Classified one saved literal e45=0 complete-link witness for each of 376 type-4 targets under the full 10,368-element stabilizer, with an independent lift-map and primary-clause audit.

two-marked multiplicity-five-pair witness orbit census

Lift each saved aggregate witness to its five literal {4,5}-blocks, canonicalize the joint target signature and family, and measure whether symmetry supplies a useful branch compression before SAT.

Hypothesis: The 376 saved e45=0 target witnesses collapse to at most 188 joint stabilizer orbits, and each pinned literal family adds at least one baseline-absent primary unit.

Test: Canonicalize all 376 saved target-witness objects under the exact type-4 stabilizer and audit their 275 pair-containing primary variables against the baseline CNF.

Independent reconstruction, mutation rejection, byte-identical regeneration, and manifest replay validate the scoped counts. Those counts do not eliminate a target or cover, and the arbitrary-witness sample cannot support a field-level classification.

• The 376 saved e45=0 target-witness objects occupy exactly 376 orbits under the full 10,368-element type-4 stabilizer.
• The same 376 saved literal families occupy exactly 219 orbits when target signatures are discarded.
• Among the saved families, 298 have link degree pattern (2,2,1^11) and 78 have pattern (3,1^12).
• For every sampled canonical family, its five positive and 270 negative pair-block units are absent as exact unit clauses from the baseline type-4 CNF.
• No target, SAT branch, 54-cover, or covering-number bound was excluded.

• Producer command recorded in .proof-experiments/20260811-134543-859028/experiment.json; return code 0 in 43.833 seconds.
• Independent adversarial checker command recorded in .proof-experiments/20260811-134845-0554eb/experiment.json; return code 0 in 71.715 seconds.
• sha256sum -c artifacts/type4-two-marked-pair-witness-orbits-20260811/manifest.sha256: all entries OK.
• Fresh regeneration produced SHA-256 f2e099b5dd66c100d1da3357f4efe1c78417114c25052fa2c71f4f02e6aea26c, byte-identical to the original.

• .proof-experiments/20260811-134543-859028: 376 targets produced 376 joint and 219 family-only orbits; gate REDIRECT.
• .proof-experiments/20260811-134845-0554eb: independent reconstruction passed and rejected five mutations.

checkers/check_type4_two_marked_pair_witness_orbits_v1.py uses generator closure rather than the producer's direct-product enumeration and independently rebuilds every residual literal cell and CNF unit.

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

• Finite-group orbit compression -> predicted at least 2x reduction of target-witness states -> observed no joint reduction, so arbitrary-witness symmetry is rejected as a scaling mechanism.
• Exact branch pinning -> predicted a nonzero formula delta absent from link-coverage clauses -> observed 275 baseline-absent units per sampled family, but no tractability or exclusion claim followed.

• The saved 376 joint e45=0 target-witness records form 376 stabilizer orbits.
  result SHA-256 f2e099b5dd66c100d1da3357f4efe1c78417114c25052fa2c71f4f02e6aea26c and independent check SHA-256 092c96c3c9146adc62c7bc8d61e0d9cf914db3336d59374ec7841580adc5d702. · Exactly one saved positive witness per frozen e45=0 target. · computed
• The baseline type-4 CNF contains no primary unit clauses among its 2,717 block variables.
  Two independent DIMACS parsers found 30 auxiliary units and zero primary units. · Baseline CNF SHA-256 2146afbf93b8d914d4faf42e9c08a2bdcdebe4dc9e10bd358f98b8fde596754f. · computed

• Scale target-plus-one-saved-witness stabilizer compression into SAT leaves.
  The complete set of 376 saved e45=0 target witnesses and the predeclared 2x gate. · Every joint object is in a distinct orbit; the reduction factor is exactly one. · artifacts/type4-two-marked-pair-witness-orbits-20260811/result.json and independent-check.json. · A complete feasible-family census or target-independent canonical invariant must show material bulk compression; choosing different arbitrary positive witnesses is insufficient.
• Rerun complete fixed-pair-link coverage as a strengthening.
  All 754 saved type-4 signature/e45 targets and all labelled {4,5,z} coverage clauses. · Every target already has a checked positive witness, and the later CNF audit found zero link-coverage clause delta. · artifacts/type4-complete-pair-link-gate-20260809/result.json and the prior pair-link CNF-delta audit. · A labelled constraint beyond existing coverage clauses and exact pair identity must be exhibited.

• Exact three-way count({4,5}) in {5,6,7} CNF split.
  It is target-independent and avoids enumerating 12.6 billion literal families while retaining the genuine second-pair count delta. · Anti-rediscovery audit followed, only if novel, by three independently compiled matched-cap type-4 branches. · high · open
• Materially new exact-degree constructive move family.
  A 54-cover is directly checkable, while the current negative encodings remain unresolved. · Specify a variable-length degree-preserving trade or ejection mechanism distinct from completed 2-for-2, 3x3, 4x4, and strict-five routes; accept only a defect below ten. · normal · open

Objective: Find a target-independent, non-duplicative discriminator with real semantic delta before more proof-scale search.

First action: Run rg across records/attempts, scripts, and artifacts for exact type-4 pair45 count branches and compare their mechanism to the global pair-envelope and pair-upper experiments.

Stop condition: Stop the count-split route if an equivalent experiment exists, if independent clause reconstruction finds zero delta, or if the matched pilot shows no material decision or propagation improvement.

• Audit the attempt registry for an existing exact count({4,5})=5,6,7 type-4 CNF split; stop immediately if it duplicates the global pair-envelope or pair-upper experiments.
• If genuinely absent, independently compile the three disjoint exact-count branches and run a small matched propagation pilot before any family enumeration.
• In parallel planning, prefer a materially new exact-degree constructive move family and require a directly checked defect below ten before scale-up.

• 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 ↗

GPT-5.6 Sol acted as principal investigator. GPT-5.6 Terra challenger/prior-art and experiment-verification delegates supplied advisory reconnaissance only; no model agreement was used as validation. Deterministic Python 3.12.3, exact finite-group enumeration, integer incidence reconstruction, DIMACS parsing, SHA-256, mutation testing, byte-identical regeneration, the computational-researcher harness, and a web-reader status attempt were used. No SAT solver, CAS, proof assistant, lab job, package installation, system change, external write, or publication was used.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1517.1s

Review state

not a result claim

Attempt ID

covering-c1553-20260811-135640-3ae07c

No human review recorded.