Clean-room global orbit-closure regeneration of the type-(8,4^13) root-link frontier through depth four, followed by exact comparison with the historical canonical-augmentation receipt and an independent adversarial checker.

canonical root-link enumeration

Extend every previous colored-incidence orbit representative by all 2002 five-subsets, apply hereditary feasibility filters, canonically label all survivors, and globally deduplicate without using canonical-parent acceptance during enumeration.

Hypothesis: Independent global orbit closure exactly reproduces all 2403 reported type-0 nodes through depth four, including 2258 depth-four keys and every canonical deletion parent.

Test: Compare the complete sorted (depth,key,parent) list and its hashes, then independently reconstruct all graphs and parents and require omission, duplication, wrong-type, wrong-color, and permutation controls to fail closed.

The enumerator covers every feasible orbit by a deletion-heredity induction and does not use the producer's canonical-parent acceptance mechanism. Exact full-record agreement, separate reconstruction, deterministic reproduction, and mutation controls support the scoped frontier claim, but no SAT leaf or remaining root type was settled.

• Under the declared filters, the type-(8,4^13) root-link orbit counts at depths zero through four are exactly 1, 2, 14, 128, and 2258.
• The 2403 clean-room records exactly match the historical source records, with depth-four key digest c735e64ca3f30cff8dbb95dc70d188f450211395c7cb0a8771947b352923b65b.
• The maintained covering-number range remains 30 <= C(15,6,3) <= 31.

• Primary: python3 scripts/cleanroom_type0_frontier_v1.py --source-receipt artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --receipt artifacts/epoch86-20260811/cleanroom-type0-frontier-primary.json --max-depth 4
• Checker: python3 checkers/check_cleanroom_type0_frontier_v1.py --audit-receipt artifacts/epoch86-20260811/cleanroom-type0-frontier-primary.json --source-receipt artifacts/epoch19-20260809/root_link_canonical_primary_receipt.json --reproduction-receipt artifacts/epoch86-20260811/cleanroom-type0-frontier-reproduction.json --receipt artifacts/epoch86-20260811/cleanroom-type0-frontier-independent-check.json
• Primary experiment 20260811-122733-1581ec returned 0 in 13.837 seconds.
• Fresh reproduction 20260811-122859-84f048 returned 0 and matched all stable fields.
• Final independent checker 20260811-122936-05e264 returned 0 in 0.733 seconds.

• .proof-experiments/20260811-122733-1581ec: primary enumeration passed with 2403 records and 2258 depth-four orbits.
• .proof-experiments/20260811-122802-3219e9: checker failed closed because the first-16 wrong-color sample was insensitive.
• .proof-experiments/20260811-122859-84f048: fresh enumeration reproduction passed.
• .proof-experiments/20260811-122936-05e264: repaired full-frontier checker passed all controls.

checkers/check_cleanroom_type0_frontier_v1.py is separately written, does not import the producer or primary audit code, reparses graph6 independently, reconstructs all 2402 parents, checks all structures and hashes, compares the complete record set, and exercises omission, duplication, type, color, permutation, and rerun 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

• Krug's certified link-orbit decomposition for C(12,6,4) -> a local proof portfolio is meaningful only after independent frontier coverage -> the C(15,6,3) type-0 depth-four frontier prerequisite now passes, but global ownership and four root types remain.

• The filtered type-0 orbit frontier through depth four has counts 1,2,14,128,2258.
  Primary receipt, exact historical comparison, independent checker, and fresh reproduction. · Target degree type (8,4^13), depths zero through four, declared filters. · computed
• All four filters are hereditary under deleting a block.
  Deleting a block increases remaining global pair capacity by 10 and affected point capacity by 4, at least matching newly uncovered pairs, while relaxing degree deficits. · Simple partial 5-uniform links under the declared target degree vector. · proved
• The three retained q0/q1/q3 raw DRAT+LRAT packages project to 8.323538 GiB over 2258 equally sized leaves.
  Direct sizes 5025465, 3452790, and 3395967 bytes; arithmetic mean 3958074 bytes. · A projection from exactly three nonrepresentative terminal packages, not a frontier-wide measurement. · computed

• Infer C(15,6,3) >= 31 or even exclude all type-0 completions from the frontier audit.
  Global target and type-0 full-completion family. · No remaining leaf was solved and no global ownership union or other root type was checked. · The audit stops at partial-link depth four and its receipt explicitly scopes out completion. · Replayable UNSAT proofs for a complete independently checked leaf union, plus coverage of all root-degree types.
• Use the first 16 frontier keys as a wrong-color detection control.
  That fixed 16-key sample only. · All 16 retained the same canonical strings under the coarser coloring. · .proof-experiments/20260811-122802-3219e9 failed closed; the full frontier found 2022 differences. · Use a preverified color-sensitive witness or audit the full frontier.
• Promote the Terra A5 orbit-union miss as evidence this epoch.
  A5-invariant 30-block families. · The delegate computation was advisory and not independently rechecked by Sol this epoch. · No delegate artifact appears in evidence_files. · Promote the script into the main artifact set and independently reconstruct all orbits and all 455 labelled triple checks.

• Representative 32-key DRAT/LRAT terminal-yield pilot.
  The prerequisite frontier audit passed, and q0, q1, and q3 already demonstrate terminal proof transport. · Freeze eight midpoint ranks per quartile after excluding q0-q3, independently validate the manifest, then submit isolated leaves to the checkpointed lab. · high · open
• Global ownership bridge from canonical full links or prefixes to completion cylinders.
  Even complete type-0 leaf proofs require an independently checked coverage map before aggregation. · Formalize the canonical-deletion ownership map and test uniqueness and coverage on every completed link obtained in bounded calibration cases. · normal · open
• Constructive incidence search with a material encoding change.
  A 30-block witness remains the cheapest terminal certificate if found, but unchanged short incidence scans were nonterminal. · Test one independently audited symmetry or propagation enhancement against the six-case baseline before any solver scale-up. · normal · open

Objective: Measure whether independently replayable type-0 completion certificates are representative and storage-feasible.

First action: Implement scripts/freeze_type0_leaf_pilot_v1.py exactly as specified in artifacts/epoch86-20260811/continuation-checkpoint.json, then independently verify the frozen manifest before lab submission.

Stop condition: Stop on any frontier/selection/CNF/replay/control mismatch, more than 8 nonterminal leaves, or projected retained proof storage above the predeclared 8-GiB semantics.

• Implement the exact frozen 32-key selection protocol in continuation-checkpoint.json and independently verify its manifest.
• Define whether the 8-GiB budget counts raw DRAT+LRAT, compressed archives, or both.
• Submit the isolated 32-leaf pilot to the checkpointed lab with 60-second and 8-MiB DRAT caps per leaf.
• Stop or redirect if more than 8 leaves are nonterminal, any replay/control fails, or representative proof storage exceeds budget.
• Do not infer type-0 or global exclusion from the sample.

• 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 principal designed, implemented, and audited the epoch. Two pre-completed GPT-5.6 Terra delegates supplied advisory reconnaissance; neither served as an independent validator, and no delegate artifact was claimed as evidence. Deterministic tools were CPython 3.12.3, nauty-labelg 2.8.8+ds-5, exact graph6 reconstruction, SHA-256, and the computational-researcher experiment harness. The web connector was queried for current sources but returned no usable content; direct curl failed because workspace DNS was disabled, so the same-day pre-acquired source audit was retained. No SAT solver, PB solver, CAS, proof assistant, cloud lab, external proof service, system installation, publication action, or human validator was used this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1029.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260811-123459-33e94c

No human review recorded.