Canonical missing-triple hitter plus a 1+2+2 exact incidence-profile meet-in-the-middle census for one fixed strict five-deletion cell.

canonical-hitter meet-in-the-middle incidence census

Assign the least added block covering an original missing triple, split the other four sorted additions into two canonical pairs, join exact 15-coordinate degree profiles, then evaluate packed 455-bit coverage masks.

Hypothesis: For the five deletion blocks selected by the locked boundary fixture, every strict degree-preserving five-addition completion has at least ten uncovered triples.

Test: Enumerate every completion that could have defect at most nine and compute its exact defect; the decisive observation is whether the minimum is at most nine or at least ten.

The hitter lemma proves coverage of the relevant candidate family, canonical anchor and pair rules give unique enumeration, two materially different encodings agree on the entire census and digests, all five mutations fail closed, and regeneration is byte-identical. The evidence supports only the fixed-cell exclusion.

• For deletion blocks {1,4,6,7,10}, {1,5,6,11,13}, {2,6,11,12,13}, {3,4,6,10,11}, and {9,11,12,13,14}, every strict degree-preserving five-addition completion has at least ten uncovered triples.
• Exactly 1451104 canonical completions relevant to defect at most nine exist in this cell, with minimum defect ten.
• The locked boundary fixture is the unique defect-10 minimizer in this cell.
• No claim is made about the other 3162509 deletion cells or the exact value of C(15,5,3).

• Producer result SHA-256 4e387dbd632f8e119e4df3edd5b9a8d58404f27cb366ba6222fc628cb4282450.
• Independent check SHA-256 d08e3da4d43a0a6bb016bba65738935dde2d4f87024397d609a3258fe881f566, valid=true.
• Regeneration returned byte_identical=true with the same result SHA-256.
• Five mutations altering the minimum, histogram, demand, minimizer, and hitter guard were all rejected.
• sha256sum -c artifacts/degree18-strict5-mitm-cell-20260811/manifest.sha256 passed.

• .proof-experiments/20260811-125626-58d620: final producer checked 1451104 completions and returned minimum defect ten.
• .proof-experiments/20260811-125723-fc6c9b: independent bitplane census matched every critical field and returned valid=true.
• .proof-experiments/20260811-130001-77a68c: fresh producer regeneration was byte-identical.
• .proof-experiments/20260811-130051-0156c8: all five receipt mutations were rejected.

checkers/check_degree18_strict5_mitm_cell_v1.py uses two 15-bit profile bitplanes and ordered canonical pair positions, does not import the base-5 producer, and independently reconstructs all 1451104 candidates, their defects, and order-independent digests.

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

• Set-cover repair -> any improvement must hit an originally uncovered element -> the canonical hitter restricted the complete relevant family but alone gave only 1.607855x.
• Subset-sum meet in the middle -> exact 15-coordinate pair profiles should collapse five-block degree matching -> 2476282373712 profile-pair slots collapsed to 135508 compatible cubes.
• Packed graph-neighborhood masks -> evaluate coverage only after exact incidence joins -> all 1451104 survivors were classified in bounded local runs.

• Any defect-at-most-nine strict-five completion around the locked defect-10 seed contains an original-missing-triple hitter.
  Direct monotonicity lemma: deletions cannot cover a missing triple. · Every fixed five-deletion cell around this seed. · proved
• The recorded fixed deletion cell has 1451104 canonical relevant completions with minimum defect ten and one minimizer.
  Producer and independent bitplane histograms and digests agree. · The five recorded deletion blocks only. · computed
• The 798216 eligible unordered block pairs induce exactly 127637 degree profiles.
  Both implementations and the pair-profile digest agree. · The demand-eligible addition pool for the recorded cell. · computed

• Reach defect at most nine in the recorded strict five-deletion cell.
  Every strict degree-preserving five-addition completion in that cell capable of improving the seed. · The complete independently reconstructed defect histogram has minimum ten. · artifacts/degree18-strict5-mitm-cell-20260811/independent-check.json · A demonstrated omission in the canonical-hitter lemma, a producer/checker defect, or a change to the locked seed or deletion set.
• Rerun the injected complete fixed-pair link as a new strengthening.
  The previously audited 5460 labelled pair-link requirements over four canonical baselines. · Each requirement is a fixed-block tautology or an existing triple-coverage clause, giving zero CNF delta; the weaker orbit gate is subsumed. · artifacts/pair-link-cnf-delta-audit-20260811/independent-check.json · A literal-formula non-subsumption witness or separately justified pair-count information absent from the baseline.

• Deletion-signature amortization of the exact MITM certificate.
  Pair groups depend only on point demand, while final defects depend on retained coverage; repeated joint signatures could eliminate cells in bulk. · Enumerate and independently count all demand and joint demand/coverage signatures. · high · open
• Constructive move family outside the closed 2-for-2 through strict-5 neighborhoods.
  A directly checked 54-cover remains terminal and the present local minimum identifies a rigid defect-10 basin. · Define a genuinely new variable-length trade or ejection mechanism and require a directly checked defect below ten. · normal · open
• Globally complete pair-normalized proof branches.
  They retain terminal scope but previously remained solver-UNKNOWN. · Only retry after a measured decomposition or propagation change with independent proof replay. · low · open

Objective: Determine whether exact deletion signatures make the fixed-cell MITM method a bulk-elimination route.

First action: Enumerate all C(54,5)=3162510 deletion cells into (point-demand, retained-coverage-mask) signatures and independently reproduce the histogram.

Stop condition: End or redirect on checker disagreement or if at least 90 percent of joint signatures are singletons.

• Enumerate all 3162510 deletion cells into exact point-demand signatures and joint point-demand/retained-coverage-mask signatures.
• Independently reconstruct both signature histograms and bind them to the seed hash.
• Redirect if at least 90 percent of joint signatures are singletons; otherwise pilot one repeated signature class before scale-up.
• Preserve constructive witness search and globally complete proof branches as alternative routes.

• 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/2607.23766 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol principal designed, implemented, audited, and interpreted the epoch. Two GPT-5.6 Terra delegates supplied advisory reconnaissance; their agreement was not evidence, and the fixed-pair proposal was rejected using deterministic main-workspace artifacts. Python 3.12.3 with arbitrary-precision integer bitsets performed the producer, independent reconstruction, mutation controls, and regeneration. No SAT solver, CAS, proof assistant, external lab job, system package installation, or host configuration change was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

2065.9s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260811-131019-3f2dce

No human review recorded.