Materialized and independently classified the complete depth-four pair-surplus ownership bucket whose processed internal weighted graph is a unit perfect matching.

canonical pair-surplus prefix augmentation

Enumerate exact external-vector multiplicity tables for one complete S4 internal-edge orbit, canonicalize under its stabilizer, map every record to all canonical depth-three deletion parents, and validate completeness with a separate Burnside/polynomial encoding.

Hypothesis: The complete unit-perfect-matching depth-four bucket has at most 10000 canonical profiles, can be materialized within 120 seconds and 1 GiB, and every deletion parent belongs to the frozen exact 1775-key depth-three ledger.

Test: Explicitly materialize the whole bucket, require a separate stabilizer-Burnside polynomial DP and ordered-sequence DP to reproduce aggregate totals, validate every record and parent, reject seven mutations, rerun byte-identically, and fail closed at a cap one below the exact count.

The producer exhausts the exact-row-sum multiset universe for the frozen internal orbit, while the checker proves the required orbit count without depending on that enumeration and then validates every retained record. The evidence is decisive for the stated bucket and has no quantified implication outside it.

• The complete degree-feasible depth-four pair-surplus bucket with internal weighted graph equal up to S4 to a unit perfect matching has exactly 2548 canonical profiles.
• That bucket contains exactly 17337 S11 multiset tables and represents exactly 18667722645 labelled prefixes across the three internal matchings.
• All deletion parents of all 2548 profiles occur in exactly 296 keys of the frozen 1775-key depth-three ledger; 225 keys own at least one child under minimum-parent ownership.
• The maintained covering range remains 30 <= C(15,6,3) <= 31.

• Producer: python3 scripts/pair_surplus_depth4_matching_bucket_v1.py --out artifacts/epoch106-20260812/depth4-matching-bucket-v1/producer-receipt.json --max-records 10000 --max-seconds 120; PASS_COMPLETE, 2548 profiles.
• Checker: python3 checkers/check_pair_surplus_depth4_matching_bucket_v1.py --receipt artifacts/epoch106-20260812/depth4-matching-bucket-v1/producer-receipt.json --out artifacts/epoch106-20260812/depth4-matching-bucket-v1/independent-check.json; PASS_INDEPENDENT and seven mutations rejected.
• Producer and rerun SHA-256 56a820f415d3990f6085b7f0e89f2112a4e0e53f3ebe25213d1eb4eae8370dc8; independent check SHA-256 632389fcddb5a7a607571ade43199874625b31e26ff70ecedd42fc52e8ae5551.
• Boundary control with max-records 2547 returned CAP_REACHED and exit code 2.

• .proof-experiments/20260812-031920-8362b5: producer PASS_COMPLETE, 2548 profiles, 9.407 seconds, 44804 KiB peak.
• .proof-experiments/20260812-031951-40d09d: independent checker PASS_INDEPENDENT, 32.146 seconds, 38320 KiB peak, seven corruptions rejected.
• .proof-experiments/20260812-032045-31af74: producer rerun byte-identical in 9.660 seconds.
• .proof-experiments/20260812-032132-9e0012: cap-one-below control returned CAP_REACHED and exit 2.

checkers/check_pair_surplus_depth4_matching_bucket_v1.py uses stabilizer Burnside polynomial DP and ordered-sequence DP to establish aggregate completeness without enumerating the producer's multiset stream, then independently reconstructs every record, orbit weight, deletion parent, owner, and digest.

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 link/orbit decomposition for C(12,6,4) -> predict that exact ownership layers plus independent orbit counts can support replayable exhaustive partitions here -> a complete 2548-profile depth-four internal-edge bucket and its parent ledger passed all checks, but no terminal leaf was reached.

