We study impossibility analysis as an auditable search problem over axiom levers rather than as a claim of general theorem automation. Our target is the fixed Sen base case sen24 (n=2, m=4), where we build a small-scope possibility atlas that records which axiom combinations are SAT or UNSAT and ties each result to replayable evidence. The pipeline separates specification, encoding, solving, and checking: Lean fixes the semantic layer, Python emits DIMACS plus manifests, external SAT solvers search, committed LRAT traces are replayed in Lean, and reported SAT models are checked independently by a witness validator. Within this scope, the atlas identifies the sen24 SAT/UNSAT boundary, explains boundary UNSAT cases by extracting one MUS and one small MCS candidate, presents validated SAT rule examples through deterministic gallery and rule-card exports, and separates that local explanation stage from a stronger repair-enumeration stage checked by triangulation. To keep the trust model explicit, we distinguish Lean proofs, mechanical audits, witness validation, and remaining assumptions: the sen24 semantic theorem is proved in Lean; committed LRAT replays are kernel-checked; CNF schema conformance is audited; SAT witnesses are validated against concrete CNF instances; and the rationality-side short-cycle encoding is justified only for sen24 by a finite check showing that, under asymmetry on four alternatives, forbidding directed 3-cycles and 4-cycles coincides with acyclicity. The repository also packages commands, hashes, metadata, and paper-facing artifacts into a reproducible evidence bundle so that the sen24 frontier, boundary explanations, stronger repair artifacts, and SAT witnesses can be regenerated and audited without trusting the solver alone.
Shunya Hayashida (Thu,) studied this question.