Compiled the source-verified labelled type-(5^4,4^10) C(14,5,2)=12 root link into sequential-unary selector CNF and ran matched forced and unforced CaDiCaL controls.

root-link selector CNF positive-control calibration

A 2002-selector DIMACS encoding with 91 pair-cover rows and fourteen exact-degree unary counters compares a source-forced compilation arm with a cold unforced search arm.

Hypothesis: The source-verified labelled type-(5^4,4^10) link is recovered by both source-forced and unforced selector-CNF arms within five solver seconds.

Test: Run the forced arm first and the identical base formula unforced second using CaDiCaL 1.7.3, seed 0, CPU 0, and five solver seconds; qualify only if both return directly checked SAT models.

The verification contract requires a 30-cover witness or a complete replayed exclusion. This epoch produced neither. Its decisive evidence is operational: the search mechanism failed its known-SAT gate.

• The hash-bound forced formula is SAT, and its assignment satisfies all 201019 clauses and directly encodes a valid twelve-block C(14,5,2) link.
• The hash-bound unforced formula returned UNKNOWN after the five-second solver cap and 8458 conflicts, with no assignment.
• The forced formula is exactly the unforced 201007-clause formula plus twelve archived selector units.
• No unknown root-link type or C(15,6,3) family was excluded or witnessed.

• Producer experiment .proof-experiments/20260812-113205-fa3e3d.
• Independent audit .proof-experiments/20260812-113354-7a283a.
• Forced CNF SHA-256 7c1a43bb4962019d6c863a058abf6a9529d718262a4db1237792cd3e46e69b97; model SHA-256 039d2a6162a021893478b9002faa102a4c91df2e38d51b3937819676a45a5e32.
• Unforced CNF SHA-256 0c22edb3a3dceb8174502d457d02f08f43e054e0977b77d08666489ffa4b43a0; UNKNOWN marker SHA-256 8fba55cea0f98be36fab7b65349dda867a58aabfcf974a46098f5123830ac5cb.
• sha256sum -c artifacts/epoch117-20260812/SHA256SUMS passed.

• .proof-experiments/20260812-113205-fa3e3d: forced SAT in 0.2307215263 seconds; unforced UNKNOWN in 5.0276359702 seconds.
• .proof-experiments/20260812-113354-7a283a: independent audit PASS_FORCED_ONLY_REJECT_SEARCH with three mutations rejected.

checkers/check_root_link_selector_cnf_calibration_v1.py parses and evaluates DIMACS models, recognizes all 91 coverage rows, validates the link and formula delta, and rejects three semantic mutations.

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

None recorded.

• The hash-bound source-forced formula is SAT and its recorded model is a valid labelled C(14,5,2)=12 link.
  artifacts/epoch117-20260812/root-link-selector-cnf-independent-check.json, SHA-256 f25f89c1fba88bf56e1cce5cfa848ebd19034e120eaa2cbd6332400a2553c128 · Forced CNF SHA-256 7c1a43bb4962019d6c863a058abf6a9529d718262a4db1237792cd3e46e69b97 only. · computed
• The fourteen exact labelled degrees imply exactly twelve selected 5-subsets because their sum is 60.
  Five times the number of selected blocks equals the sum of selected point incidences. · Any satisfying assignment of the fixed labelled root-link degree constraints. · proved

• Use the frozen unseeded sequential-unary 2002-selector CNF with CaDiCaL 1.7.3, seed 0, and a five-second cap as the root-link classifier.
  The maintained known-SAT labelled type-(5^4,4^10) control under CNF SHA-256 0c22edb3a3dceb8174502d457d02f08f43e054e0977b77d08666489ffa4b43a0. · The unforced arm returned UNKNOWN; forced SAT establishes compilation only. · Receipt SHA-256 97d855cc586036eb78ed2d47f2aef2fe6d0ef85262c5e03ce8adb881d47d11fa and check SHA-256 f25f89c1fba88bf56e1cce5cfa848ebd19034e120eaa2cbd6332400a2553c128. · A proved symmetry restriction, materially different encoding or solver, or other search change that recovers the same control within five seconds; timeout extension alone is insufficient.

• Degree-color first-block normalization for the type-(5^4,4^10) control.
  The four high-degree points contribute 20 incidences, forcing a selected block with h>=2; S4 x S10 leaves h=2,3,4 canonical cases. · Compile the source-matching h=2 case and run a five-second unforced-within-case control with an independent orbit checker. · high · open
• Complete the parent-rich pair-surplus profile ledger.
  It remains the prerequisite for globally aggregatable certified negative leaves. · After explicit human approval, materialize the exact remaining 38705 profiles and reconcile the once-only union. · high · open

Objective: Qualify a proved degree-color first-block normalization on the maintained positive control.

First action: Encode the h=2 canonical first-block unit under S4 x S10, independently prove its orbit meaning and source membership, then run the unforced-within-case formula for five solver seconds.

Stop condition: Redirect on timeout, orbit-coverage error, invalid model, or formula mismatch; do not contact unknown types unless the control passes.

• Prove and check the S4 x S10 normalization: the four degree-5 points contribute 20 incidences, forcing a selected block with h in {2,3,4}.
• Compile only the source-matching h=2 control and require unforced-within-case SAT within five seconds.
• Keep the remaining 38705-profile parent materialization held until explicit human approval and native PB held until the pinned dual-replay toolchain exists.

• https://www.coveringrepository.com/systems.aspx?k=6&t=3&m=-1 ↗
• https://ljcr.dmgordon.org/cover/show_cover.php?k=5&t=2&v=14 ↗
• https://arxiv.org/abs/math/9502238 ↗

GPT-5.6 Sol was principal investigator. Two GPT-5.6 Terra delegates supplied advisory memos; Sol used and promoted the forced/unforced gate guidance, independently implemented and audited all evidence, and did not count model agreement as validation. Deterministic tools were Python 3.12.3, CaDiCaL 1.7.3, exact set arithmetic, DIMACS evaluation, SHA-256, py_compile, the computational-researcher experiment harness, and web status search. No CAS, PB checker, proof assistant, cloud lab, external proof service, system installation, or human validator produced evidence.; orchestration: gpt-5.6-sol principal with gpt-5.6-terra delegates.

Duration

1038.1s

Review state

not a result claim

Attempt ID

covering-c1563-20260812-114219-748668

No human review recorded.