RIGOR MORTIS: From First-Fatal-Step Diagnosis to Rigorous Proof Repair — Counterfactual Olympiad Proofs, Leakage-Aware Evaluation, and Exact Mathematical Repair

Abstract A true theorem can be supported by an invalid argument. The challenge of proof criticism is therefore not merely determining whether a mathematical statement is true, but identifying the earliest unsupported inference and constructing a rigorous replacement. We present RIGOR MORTIS, an Olympiad-inspired research and training platform for mathematical proof diagnosis, contrastive validity assessment, and exact proof repair. The public training library contains 111 project-authored proof fragments across 19 source-problem families, including 61 author-labelled clean arguments and 50 intended invalid arguments. We introduce a family-aware evaluation framework designed to distinguish genuine mathematical reasoning from superficial proof-pattern recognition and benchmark leakage. Mathematical case studies based on International Mathematical Olympiad problems illustrate first-fatal-step localization, full-hypothesis counterexamples, and rigorous repair. We additionally develop constructive finite-increment envelopes, exact phase-transition results, and weighted repair formulas for a class of functional inequalities. The accompanying methodology specifies independent mathematical adjudication, validity-preserving controls, family-disjoint evaluation, and explicit criteria for complete proof repair. Structural verification of the public materials is documented, but independent mathematical validation and experimental evaluation remain pending. This non-peer-reviewed preprint presents mathematical and software methodology alongside a proposed research protocol. It does not claim completed human-subject experiments, demonstrated model superiority, independently certified mathematical novelty, or endorsement by the International Mathematical Olympiad. Substantial AI assistance in mathematical exploration, implementation, and manuscript preparation is disclosed in the accompanying paper.