-three pair-surplus frontier from all 82 exact two-row keys.

First action: Create scripts/pair_surplus_depth3_frontier_v1.py and a separately encoded checker, then run the producer from artifacts/epoch98-20260811/pair-surplus-depth2-ownership-v1/producer-receipt.json under a 10000-child/120-second cap.

Stop condition: End or redirect on inconsistent owner/parent, checker disagreement, any missing or duplicate child, cap breach before a closed declared layer, or a complete-H/certificate projection beyond the declared budget.

• Implement a canonical depth-three transition from each of the exact 82 two-row keys, capped at 10000 children or 120 seconds, with no SAT solver.
• Write a materially different independent checker that reconstructs every declared parent transition, child key, count, and sorted digest and rejects deletions, duplications, parent edits, and digest edits.
• Estimate complete-H frontier and proof-certificate volume before compiling any owned SAT cylinder; redirect if the projection is infeasible.
• Keep a materially different direct constructive exact-degree-12 witness route active because a checked 30-block list remains the shortest terminal certificate.

• 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; two injected GPT-5.6 Terra delegates supplied advisory route-selection memos that were promoted with hashes and were 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, jq for inspection, 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 produced evidence this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1053.1s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-232845-6ca794

No human review recorded.