A Provenance-Aware Proof Ledger for Long-Horizon AI-Assisted Mathematical Research: Specification, Status Discipline, and a Reference Implementation

Abstract

This preprint introduces a provenance-aware proof ledger for long-horizon mathematical research, including AI-assisted workflows. It provides a status taxonomy that separates external theorems, exact derived results, rigorous computation-assisted results, finite-only results, numerical scouts, candidates, explicit missing bridges, no-go routes, and retracted claims. The framework defines dependency-closure rules, scope-preservation requirements, evidence and provenance fields, and explicit safeguards against promoting finite or numerical results into unrestricted mathematical claims without a valid proof bridge. The release includes a machine-readable JSON Schema Draft 2020-12 specification, a domain-neutral example ledger, and a dependency-free Python verifier for structural consistency checks. The verifier checks ledger integrity and dependency discipline; it does not certify mathematical truth. The package is intended for reuse in mathematical and computational research projects that require durable provenance, explicit proof state, reproducible evidence, preservation of failed routes, and auditable long-horizon research workflows. DOI: 10.5281/zenodo.21863820