Clean-room static reconstruction of the 105 pair-threshold outputs already present in U5, followed by an exact size gate for a counter-sharing E5 encoding.

incidence-matrix SAT with inherited threshold reuse

Reuse each retained pair totalizer's lambda>=5 and lambda>=6 outputs, add 105 lambda<=5 units, 3150 support conjunctions, and thirty exact-five column counters; reject before CNF generation if either raw dimension exceeds 1.35 times U5.

Hypothesis: The 105 pair thresholds already present in U5 yield a semantically correct E5 projection with variables and clauses each at most 1.35 times U5.

Test: Byte-exact reconstruction of the retained cardinality layer and threshold map, followed by exact dimension arithmetic and 4/5/6 semantic controls without materializing or solving the projected CNF.

The producer and independent checker agree exactly, all support and boundary controls pass, and four mutations fail closed. These results justify rejecting this precise encoding implementation under its predeclared gate, but they say nothing about satisfiability.

• The retained base exposes 105 distinct lambda>=5 and lambda>=6 pair-threshold outputs.
• The sound reused E5 projection has exactly 50400 variables and 282393 clauses.
• The projection exceeds floor(1.35*36330)=49045 by 1355 variables.
• No C(15,6,3) covering bound changed.

• python3 scripts/audit_e5_threshold_reuse_v1.py --out artifacts/epoch59-20260810/e5-threshold-reuse-receipt.json
• python3 checkers/check_e5_threshold_reuse_v1.py --receipt artifacts/epoch59-20260810/e5-threshold-reuse-receipt.json --out artifacts/epoch59-20260810/e5-threshold-reuse-independent-check.json
• python3 checkers/test_e5_threshold_reuse_fail_closed_v1.py --receipt artifacts/epoch59-20260810/e5-threshold-reuse-receipt.json --out artifacts/epoch59-20260810/e5-threshold-reuse-fail-closed-controls.json
• sha256sum -c artifacts/epoch59-20260810/SHA256SUMS: all entries OK

• .proof-experiments/20260810-165106-e170c9: static producer returned REJECTED_BY_STATIC_GATE with 50400 variables and 282393 clauses.
• .proof-experiments/20260810-165121-c8c76d: independent reconstruction PASS.
• .proof-experiments/20260810-165128-37a9cb: four fail-closed mutations rejected.

checkers/check_e5_threshold_reuse_v1.py is a separately written totalizer oracle that reproduced 89400 retained clauses, 105 threshold maps, 3150 support equivalences, boundary semantics, dimensions, and the gate decision.

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

• Certified C(12,6,4)=41 SAT workflow -> demand replayable terminal certificates and fail-closed controls -> this epoch stopped before solving because the static encoding gate failed.
• Unary totalizer threshold reuse -> predict pair counters can be removed without semantic loss -> confirmed, provided 105 separate -ge6 units are retained.

• The retained incidence base contains 105 independently identified pair roots for thresholds >=5 and >=6.
  Byte-exact reconstruction of 89400 cardinality clauses and map digest 28e8a5e0d6adf8b174e5d574cde9c85356ca4a2a6f531c13dec8fa03eee7722d. · Base CNF SHA-256 34406098dfaf1d08f18f975f7be87c561de8ee19866a1e1455dbfd5bfed53c8f. · computed
• The exact reused E5 projection has 50400 variables and 282393 clauses.
  Producer receipt SHA-256 544fada9a7a70dced2e8bb29aac1254d74310e8bdb81f002031d08a402bcebbe and independent-check SHA-256 3baa2199764430e27d3bf338e50677043de03bca8eaa9c1ee68367879290099e. · Fixed-first q=5 E5 encoding using explicit conjunctions and the retained balanced exact-five column totalizer. · computed

• Scale the exact inherited-threshold E5 projection under the frozen 1.35-both-dimensions gate.
  U5 plus 105 reused <=5 units, 3150 explicit conjunctions, and thirty balanced exact-five column counters. · 50400 variables exceed the permitted 49045 by 1355. · Independent static receipt and mutation controls. · A sound encoding saving at least 1355 more variables, or a proof-prefix reuse design that explicitly supersedes the raw-dimension gate.
• Use 282288 clauses as the sound reused E5 projection.
  The same inherited-threshold construction. · That count omits the 105 -ge6 units required to enforce lambda<=5. · 4/5/6 boundary controls and rejected clause-count mutation. · A proof that the 105 upper units are implied by other retained constraints.

• Six second-block representative orbit-completeness audit
  It is a zero-solver prerequisite for a small, replayable proof frontier and directly checks a saved open lead. · Independently reconstruct stabilizer orbits from artifacts/epoch9-20260808/incidence_orbit_inputs_v1.json and reject representative mutations. · high · open
• Alternative E5 column cardinality encoding
  The current projection misses authorization by exactly 1355 variables while passing the clause gate. · Statically count a sound encoding that avoids explicit conjunction variables or uses a smaller exact-five construction. · normal · open
• Canonical root-link catalogue
  Fixing a 12-block root link reduces completion membership variables and offers an independently checkable frontier. · Run a capped no-solver stabilizer-orbit audit before canonical enumeration. · normal · open

Objective: Validate whether the six second-block representatives form a complete and disjoint orbit frontier suitable for proof-producing incidence/PB cubes.

First action: Read artifacts/epoch9-20260808/incidence_orbit_inputs_v1.json and independently reconstruct the stabilizer action and orbit coverage.

Stop condition: Stop or redirect on any orbit-coverage gap, overlap inconsistent with the intended split, representative mutation acceptance, or proof-format incompatibility.

• Independently reconstruct the stabilizer orbits underlying artifacts/epoch9-20260808/incidence_orbit_inputs_v1.json.
• Require a complete, disjoint six-representative frontier and mutation rejection before formula compilation.
• Only then compile the smallest proof-producing incidence/PB calibration case with exact degree-12 constraints.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?v=15&k=6&t=3 ↗
• https://arxiv.org/abs/2607.23766 ↗

GPT-5.6 Sol principal designed, implemented, and audited the experiment. Two GPT-5.6 Terra delegate memos were advisory only: one failed its injected SHA-256 check, and neither delegate artifact was used as evidence. Python 3.12.3 deterministic scripts parsed DIMACS and reconstructed balanced totalizers. No SAT solver, CAS, proof assistant, external proof service, or cloud lab ran this epoch. Web search/open checked the maintained covering source and arXiv:2607.23766.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

861.6s

Review state

not a result claim

Attempt ID

covering-c1563-20260810-165611-4cc90a

No human review recorded.