Qualify a deterministic high-bit owner for every canonical profile in the two remaining oversized depth-four pair-surplus orbits, using exact C++ enumeration and an independent cardinality/canonicality checker.

checkpointed canonical pair-surplus augmentation

Compress four processed vertices against eleven exchangeable external vertices to canonical 70-byte multiplicity tables, partition oversized internal-edge orbits by high FNV bits, and validate exact finite coverage before parent reconstruction or SAT compilation.

Hypothesis: The frozen high-three-bit FNV owner partitions all 18316 orbit-0 and 7798 orbit-5 canonical profiles into eight nonempty buckets per orbit, each of size at most 5000.

Test: Emit every packed canonical key for orbits 0 and 5, independently check degrees, stabilizer canonicality, owner and uniqueness, and use equality with hash-bound independent Burnside cardinalities as a coverage proof.

Unique valid canonical keys with correct owners inject into the independently counted finite orbit universes; equality of cardinalities proves exact coverage. The claimed improvement concerns only restart geometry, so it does not support a cover or exclusion claim.

• All 18316 canonical depth-four profiles in internal orbit 0 are partitioned by the frozen high-three-bit owner into [2231,2342,2283,2251,2273,2323,2311,2302].
• All 7798 canonical depth-four profiles in internal orbit 5 are partitioned into [933,962,993,973,995,983,1030,929].
• Combining these partitions with the prior qualified orbit-1 partition and the other 58 coarse orbits gives an exact count-level 82-chunk representation of all 62437 profiles with maximum chunk 3682.
• No profile or cover was excluded, and the exact covering-number range remains 30 <= C(15,6,3) <= 31.

• artifacts/epoch115-20260812/pair_surplus_depth4_oversized_highbits_v1 --ledger ... --summary ... -> PASS_CPP_OVERSIZED_HIGHBITS in 1.226 seconds
• python3 checkers/check_pair_surplus_depth4_oversized_highbits_v1.py ... -> PASS_INDEPENDENT_OVERSIZED_HIGHBITS in 3.146 seconds, maximum 2342, five mutations rejected
• python3 checkers/check_pair_surplus_depth4_chunk_geometry_v1.py ... -> PASS_EXACT_82_CHUNK_GEOMETRY in 0.071 seconds, total 62437, maximum orbit 2 size 3682, three mutations rejected
• cmp clean rerun ledgers and summaries -> both byte-identical
• baseline artifacts/epoch109-20260812/all-orbit-cap-result.json has SHA-256 4fa70b9d0c10cc917082988f45dc353ee330b8f97a6ed064ebb2ac8f600c5dee

• .proof-experiments/20260812-100640-b26b84: producer passed in 1.226 seconds with exact totals and bucket vectors.
• .proof-experiments/20260812-100658-3888b9: first independent checker timed out at 30 seconds; no receipt.
• .proof-experiments/20260812-100756-ef011f: reordered-control checker still timed out at 30 seconds; no receipt.
• .proof-experiments/20260812-100903-b35e1d: precomputed-map checker passed in 3.146 seconds and rejected five mutations.
• .proof-experiments/20260812-100920-37b69d: clean producer rerun passed in 1.124 seconds and was byte-identical.
• .proof-experiments/20260812-101559-6ad678: independent receipt composition proved the exact 82-chunk geometry and rejected three mutations in 0.071 seconds.

checkers/check_pair_surplus_depth4_oversized_highbits_v1.py uses a separate Python packed-key parser and permutation encoding, binds independent Burnside universe sizes, verifies all 26114 keys, and rejects five mutations. checkers/check_pair_surplus_depth4_chunk_geometry_v1.py separately composes hash-bound receipts into the exact 82-chunk full-frontier geometry and rejects three mutations.

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)=41 cube ownership -> predict that bounded hash-owned leaves need replayable exact-union receipts before SAT scale-up -> the ownership prerequisite passed for orbits 0 and 5, but no SAT scale-up was authorized.
• Hash partitioning from distributed search -> predict high FNV bits will avoid the parity collapse seen in low bits -> all 16 high-bit buckets were nonempty and below cap.

• The exact orbit-0 high-bit bucket vector is [2231,2342,2283,2251,2273,2323,2311,2302].
  26114-key producer ledger, independent canonicality/cardinality receipt, and byte-identical rerun · All 18316 canonical profiles of internal orbit 0 · computed
• The exact orbit-5 high-bit bucket vector is [933,962,993,973,995,983,1030,929].
  26114-key producer ledger, independent canonicality/cardinality receipt, and byte-identical rerun · All 7798 canonical profiles of internal orbit 5 · computed
• The full depth-four count-level frontier has an exact 82-chunk geometry with maximum chunk 3682.
  Epoch-109 all-orbit count receipt, epoch-112/113 orbit-1 receipt, and epoch-115 orbit-0/orbit-5 receipt · All 62437 canonical depth-four profiles · computed

• Use per-record stabilizer reconstruction and late-failing full-scan mutations in the Python checker under a 30-second cap.
  The exact 26114-key orbit-0/orbit-5 checker implementation attempted twice in epoch 115 · Both runs timed out at 30 seconds without a receipt; precomputing invariant maps reduced the same positive checks to 3.146 seconds. · .proof-experiments/20260812-100658-3888b9 and 20260812-100756-ef011f; passing replacement 20260812-100903-b35e1d · None; use the validated precomputed-map implementation instead.

• Complete the 62437-profile parent-rich depth-four ownership ledger.
  Every oversized count-level owner now passes and the remaining scope is exactly 38705 profiles; a complete ledger is the prerequisite for exhaustive certified leaves. · After explicit approval, run clean/resume parent materialization in the qualified 82-chunk geometry and the independent full-union checker. · high · open
• Proof-producing incidence/PB calibration.
  A replayable proof chain could create terminal evidence, but the required native emitter and replayers are not provisioned. · Only after a pinned toolchain is available, generate the retained smallest calibration proof and require dual replay plus mutation rejection. · normal · open
• Constructive 30-cover search with direct 455-triple checking.
  A witness would settle the problem with a much smaller verification surface than a global exclusion. · Design a bounded exact-degree-12 local-search discriminator with an archival 31-cover positive control and direct witness checker before allocating scale compute. · normal · open

Objective: Complete the exact depth-four parent-rich ownership prerequisite without compiling SAT leaves.

First action: Obtain explicit approval for the 38705-profile scope, then invoke the generalized clean/resume parent materializer over the qualified 82-chunk geometry.

Stop condition: Stop on missing approval or any hash, coverage, parent, owner, restart, resource, or independent-check mismatch; do not infer a covering result from ownership alone.

• Obtain explicit human-owner approval for parent-materializing the exact remaining 38705 profiles.
• After approval, generalize the retained parent producer to the qualified 82-chunk geometry and require clean/resume byte identity.
• Independently reconcile all 62437 profile keys, deletion parents, owners, and orbit weights against the frozen 1775-key depth-three ledger.
• Compile no SAT leaf until that complete union passes; keep native PB held until a pinned proof-emitter/replayer calibration succeeds.

• 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 ↗
• https://veripb.org/ ↗

GPT-5.6 Sol principal; two GPT-5.6 Terra delegates for advisory reconnaissance only. Python 3.12.3, g++ 13.3.0/C++17, exact enumeration, stabilizer canonicalization, FNV-1a-64, SHA-256, cmp, and the computational-researcher harness were used. No SAT/PB solver, CAS, proof assistant, cloud lab, external proof service, or human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1249.8s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-101946-a8b8d6

No human review recorded.