Proof‑assistant‑verified LLMs

Wrap large language models with proof assistants (e.g., Lean4) so model‑proposed reasoning steps are autoformalized and mechanically proved before being accepted. Verified steps become a retrievable database of grounded facts, and failed proofs feed back to the model for revision, creating an iterative loop between probabilistic generation and symbolic certainty. — If deployed, this approach could change how we trust AI in math, formal sciences, safety‑critical design, and regulatory submissions by converting fuzzy model claims into machine‑checked propositions.