Complete count-only census of strict degree-preserving 3-for-3 neighbors of the independently checked defect-10 seed.

complete local trade capacity census

Group all outgoing block triples by their exact point-incidence vector, count distinct incoming triples by coefficient extraction, and exclude incoming triples touching the seed by exact inclusion-exclusion.

Hypothesis: The complete strict degree-preserving 3-for-3 neighborhood of the hash-bound defect-10 seed has at most 2^22 members and is therefore affordable to score exhaustively.

Test: Count every strict no-seed incoming triple for all C(54,3)=24,804 outgoing triples and independently reconstruct the result; advance only if the count is at most 4,194,304.

The producer and independent checker agree on every exact incidence-signature cell and aggregate, while direct assignments and mutation tests attack the counting identity. Because the predeclared capacity gate failed, the justified progress is an exact local classification and route redirect, not a covering-number result.

• There are exactly 52,472,921 strict incidence-preserving 3-for-3 neighbors of the hash-bound defect-10 seed.
• The 24,804 outgoing triples occupy 24,263 exact incidence signatures.
• Forbidding incoming seed blocks removes exactly 3,675,013 of 56,147,934 unrestricted distinct degree-compatible candidates.
• These claims are local to one seed and do not bound C(15,5,3).

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 scripts/complete_degree18_3x3_capacity_v1.py --protocol artifacts/degree18-complete-3x3-capacity-20260810/protocol.json --output-dir artifacts/degree18-complete-3x3-capacity-20260810
• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 checkers/check_complete_degree18_3x3_capacity_v1.py --protocol artifacts/degree18-complete-3x3-capacity-20260810/protocol.json --artifact-dir artifacts/degree18-complete-3x3-capacity-20260810 --output artifacts/degree18-complete-3x3-capacity-20260810/independent-check.json --mutations-output artifacts/degree18-complete-3x3-capacity-20260810/mutation-controls.json
• sha256sum -c artifacts/degree18-complete-3x3-capacity-20260810/manifest.sha256

• .proof-experiments/20260810-024931-e58b8c: producer completed in 23.662 seconds and counted 52,472,921 strict neighbors.
• .proof-experiments/20260810-025537-d81c46: independent checker completed in 48.064 seconds with exact agreement, 3,225,096 direct assignments across 18 profiles, and four rejected mutations.

checkers/check_complete_degree18_3x3_capacity_v1.py uses an ordered-row inclusion-exclusion formulation rather than the producer's unordered formulation, reconstructs every outgoing signature, and directly enumerates 3,225,096 row assignments over 32 stratified 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

• Exact trade theory -> quotient row labels and preserve degree equations -> exact generation became a small coefficient problem, but coverage-unaware capacity remained 52,472,921.
• Constraint-programming capacity gates -> measure a complete neighborhood before scoring -> the measured count rejected 3-for-3 exhaustive scoring at 12.5105 times the cap.

• The complete strict incidence-preserving 3-for-3 neighborhood has 52,472,921 members.
  Producer/checker equality on 24,263 signature rows and aggregate; manifest SHA-256 c5e420b1edcadabc196a3847a524b2d2f31827202e380ee47b31eaed7359d47f. · Seed SHA-256 138e85fe20274972db4a93597c79ef32c17858cc2d4e6c9b0a9f0c7b30b48088 only. · computed

• Exhaustively score the complete strict 3-for-3 neighborhood under the predeclared 2^22 cap.
  All strict incidence-preserving 3-for-3 neighbors of the hash-bound defect-10 seed. · The exact count is 52,472,921, which is 12.5105 times the cap and would require 3,148,375,260 signed incidence updates under the saved incremental scorer. · artifacts/degree18-complete-3x3-capacity-20260810/independent-check.json · A sound coverage-aware quotient or prefilter reducing the independently checked retained set to at most 2^22, or a separately approved checkpointed high-throughput implementation with an external contribution path.

• Proof-producing radius-four exact repair from the defect-10 seed.
  A symbolic add/remove encoding can enforce degree balance and coverage without materializing 52 million local trades; SAT gives a terminal 54-cover and replayed UNSAT gives an exact local exclusion. · Generate one exact four-out/four-in CNF or OPB, independently reconstruct its semantics, and run a fixed-cap proof-stack pilot. · high · open

Objective: Test whether symbolic radius-four exact repair supplies stronger coverage-aware propagation than explicit 3-for-3 enumeration.

First action: Create a protocol and generator for four removed seed blocks and four added non-seed blocks with exact point-incidence balance and all final triple multiplicities at least one.

Stop condition: Stop on semantic checker disagreement; promote SAT only after direct cover verification, promote UNSAT only after proof replay, and redirect if a matched bounded pilot shows no useful propagation.

• Do not score the complete 52,472,921-neighbor 3-for-3 census under the current protocol.
• Generate a proof-producing radius-four add/remove formula with exact four-out/four-in cardinalities, exact point-degree balance, and all 455 final coverage constraints.
• Independently reconstruct that formula and run one bounded proof-stack pilot; accept SAT only after direct 54-cover checking and UNSAT only after proof replay.

• https://www.coveringrepository.com/systems.aspx?k=5&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=3&v=15 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol served as principal investigator. Two pre-existing GPT-5.6 Terra delegate memos supplied advisory route and verification suggestions only and were promoted with provenance; they were not treated as evidence or votes. Deterministic evidence used Python 3.12.3 standard-library code, exact integer arithmetic, SHA-256, and the computational-researcher experiment wrapper. Web search refreshed source status and prior art. No SAT solver, CAS, proof assistant, or newly spawned sub-agent was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1621.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260810-030448-e5ac97

No human review recorded.