Implemented and audited a capped canonical-construction-path enumeration of partial root links using colored point-block incidence graphs.

canonical root-link catalogue

Batch nauty canonicalization, canonical deletion parents, and hereditary degree/pair-capacity filters measure the symmetry-reduced partial-link frontier.

Hypothesis: The five forced root-link degree types have at most 10000 accepted canonical-construction nodes within 1800 seconds.

Test: Enumerate canonical-parent nodes until all five degree types finish, 1800 seconds elapse, or cumulative node 10001 is independently validated.

Pairwise colored nonisomorphism and canonical-parent validity were independently replayed, so the recorded objects alone falsify the 10000-node upper gate. The computation stopped before exhaustive depth-five or all-type coverage and cannot support a covering-number conclusion.

• The specified unfiltered canonical construction has at least 10001 recorded valid, pairwise colored-nonisomorphic canonical-parent nodes within root-link degree type (8,4^13).
• All 10000 nonroot parent links in the receipt replay under the declared canonical deletion rule.
• No 30-cover or exclusion of 30 was obtained.

• Primary command completed with return code 0 in 85.624 captured seconds.
• Primary receipt SHA-256 0ad095a6c238147d6f8f3236570ef5ad8caa99d8dce068f72efeec26fb5161eb.
• Checker receipt SHA-256 0f93ed82a4d19adb41f3f301f6420b28440350819140ce05a6219f608b94468b.
• Hash manifest replay passed for 12 files and three nauty binaries.

• .proof-experiments/20260809-041745-94391e: primary two-worker pilot, node cap exceeded at 10001 in 85.374 script seconds
• .proof-experiments/20260809-042308-790f3c: independent checker passed in 3.144 seconds

checkers/check_canonical_root_link_pilot_v1.py independently reparses all graph6 objects, recomputes structural constraints, reconstructs canonical parents, checks colored-isomorphism counts with nauty-shortg, and runs relabeling/duplicate controls. It does not re-enumerate omitted extension candidates, which is unnecessary for the validated lower witness of 10001 nodes.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• Certified C(12,6,4) canonical link decomposition -> predict a manageable C(15,6,3) root-link frontier -> the unfiltered frontier exceeded 10000 nodes before completing the first degree type.

• A root link in any hypothetical 30-cover has one of five target degree types induced by the partitions of four excess degree units.
  artifacts/epoch19-20260809/technical_report.md · Every root point of every hypothetical 30-block C(15,6,3) cover. · proved
• The recorded prefix contains 10001 distinct valid canonical-parent nodes for type (8,4^13).
  Primary and checker receipts with matching hashes and shortg counts. · The declared colored-incidence representation and hereditary filters. · computed

• Scale the unfiltered canonical partial-root-link catalogue under the 10000-node tractability gate.
  The current canonical-parent construction with degree and pair-capacity filters. · The first degree type alone produced 10001 independently validated recorded nodes before completion. · artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json and root_link_canonical_checker_receipt.json · A sound bulk completion filter or different decomposition with a measured pilot below the cap.

• Proof-producing exact completion filtering at depth four.
  It directly tests whether most shallow canonical nodes are dead and could eliminate whole subtrees. · Run a small deterministic stratified sample with replayable UNSAT proofs and require at least tenfold certified elimination. · high · open
• Materially changed direct 30-cover encoding.
  A SAT witness would still settle the target and is directly checkable. · Specify a new encoding or proof-prefix reuse mechanism before any solver run; do not repeat the failed incidence throughput control. · normal · open

Objective: Determine whether certified exact-completion pruning can compress the recorded depth-four root-link set enough to justify reopening canonical decomposition.

First action: Run `jq '[.nodes[] | select(.type_index==0 and .depth==4)] | length' artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json`, then freeze a deterministic stratified sampling rule and proof-producing completion encoding.

Stop condition: Redirect if the matched pilot cannot certify at least tenfold dead-node elimination, any UNSAT proof fails replay, or surviving-node extrapolation is required to support a claim.

• Extract a deterministic stratified sample from the recorded 2258 depth-four nodes.
• Specify an exact link-completion SAT encoding with replayable UNSAT proofs and a matched no-filter control.
• Continue only if the sample predicts at least tenfold certified dead-node elimination.
• Preserve direct 30-cover search, but require a material encoding or proof-prefix change before reopening incidence SAT.

• 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/2607.23766 ↗

GPT-5.6 Sol principal performed synthesis, implementation, source audit, and interpretation. Pre-existing GPT-5.6 Terra delegate memos supplied advisory route reconnaissance only and were not counted as validation. Python 3.12.3 executed deterministic code; Debian nauty 2.8.8+ds-5 provided labelg, shortg, and dreadnaut. No SAT solver, CAS, proof assistant, or external human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1337.0s

Review state

not a result claim

Attempt ID

covering-c1563-20260809-042813-d089c5

No human review recorded.