Exhaustively classify all 32,768 labelled point-boundary interfaces for compatible lifted-Pasch trades around canonical fixed-family type 1 using hidden-vertex masks and an exact subset-zeta transform.

hidden-mask point-boundary separator classification

Aggregate every compatible trade by its 15-bit hidden-vertex mask, then obtain every boundary-disjoint trade count with a subset-zeta transform.

Hypothesis: Every canonical type-1 point-boundary of size at most 12 hides a compatible lifted-Pasch trade, while boundaries of size at least 13 hide none.

Test: Enumerate all 2,702,700 labelled trades once, aggregate their hidden masks over all 32,768 boundaries, and independently reconstruct every count by direct submask summation.

The producer exhaustively covered the finite trade and boundary universes. The independently derived checker reproduced the same count digest with a different aggregation algorithm, verified the extremal block witness semantically, and rejected all mutations. Byte-identical regeneration and a passing hash manifest bind the packet.

• Exactly 2,059,200 of 2,702,700 labelled lifted-Pasch trades are compatible and coverage-changing under the tested canonical type-1 definition.
• These trades occupy exactly 5,165 nonzero hidden-vertex masks.
• Every point-boundary of size at most 9 is blind to at least one tested trade.
• The minimum separating point-boundary size is 10; {0,1,2,3,4,5,6,7,8,9} is one separator.
• At size 10, 218 boundaries are blind and 2,785 separate; at size 11, 12 are blind and 1,353 separate.
• Every boundary of size at least 12 separates every tested trade.
• No 54-block covering family was constructed or excluded.

• Producer experiment 20260810-112948-84adb5 completed in 47.585 seconds; result SHA-256 2ac1f6e7a9214bdb1bb96768a427578f40fefc565d7991a5da93641cdafd0606.
• Independent checker experiment 20260810-113213-e3d664 completed in 49.691 seconds with valid=true and 14,348,907 direct submask lookups; output SHA-256 c17dac10cc2022504006bd0e8c9c67ad3ef8f40c3424ececd2c9255a4e7010c4.
• Regeneration experiment 20260810-113322-67e1e9 completed in 46.044 seconds and was byte-identical.
• sha256sum -c artifacts/type1-lifted-pasch-full-boundary-census-20260810/manifest.sha256 passed for every listed artifact; manifest SHA-256 6188c5887ceb88dbf942ce300bcb1983bd0057b7f2013ba978d2cfb377a842e6.

• .proof-experiments/20260810-112948-84adb5: producer PASS; hypothesis falsified, minimum separating size 10.
• .proof-experiments/20260810-113213-e3d664: independent checker PASS; every count matched and five mutations were rejected.
• .proof-experiments/20260810-113322-67e1e9: clean regeneration PASS; result byte-identical.

checkers/check_type1_lifted_pasch_full_boundary_census_v1.py derives the 15 trades by enumerating linear 2-regular four-triple systems, reconstructs all 2,059,200 compatible trades, and computes all boundary counts using direct submask sums rather than the producer's base-trade derivation and zeta transform.

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

• Design trades -> hidden coverage-difference vertex sets -> a point-boundary separates a trade exactly when it intersects that hidden set; observed exact separator size 10.
• Hypergraph transversals -> minimum separating boundary becomes a hitting-set question -> observed minimum 10, but the induced interface retains 445 of 455 triple bits.

• The minimum point-boundary size separating every compatible lifted-Pasch trade around canonical fixed-family type 1 is exactly 10.
  Exhaustive producer, independent all-count reconstruction, semantic witness checks, and hash-bound regeneration. · All 32,768 labelled boundaries and all 2,059,200 compatible coverage-changing trades in the specified family. · computed
• Every boundary of size at least 12 separates the tested trades, while some size-11 boundaries remain blind.
  Size-layer counts independently reconstructed as 12 positive at size 11 and zero positive at sizes 12 through 15. · Same finite trade family. · computed

• Every point-boundary through size 12 remains blind.
  The predeclared full-boundary hypothesis for canonical type 1. · 2,785 size-10 boundaries, 1,353 size-11 boundaries, and every size-12 boundary have zero hidden-trade count. · result.json and independent-check-final.json · None for this exact finite claim; only a changed trade or interface definition would create a different question.
• Use a point-boundary interface as a materially compact exact summary of these trade directions.
  All interfaces consisting of triple-coverage bits meeting a point-boundary. · The smallest separator has size 10 and therefore retains 445 of 455 bits; every such interface retaining at most 435 bits is blind. · Exact minimum boundary size 10 and the identity |I_B|=455-C(15-|B|,3). · A different interface family with proved equivalence and materially fewer than 445 retained bits, or an actual-54 theorem eliminating the recorded collisions.
• Rerun the complete fixed-pair-link relaxation as a new discriminator.
  The prior 395 signatures and 754 type-4 signature/e45 targets. · Epoch 28 already retained all 754 targets with independently checked literal witnesses. · records/attempts/epoch-0028-type4-complete-pair-link-20260809.json · Add labelled information outside that link or a measured proof-search mechanism.

• Proof-producing canonical SAT leaf
  It is the active route with a terminal UNSAT certificate path. · Run one canonical type-1 leaf under a fixed cap and replay any DRAT conversion through LRAT. · high · open
• Constructive exact-degree repair
  A directly checked defect below the current best 10 would provide measurable constructive progress. · Run one deterministic repair tranche with a strict below-10 acceptance gate. · normal · open
• Actual-target trade completion filter
  Exact 54-block constraints might forbid unrestricted partial-history collisions. · Encode one representative hidden trade with exact degree, pair-excess, and completion constraints and require a replayable UNSAT certificate or checked completion. · normal · open

Objective: Obtain a proof-producing signal from one globally valid canonical SAT branch.

First action: Generate one canonical type-1 CNF under the saved degree-18 normalization, run a fixed-cap proof-producing solver, and replay any UNSAT proof through DRAT-to-LRAT.

Stop condition: Promote only after complete replay; switch to constructive repair if the leaf remains UNKNOWN or proof conversion fails.

• Generate one canonical type-1 SAT leaf under a fixed cap and require complete DRAT-to-LRAT replay for any UNSAT result.
• Switch immediately to a deterministic constructive repair tranche if the proof-producing leaf remains UNKNOWN.
• Test actual-54 completion constraints against a representative hidden trade only if they couple information not present in the exhausted point-boundary family.
• Do not reopen point-boundary compression without its recorded reopen evidence.

• 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 principal designed, implemented, ran, and interpreted the experiment. GPT-5.6 Terra challenger-prior-art and experiment-verification delegates supplied advisory reconnaissance only; their memos were promoted with provenance but were not evidence. Python 3.12.3 standard library, SHA-256, web search, and the computational-researcher experiment harness were used. No SAT solver, CAS, proof assistant, cloud lab, external write, or publication was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1180.4s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260810-114038-541050

No human review recorded.