Mathematical Theorem Proving & Formal Verification AI

Translates informal natural language mathematical problems into syntactically valid Lean 4 definitions and theorem statements.

Models generate proof tactics (such as `induction`, `rw`, `simp`) that transform open goals until all branches are closed.

A tiny, mathematically audited core kernel verifies that the compiled proof contains zero logical errors.

Generates millions of synthetic mathematical conjectures and attempts to prove them autonomously to expand capability.

Executes deterministic geometric and algebraic coordinate transformations without relying on probabilistic next-token guesses.

Guides Monte Carlo Tree Search using value networks that evaluate the likelihood of closing remaining proof obligations.

Formally proves that operating system microkernels (like seL4) are immune to buffer overflows and memory leaks.

Verifies that zero-knowledge proofs and post-quantum cryptographic primitives adhere strictly to mathematical specifications.

Proves mathematical correctness of custom silicon ASIC register-transfer level (RTL) circuit designs.