Enumerate the previously untested (6,6,4^12) root-link type through depth four using canonical-parent augmentation and an independent global orbit-closure encoding.

colored root-link orbit frontier classification

Two generators quotient partial 5-uniform links by target-degree-preserving point permutations and block permutations while applying hereditary degree and uncovered-pair capacity filters.

Hypothesis: The (6,6,4^12)-colored feasible root-link frontier through depth four contains at most 10000 orbits and is reproduced exactly by canonical construction paths and global orbit closure.

Test: Compare every sorted (depth, graph6 key, canonical deletion parent) record from the two generators, then independently reparse all records and parents under fail-closed mutation controls.

Exact cross-generator equality and complete structural reconstruction are net-new reproducible infrastructure. The missing predeclared replay and absence of a 30-cover or exhaustive full-family proof prevent candidate status.

• The two generator receipts contain identical sorted 9844-record streams with common digest d44eb48f0817fdca1df7d2d06de99e9ce4d68fbbadcc22734a42b3d0d0dae27f.
• Both generators report orbit counts [1,3,30,381,9429] through depth four.
• The separate structural checker validated 9844 records and reconstructed 9843 canonical deletion parents.
• No 30-block cover or global exclusion was produced; 30 <= C(15,6,3) <= 31 remains unchanged.

• python3 scripts/type2_canonical_frontier_v1.py --receipt artifacts/epoch92-20260811/type2-canonical-frontier.json --max-depth 4 --node-cap 10000 --seconds-cap 180
• python3 scripts/type2_orbit_closure_v1.py --receipt artifacts/epoch92-20260811/type2-orbit-closure.json --max-depth 4 --node-cap 10000 --seconds-cap 180
• python3 checkers/check_type2_frontier_v1.py --canonical-receipt artifacts/epoch92-20260811/type2-canonical-frontier.json --closure-receipt artifacts/epoch92-20260811/type2-orbit-closure.json --receipt artifacts/epoch92-20260811/type2-frontier-structural-check.json --structural-only
• sha256sum -c artifacts/epoch92-20260811/SHA256SUMS

• .proof-experiments/20260811-165314-d2cdc9: canonical generator passed in 136.443 seconds with depth counts [1,3,30,381,9429]
• .proof-experiments/20260811-165543-0b6756: global closure generator passed in 156.690 seconds with identical records and counts
• .proof-experiments/20260811-170259-0c5614: structural audit returned partial_pass after checking 9844 records and 9843 parents

check_type2_frontier_v1.py structurally checked every object and parent using a separately written decoder and feasibility kernel. Its full exhaustive extension mode is implemented but not yet run because lab submission failed.

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

• Type-(8,4^13) global orbit closure -> predict the same hereditary closure argument works for color partition (6,6,4^12) -> two generators matched on 9429 depth-four records, but the frontier was 4.18 times larger than type 0.

• For a fixed root in a putative 30-cover, the 14 root-link degrees are at least four and their excesses above four sum to four.
  The 12 root blocks contribute 60 link incidences, while covering the 13 pairs incident with each non-root point using 5-subsets requires degree at least ceil(13/4)=4. · Any 30-block C(15,6,3) cover, using the forced point degree 12 lemma · proved
• Two independently structured programs emitted identical 9844-record streams for the claimed type-(6,6,4^12) depth-four frontier.
  Generator receipt hashes 557b5e1f158a5026a9bac8160053cd848c72318bab7f6b846877f0fed364a3cd and 78a75937d80f25a18f065a7ee289fdf2ce36fc74c442c03f5db2d1f25d05f5a4; common internal record digest d44eb48f0817fdca1df7d2d06de99e9ce4d68fbbadcc22734a42b3d0d0dae27f. · The exact emitted record streams only; completeness promotion awaits the frozen third replay · computed
• All emitted records are structurally valid under the declared target and filters, and all non-root parent fields reconstruct correctly.
  artifacts/epoch92-20260811/type2-frontier-structural-check.json · All 9844 emitted records and 9843 non-root parents · computed

• Promote the type-2 frontier as an independently closed exhaustive classification in this epoch.
  The claimed (6,6,4^12) depth-zero-through-four frontier · The predeclared third exhaustive extension replay was not completed. · Lab submission failure plus structural checker result partial_pass · A full checker result pass with exact child sets, extension counts, parents, hashes, and mutation controls

• Full third replay of the type-2 frontier
  It is the smallest remaining test separating a reusable exhaustive frontier from unpromoted matching output. · Run check_type2_frontier_v1.py without --structural-only in a 300-second checkpointed segment. · high · open
• Five-bit triple-support-index incidence encoding
  It directly targets the active-variable regression that killed the one-direction one-hot support encoding. · Compile the frozen binary-index variant and compare paired CaDiCaL preprocess dimensions. · high · open
• Hash-ranked type-2 completion sample
  After frontier validation, a small sample can estimate SAT/proof yield and certificate storage before any 9429-leaf scale-up. · Select deterministic hash ranks and compile one completion leaf with exact CNF reconstruction. · normal · open

Objective: Close or reject the type-(6,6,4^12) depth-four frontier validation gate.

First action: Submit checkers/check_type2_frontier_v1.py without --structural-only against the two immutable receipts under one 300-second, 1024-MiB lab segment.

Stop condition: Any mismatch ends the route; a full pass permits only a bounded completion pilot, not a global exclusion claim.

• Restore writable checkpointed-lab authority and run the full type2 frontier checker without --structural-only.
• Redirect on any child-set, count, parent, digest, color, target, or mutation-control discrepancy.
• If validation passes, run a storage-capped hash-ranked completion sample rather than scaling all 9429 leaves.
• In parallel, retain the five-bit triple-support-index preprocessing test as the cheapest constructive-route discriminator.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol principal; two GPT-5.6 Terra advisory delegates; deterministic Python 3.12.3; nauty 2.8.8 labelg; SHA-256; Proof Factory run_experiment harness; web search. The lab submission failed before queueing. No SAT/PB solver, CAS, proof assistant, proof checker, cloud computation, or external human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1437.2s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-170736-c18481

No human review recorded.