Independent exhaustive replay of the type-(6,6,4^12) root-link frontier through depth four.

colored root-link orbit frontier validation

Extend every prior orbit representative by every unused 5-subset, apply packed hereditary feasibility filters, canonicalize with nauty, and compare exact child sets against two prior generators.

Hypothesis: A separately written packed checker reproduces every exact canonical child set for the (6,6,4^12) partial root-link frontier through depth four within 110 seconds and 1024 MiB.

Test: Reconstruct every prior representative, enumerate all 829624 unused-block extensions, compare all four exact child sets and counts, reconstruct every deletion parent, and reject four frozen mutations.

Agreement among two differently structured generators and a separately written exhaustive checker supports the bounded classification. The exact-value verification contract remains unmet because there is neither a 30-block witness nor a complete proof-replayed exclusion.

• The complete colored-isomorphism frontier for partial (6,6,4^12) root links through depth four under the declared filters has counts [1,3,30,381,9429].
• The checker tested 829624 raw extensions, 502785 feasible extensions, 9844 structures, and 9843 deletion parents.
• The maintained range remains 30 <= C(15,6,3) <= 31.

• Harnessed checker returned 0 without timeout in 56.784 seconds at 138652 KiB peak child RSS.
• Checker result pass with child-orbit sizes [3,30,381,9429] and all four controls rejected.
• sha256sum -c artifacts/epoch93-20260811/SHA256SUMS passed for every bound artifact.

• .proof-experiments/20260811-175034-d3aeba: PASS in 56.784 seconds; exact depth-four child set contains 9429 orbits.

scripts/check_type2_frontier_parallel_v2.py is separately written from both generators, reconstructs graph6 records, uses a packed feasibility kernel, exhaustively rebuilds every child set, and rejects omitted-record, duplicate-record, wrong-target, and wrong-color controls.

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 C(12,6,4) link-orbit decomposition -> predict that a forced-link colored frontier can be hash-bound and independently replayed -> the bounded type-2 depth-four replay passed, with no extrapolation beyond that scope.

• The declared type-(6,6,4^12) partial-link frontier through depth four is complete up to the declared colored isomorphism and filters, with counts [1,3,30,381,9429].
  Three-way generator/checker agreement; checker receipt SHA-256 40747a864533ad30cc0edcc0ad20be1bbe11e4deb565862d32877955b6772ada. · Profile (6,6,4^12), depths 0–4, declared hereditary necessary filters only. · computed

• Treat the validated type-2 depth-four frontier as a global quotient or covering-number exclusion.
  Other root profiles, deeper links, complete links, and global completions. · The checker covers only one of five necessary profiles and only partial links through four blocks. · Explicit scope fields in the generator and checker receipts. · Hash-bound complete-link and residual-completion certificates whose union covers all five profiles.

• Hash-ranked type-2 residual-completion sample
  Cheapest way to measure terminal yield and proof storage now that the frontier is validated. · Compile fixed SHA-256 ranks into exact completion CNFs and run bounded witness/proof-producing pilots. · high · open
• Pair-surplus-multigraph-first H cube
  A materially different decomposition based on globally forced pair equations. · Construct one multigraph-capable canonical H cube and require exact reconstruction plus a complete replayed calibration proof. · normal · open
• Five-bit triple-support-index constructive encoding
  A direct witness-oriented alternative if completion cubes behave poorly. · Run the frozen paired preprocess-only control and variant. · normal · open

Objective: Measure completion and certificate behavior on a deterministic sample of the 9429 validated nodes.

First action: Select fixed SHA-256 ranks from artifacts/epoch92-20260811/type2-canonical-frontier.json and compile the first exact residual-completion CNF with independent reconstruction.

Stop condition: A verified cover ends the campaign; a replayed local proof justifies measured continuation; uniform UNKNOWN, proof-cap failure, or reconstruction mismatch redirects.

• Select deterministic SHA-256 ranks from the 9429 depth-four nodes.
• Compile and independently reconstruct a small exact residual-completion sample.
• Validate every model against all 455 triples and require complete LRAT replay for every local UNSAT claim.
• Redirect to one pair-surplus-H cube calibration if sampled leaves give no terminal or proof-size signal.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=6&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal; two GPT-5.6 Terra advisory delegates whose promoted memos were audited and not counted as validation; Python 3.12.3; nauty-labelg with binary SHA-256 96e973e3a13442c6f626012b6b1059ef88e750aff284be6bfc6cd77ee7f185bf; SHA-256; Proof Factory run_experiment.py; web search for current status and prior art. No SAT/PB solver, CAS, proof assistant, proof-log checker, 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

1197.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-180125-333833

No human review recorded.