Test the stabilizer-fixed residual pair identity count_45 = 5 + e_45 across the frozen 395-signature type-4 frontier while retaining all skeleton variables existentially.

literal pair-identity signature refinement

Meet-in-the-middle exact feasibility on the shared value e_45 in {0,1,2}, using the full 105-edge pair-excess skeleton and 185 exact-capacity residual cells.

Hypothesis: At least one of the 395 saved type-4 canonical signatures has no joint realization satisfying residual_count_45 = 5 + e_45.

Test: For every frozen signature, intersect the feasible e_45 values of the full skeleton with those of the residual margin system, preserving explicit positive witnesses and independently checking the complete ordered map.

Positive witnesses for every signature and every possible residual target prove that this constraint cannot eliminate a class; no solver-negative claim is needed.

• The recorded type-4 stabilizer has order 10,368 and fixes {4,5} setwise.
• The 2,717 residual blocks form exactly 185 augmented cells, of which 275 literal blocks contain {4,5}.
• All 395 frozen signatures survive the exact {4,5} identity.
• All 1,185 signature/e_45 residual combinations have independently checked 49-block literal expansions.

• python3 scripts/type4_pair45_identity_v1.py --frontier artifacts/type4-signature-frontier-20260809/result.json --frozen artifacts/type4-pair45-identity-20260809/frozen-input.json --source artifacts/joint-orbit-census-20260808/manifest.json --protocol protocols/type4-pair45-identity-v1.json --output artifacts/type4-pair45-identity-20260809/result.json
• python3 checkers/check_type4_pair45_identity_v1.py --frontier artifacts/type4-signature-frontier-20260809/result.json --frozen artifacts/type4-pair45-identity-20260809/frozen-input.json --source artifacts/joint-orbit-census-20260808/manifest.json --result artifacts/type4-pair45-identity-20260809/result.json --output artifacts/type4-pair45-identity-20260809/independent-check.json
• sha256sum -c artifacts/type4-pair45-identity-20260809/manifest.sha256
• Result SHA-256 128770b77b2d75bc7eed4f0a60ef4e309a463bbcde0919fc6504f4802a887df2

• .proof-experiments/20260809-085757-b45bb4: froze exactly 395 unique signatures.
• .proof-experiments/20260809-090307-39dd64: produced 395 retained rows and 1,185 residual target witnesses.
• .proof-experiments/20260809-090437-23338a: independently validated the stabilizer, skeletons, margins, pair identities, and 58,065 block occurrences.
• .proof-experiments/20260809-090444-3c0825: rejected all six adversarial mutations.
• .proof-experiments/20260809-090959-02e0a7: regenerated the final result byte-identically.

checkers/check_type4_pair45_identity_v1.py uses no Z3 and does not import the producer; it reconstructs the literal universe, stabilizer, skeleton equations, root margins, and exact pair counts.

not_requested

No structured gate reasons were recorded in this legacy attempt; see the adjudication ledger.

Original model outcome

progress

Public classification

progress

• C(12,6,4) certificate discipline -> refuse solver-only exclusions -> this epoch promoted only explicit positive witnesses and made no UNSAT claim.

• The type-4 stabilizer order is 10,368 and {4,5} is fixed setwise.
  Independent derivation as 12 root actions times point-fiber factor 864. · Recorded canonical type-4 common family. · computed
• Every frozen signature realizes every residual target e_45 in {0,1,2}.
  1,185 checked residual witnesses in the hash-bound packet. · Five-margin necessary relaxation on 395 signatures. · computed
• The final result regenerates byte-identically.
  regeneration-check.json matched SHA-256 128770b77b2d75bc7eed4f0a60ef4e309a463bbcde0919fc6504f4802a887df2. · Pinned scripts, inputs, Python, and Z3 version. · computed

• Use the single stabilizer-fixed pair {4,5} to eliminate any of the 395 saved signatures.
  Exact 185-cell five-margin relaxation. · Every signature has witnesses for all three possible pair-excess targets. · result.json plus independent-check.json · A strictly stronger joint constraint involving multiple labelled pairs or triple coverage.
• Use a single non-fixed pair such as {6,9} without branching.
  The canonical type-4 signature quotient. · Such a pair lies in a nontrivial stabilizer orbit and is not a branch-free invariant. · Independent root-action audit. · An exhaustive stabilizer-orbit split with independent coverage accounting.

• Full type-4 common-family/pair-excess-skeleton orbit coupling.
  It restores all labelled pair correlations omitted by the failed one-pair and margin projections. · Enumerate the complete orbit frontier under the 10,368-element stabilizer with a predeclared capacity. · high · open
• Coverage-orbit refinement.
  Triple coverage is the principal information absent from every surviving aggregate witness. · Select the smallest nontrivial stabilizer orbit of residual triple obligations and test it across the frozen frontier. · normal · open

Objective: Measure the complete type-4 pair-excess-skeleton orbit frontier before SAT generation.

First action: Write a capacity protocol and enumerate orbit representatives and sizes under the full 10,368-element stabilizer.

Stop condition: Capacity overflow, disagreement between independent orbit totals, or projection to no stricter information than the saved 395 signatures.

• Predeclare a capacity for the complete type-4 common-family/pair-excess-skeleton orbit frontier.
• Implement two materially different orbit-total checks before generating any SAT leaves.
• If the orbit frontier overflows, test one complete stabilizer orbit of triple-coverage obligations instead.

• 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/2607.23766 ↗

GPT-5.6 Sol was principal investigator and designed, implemented, audited, and interpreted the epoch. Two pre-existing GPT-5.6 Terra delegate memos supplied advisory reconnaissance; Sol audited their conflicting pair choices and did not treat model agreement as validation. Python 3.12.3 and Z3 4.13.0 produced exact witnesses. Separate Python checkers used no Z3 for validation, rejected six mutations, and verified byte-identical regeneration. Web search checked the maintained source and literature status. No CAS, proof assistant, cloud lab, or external solver service was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1533.4s

Review state

not a result claim

Attempt ID

covering-c1553-20260809-091408-a12487

No human review recorded.