From SAT Discovery to Fast-Verifiable Artifacts: An Infrastructure Pattern for Auditable AI-Assisted Mathematics

AI-assisted mathematical work is increasingly capable of producing useful computational searches, candidate patterns, and formal proof fragments, but it is difficult to evaluate when the output is presented only as natural-language reasoning or as a final PDF. This paper studies a concrete, infrastructure-first pattern for auditable AI-assisted mathematics. The core problem is how to put generation and verification into the same system: generated code, searches, witnesses, and proof fragments must be assigned to explicit verification boundaries before they become mathematical evidence. The pattern combines four layers: a persistent project and release infrastructure; AI-assisted coding and search orchestration; SAT-guided discovery, refutation, and finite obligation generation; and a fast-verification trust layer that uses SAT checkers, witness verifiers, proof-assistant kernels, and release audits to lower the cost of independent verification. The paper is anchored by a nontrivial Rado Numbers project for the equation x + by = bz, but it does not restate that companion paper's mathematical inventory. The Rado project is used as a proof-engineering workload: it contains analytic proof, SAT finite obligations, public witness verification, a Lean 4 + Mathlib formalization, a live axiom audit, a typed gap ledger, transcript excerpts, and release metadata. The contribution is not a new SAT solver, a new proof assistant, or a claim that SAT certificates have been fully replayed in Lean. The contribution is the demonstrated Rado artifact architecture by which AI, SAT, Lean, and release-grade evidence ledgers can turn AI-assisted exploration into auditable mathematical assets. The target is not that every artifact must be re-proved inside Lean. The target is that every load-bearing artifact has a cheap, explicit verification path. In its strongest form this path is a kernel-only Lean artifact; in many finite cases it is a SAT or witness-checking route with a small input/result interface.