• The complete unit-perfect-matching depth-four internal-edge bucket has exactly 2548 canonical profiles.
  Complete producer receipt, independent stabilizer Burnside average, byte-identical rerun, and cap boundary control. · Degree-feasible four-row prefixes of loopless weighted degree-4 graphs on 15 vertices with internal weighted graph in the S4 unit-matching orbit. · computed
• The bucket contains 17337 raw S11 tables and 18667722645 labelled prefixes.
  Explicit table count/orbit-weight sum and independent identity fixed count/ordered-sequence DP. · The same complete internal-edge orbit. · computed
• All deletion parents lie in 296 frozen depth-three keys and 225 keys own children.
  Record-by-record producer lookup and independent parent reconstruction against source SHA-256 0fb9276f5fa614828821a75322fb3e34d5d60edc4396abd2a9c2e4a105f0b5cf. · All 2548 bucket profiles and all four processed-vertex deletions. · computed

• The unit-perfect-matching depth-four bucket exceeds the declared 10000-record materialization cap.
  The complete frozen internal-edge orbit. · The exact independently reproduced count is 2548. · Producer and independent checker receipts. · A demonstrated semantic mismatch or checker counterexample.
• A truncated 2547-cap run could be accepted as a complete bucket.
  The producer's record-cap boundary. · The run returned CAP_REACHED, null raw total, and exit code 2. · artifacts/epoch106-20260812/depth4-matching-bucket-cap-reject.json and experiment 20260812-032132-9e0012. · Only a producer semantics change accompanied by new boundary tests.
• Treat this complete bucket as an exclusion of its profiles or as a 4.08% exclusion of 30-covers.
  Cover existence and complete weighted graphs. · The ledger classifies degree-feasible prefixes but solves no completion problem and eliminates none of its 2548 profiles. · Receipt scope and absence of SAT, PB, or direct cover-completion artifacts. · Replayable completion certificates tied to every represented complete case.

• Checkpointed complete depth-four ownership ledger
  The exact total is 62437 and the complete 2548-profile calibration passed with an estimated approximately 96 MB stream; completing ownership is the next prerequisite for safe later decomposition. · Implement internal-edge-orbit checkpoint/restart, verify a two-orbit resumed stream byte-for-byte, then submit the full producer/checker to the lab. · high · open
• Materially changed exact-degree-12 constructive witness search
  A 30-block witness remains the shortest terminal certificate, while previous six-representative incidence timing runs produced only UNKNOWN and cannot justify repetition. · Predeclare and compare one new encoding-level mechanism against the frozen incidence baseline on identical branches before any scale-up. · normal · open
• Surplus-profile to root-link compatibility bridge
  A complete surplus graph fixes all pair multiplicities, potentially shrinking root-link and residual-cover constraints more strongly than either decomposition alone. · After a complete-H pilot exists, compile one hash-owned H class into root-link compatibility equations and measure candidate/proof size against the direct completion encoding. · low · open

Objective: Qualify checkpointed full depth-four profile/parent materialization.

First action: Refactor scripts/pair_surplus_depth4_matching_bucket_v1.py into deterministic internal-edge-orbit chunks and run a two-orbit interruption/resume comparison.

Stop condition: Redirect on restart nondeterminism, count mismatch, foreign parent, duplicate key, checker disagreement, or measured resource projection beyond the declared lab tranche.

• Refactor the producer into checkpointable canonical internal-edge-orbit chunks and run a two-orbit restart/resume byte-stability control.
• Submit full 62437-profile materialization and its independent parent checker to the checkpointed lab with a 100000-record cap, 1 GiB limit, immutable epoch-102/105 inputs, and measured continuation thresholds.
• Forecast later complete-H and proof-certificate volumes before generating cover-completion SAT leaves.
• Keep a materially changed exact-degree-12 constructive witness route in the resolution portfolio; do not repeat the prior six-branch timing calibration without new encoding evidence.

• https://www.coveringrepository.com/ ↗
• 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/math/9502238 ↗
• https://arxiv.org/abs/2607.23766 ↗
• https://github.com/dennisonbertram/covering-number-c12-6-4 ↗

GPT-5.6 Sol served as principal investigator. Two GPT-5.6 Terra delegates supplied advisory prior-art and experiment-design memos; their memos were promoted verbatim with provenance but were not mathematical evidence or independent validators. Deterministic evidence used Python 3.12.3, exact integer/set arithmetic, SHA-256, stabilizer canonicalization, Burnside fixed-point counting, finite polynomial DP, ordered-sequence coefficient DP, and the computational-researcher experiment harness. Web search supported source/status audit. No SAT/PB solver, CAS, proof assistant, cloud lab, external proof service, human validator, system installation, or publication action produced evidence this epoch.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1343.0s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1563-20260812-033035-35ec97

No human review recorded.