The AI Safety Formalization Atlas: a machine-checked memory for AI safety mathematics

When AI systems write proofs, the characteristic failure is a specification failure: a correct proof of a statement that is not the one intended. A proof checker cannot see it, so the bottleneck has moved from proving to stating. We present the AI Safety Formalization Atlas (AISFA), an open Lean 4 library and ledger built for the mathematics of AI safety: results on
verification, learning, control, oversight, reward corruption, preference inference, causal identifiability and governance that today live in prose, scattered across fields. The Atlas holds about 156k lines of kernel-checked Lean and 138 catalogued results. Each formal statement is graded against the published wording. Theorems about models must come with an example that satisfies their hypotheses, so they are not vacuously true, and unproved inputs are explicit hypotheses, never axioms. Shared kernels let one result serve several fields, down to a governance result, proved in a model, that an audit’s evidence can determine the version audited but not the version deployed. Grading 356 printed statements has produced machine-checked refutations of printed claims and made hidden hypotheses explicit. The Atlas also checks community solutions to open problems in public, where a referee reads a few hundred lines instead of tens of thousands.

Repository: https://github.com/mbrcic/ai-safety-formalization-atlas.
Site: https://mbrcic.github.io/ai-safety-formalization-atlas/