An Auditable Possibility Atlas for Social Choice: Proof-/Witness-Carrying Evidence from the Sen24 Case Study

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.