A Three-Layer Dependency-and-Logic Audit for Mathematical Proofs and AI-Generated Claims: The S/M/P × D/L Framework

We introduce a structured audit framework for mathematical proofs, conjectures, and AI-generated mathematical claims. The framework operates on three layers—Semantic, Mathematical, and Programming—and for each layer examines two complementary dimensions: internal Dependency relations and internal Logic-structure discipline. The resulting S/M/P × D/L matrix provides six elementary audit cells (S*D, S*L, M*D, M*L, P*D, P*L) plus cross-layer mapping checks. Version 4 expands the case corpus to include a corpus-level audit of the OpenAI 700+ mathematical-proofs repository (github.com/openai/math) and three representative high-risk samples, alongside the previously audited cases spanning correct proofs, classical fallacies, disproved conjectures, a research-level computer-assisted proof, open diagnostics (Riemann Hypothesis, Andrews–Curtis conjecture), and the 2026 Navier–Stokes AI-formalization incident in which a Lean-verified claim failed at the semantic-translation layer despite passing the programming layer (Bastounis–Circelli–Hansen, arXiv:2610.08144). The attached SMPDL_v1.5_sample_reports.zip contains 50 markdown reports used to compute the joint SHA-256 fingerprint.