Complete exact-degree union-crossover census over all unordered pairs in the fixed stored labelled alignments of 91 validated degree-18 defect-ten representatives.

exact-degree two-basin union crossover

For each parent pair, match equal-cardinality subsets with equal 15-point incidence vectors, generate every proper degree-18 child contained in that fixed parent union, and score exact triple coverage.

Hypothesis: At least one proper exact-degree offspring has defect below ten; a child at block-replacement distance at least four from both parents would additionally validate genuinely deep crossover geometry.

Test: Enumerate every degree-feasible union child for all 4095 fixed labelled parent pairs and independently reconstruct the census using a different subset partition; accept defect at most nine as progress and defect zero as terminal.

The producer and materially different checker agree exactly on all pair-level digests, occurrence counts, distinct-child counts, and minima. A third compact audit reconstructs the exchange and independently obtains nine missing triples. This satisfies the campaign's explicit below-ten reopen condition but not the exact covering-number verification contract.

• The recorded child bcbf2effff530b2e6c7412bfbef22bc002ea2c66dd206b6a17a8eedf7bdecdad has 54 distinct blocks, point degrees 18^15, and exactly nine uncovered triples.
• The complete fixed-alignment union corpus has 12,210 proper occurrences representing 3811 distinct children and minimum defect nine.
• Its deep subcorpus has 2692 occurrences representing 1341 distinct children and minimum defect ten.
• These claims do not cover other relative parent relabellings or the global covering space.

• python3 scripts/degree18_two_basin_crossover_v1.py --protocol protocols/degree18-two-basin-crossover-v1.json --output-dir artifacts/degree18-two-basin-crossover-20260812
• python3 checkers/check_degree18_two_basin_crossover_v1.py --protocol protocols/degree18-two-basin-crossover-v1.json --artifact-dir artifacts/degree18-two-basin-crossover-20260812 --output artifacts/degree18-two-basin-crossover-20260812/independent-check.json
• python3 checkers/audit_degree18_two_basin_best_v1.py --protocol protocols/degree18-two-basin-crossover-v1.json --certificate artifacts/degree18-two-basin-crossover-20260812/best-certificate.json --output artifacts/degree18-two-basin-crossover-20260812/direct-audit.json
• Four integrity and semantic mutations were rejected.
• Byte-identical regeneration matched result, ledger, and best-certificate hashes.
• sha256sum -c artifacts/degree18-two-basin-crossover-20260812/manifest.sha256 passed.

• .proof-experiments/20260812-115223-c7dd44: producer completed 4095 pairs in 5.043 seconds and reported minimum defect nine.
• .proof-experiments/20260812-115545-0432ee: final independent checker completed in 81.997 seconds and matched every pair digest.
• .proof-experiments/20260812-115721-e23111: compact direct certificate audit passed in 0.122 seconds.
• .proof-experiments/20260812-115721-a04327: four fail-closed mutations passed in 1.778 seconds.
• .proof-experiments/20260812-115731-4d81b3: producer regeneration completed in 5.441 seconds with byte-identical decisive outputs.

check_degree18_two_basin_crossover_v1.py uses a lexicographic-half complementary target-sum join rather than the producer's parental-side equal-exchange join, reconstructs every pair ledger, and scores coverage by both tuple containment and packed masks. audit_degree18_two_basin_best_v1.py separately reconstructs the named parent exchange and best child.

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

• Balanced crossover from evolutionary computation -> exact degree-preserving recombination might escape a local plateau -> one shallow child improved defect ten to nine, while deep recombination did not.
• Meet-in-the-middle subset sums -> exact incidence constraints should eliminate union choices in bulk -> 1,578,888 signatures represented 94,676,026 raw selections and left 12,210 proper occurrences.

• The explicit child bcbf2effff530b2e6c7412bfbef22bc002ea2c66dd206b6a17a8eedf7bdecdad is a simple degree-18 54-block family with defect nine.
  best-certificate.json, independent-check.json, and direct-audit.json · The explicit family only. · computed
• The fixed-alignment 91-parent union corpus has exact minimum defect nine.
  All pair digests and aggregate counts agree between two complete enumerations. · 4095 fixed stored labelled parent pairs and their degree-feasible union children. · computed
• The deep subcorpus has exact minimum defect ten.
  Producer and independent checker agree over 2692 deep occurrences. · Children at replacement distance at least four from both fixed parents. · computed

• Obtain defect below ten through a deep union crossover of the fixed stored alignments of the 91 representatives.
  2692 deep occurrences representing 1341 distinct children. · Two complete encodings found minimum defect exactly ten. · artifacts/degree18-two-basin-crossover-20260812/receipt.json · Introduce blocks outside both parents, use an additional parent, or enumerate previously excluded relative point alignments.

• Complete exact-degree 2-for-2 neighborhood of the defect-nine seed.
  The new child is a two-replacement neighbor of previously unexpanded class plateau-next-46 and satisfies the campaign's explicit constructive reopen condition. · Enumerate every legal two-delete/two-add degree-preserving move from child bcbf2eff... and independently require defect below nine. · high · open
• Proof-producing native-PB calibration.
  This remains the globally decisive negative route but is blocked until pinned RoundingSat, VeriPB, and CakePB controls pass. · Run the saved C(5,3,2) SAT/UNSAT proof and model controls after a hash-recorded tool bundle is available. · normal · open

Objective: Determine whether the defect-nine seed has a legal exact-degree neighbor of defect at most eight or a complete cover.

First action: Create protocols/degree18-defect9-2for2-v1.json from the global_best block list in artifacts/degree18-two-basin-crossover-20260812/best-certificate.json and enumerate its complete legal degree-preserving 2-for-2 neighborhood.

Stop condition: Validate immediately on defect below nine or zero; otherwise close the exact neighborhood after independent reconstruction and redirect.

• Extract the defect-nine child from best-certificate.json.
• Predeclare and exhaust its complete legal degree-preserving 2-for-2 neighborhood.
• Use a separately written checker and require defect below nine for continuation or defect zero for terminal success.
• If the exact neighborhood does not improve, redirect to a materially larger move or a calibrated proof-producing PB stack.

• 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 ↗
• https://arxiv.org/abs/1904.10494 ↗

GPT-5.6 Sol served as principal investigator. Two injected GPT-5.6 Terra delegates supplied bounded advisory route reconnaissance; their agreement was not evidence, and the relied-on recommendation was promoted with provenance. Python 3.12.3 standard-library programs performed the producer census, independent complementary encoding, direct audit, mutation tests, and regeneration. The web reader checked the maintained repository and primary literature. No SAT/PB solver, CAS, proof assistant, cloud lab, package installation, external publication, Git commit, or remote write was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1418.1s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260812-120655-5fbc6f

No human review recorded.