Exact-capacity test of the simultaneous 13-triple link of the stabilizer-fixed pair {4,5} on all 754 frozen type-4 signature/e_45 targets

complete fixed-pair link relaxation

Aggregate all 2717 residual blocks by five root intersections, exact {4,5} incidence, and the complete labelled 13-bit {4,5,z} link vector; solve every frozen target and independently expand positive cell counts to literal blocks.

Hypothesis: At least one of the 754 previously skeleton-feasible type-4 signature/e_45 targets has no exact-capacity residual witness once all 13 triples containing {4,5} must be covered simultaneously.

Test: Run 754 incremental exact integer-feasibility checks over a capacity-preserving 431-cell quotient and require literal-expandable positive witnesses or a separately certified negative result.

The all-positive witness map is complete for the declared frontier, independently reconstructed at literal-block level, mutation-tested, and byte-identically regenerated. It decisively falsifies the route's pruning hypothesis without extrapolating beyond its necessary-relaxation scope.

• The complete fixed-pair-link feature census contains exactly 431 capacity-preserving cells: 156 nonpair cells and 275 singleton {4,5}-block cells.
• Every one of the 754 frozen type-4 signature/e_45 targets admits a 49-distinct-block residual witness satisfying the five source-indexed margins, exact {4,5} count, and all 13 {4,5,z} coverage obligations.

• python3 /root/proof-factory/skills/computational-researcher/scripts/run_experiment.py ... -- python3 scripts/run_type4_complete_pair_link_gate_v1.py --output-dir artifacts/type4-complete-pair-link-gate-20260809
• sha256sum -c artifacts/type4-complete-pair-link-gate-20260809/manifest.sha256: all entries OK
• independent-check.json: valid=true, 431 cells, 754 targets, 36946 expanded literal occurrences
• mutation-controls.json: 6 of 6 corruptions rejected
• regeneration-check.json: byte_identical=true

• .proof-experiments/20260809-162650-27bcac: return code 0 in 66.635 seconds; 431 cells and all 754 targets retained

checkers/check_type4_complete_pair_link_gate_v1.py independently enumerates all residual literal blocks without Z3, reconstructs the 431 cells, expands each witness to 49 distinct blocks, and checks all source margins, pair counts, and 13 link obligations.

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

• Terra exact-capacity advisory -> prediction of a 431-cell complete-link quotient -> Sol independently reconstructed exactly 431 cells, then found that all 754 targets survived.

• The complete-link quotient has exactly 431 cells.
  Producer and independent literal census agree; manifest-bound independent-check.json reports 156 nonpair and 275 singleton pair cells. · The 2717 residual blocks avoiding {0,1} under the fixed type-4 common family. · computed
• All 754 frozen targets have complete-link witnesses.
  36946 independently expanded literal block occurrences with complete ordered target coverage. · The five-margin, exact-{4,5}-count, complete-{4,5}-link necessary relaxation only. · computed

• Use the complete labelled link of the single stabilizer-fixed pair {4,5} to eliminate a frozen type-4 signature or e_45 target.
  All 395 signatures and all 754 previously skeleton-feasible targets in the exact 431-cell necessary relaxation. · Every target has an independently checked positive witness. · artifacts/type4-complete-pair-link-gate-20260809/independent-check.json · Couple the link to literal identities outside the anonymous root margins or demonstrate a measured proof-search use; another subset of the same link cannot prune this frontier.

• Pair-excess extended-variable SAT encoding.
  It changes the inference mechanism by exposing weighted-degree-two conservation inside a globally complete branch, rather than adding another exhausted aggregate projection. · Matched base/extended type-4 CNFs at 25000 conflicts with an independent equivalence checker. · high · open

Objective: Determine whether explicit pair-excess conservation materially improves proof search on the type-4 branch.

First action: Create the matched base/extended 25000-conflict protocol and an independent formula-equivalence checker.

Stop condition: Stop or redirect if neither run is decisive and the extended encoding fails to reduce propagation cost by at least 20 percent.

• Freeze a matched base/extended type-4 CNF protocol exposing all pair-excess variables and weighted-degree-two conservation.
• Independently reconstruct formula equivalence before measuring solver behavior.
• At 25000 conflicts, continue only for a certified decisive status or at least 20 percent lower propagation cost.

• 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 ↗

GPT-5.6 Sol principal independently audited the source and prior artifacts, designed and froze the protocol, implemented the producer/checkers, ran the experiment, and interpreted the result. GPT-5.6 Terra delegates supplied advisory reconnaissance only; their agreement was not treated as validation. Python 3.12.3 and Z3 4.13.0 generated exact integer witnesses. A separately written non-Z3 Python checker reconstructed literal semantics. Six mutation controls, SHA-256 manifest replay, and byte-identical regeneration passed.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

980.7s

Review state

evidence receipt failure; not durable progress

Attempt ID

covering-c1553-20260809-163338-6cc89a

No human review recorded.