Three weeks ago this flow was second on Lean-Eval, 149 of 219, behind a specialist prover. It is now first, with 172 research-level problems solved and machine-checked in Lean 4, using GPT-5.6 and a fully agentic workflow.

The model is one anybody can rent. What changed is the arrangement around it.

What the loop does

Argue first, formalize second. The flow writes a natural-language proof strategy before it writes any Lean, then converts that strategy into Lean statements. A formalization that starts from a plan fails in ways that are legible; one that starts from a blank file fails in ways that are not.

The compiler is the reviewer that never gets tired. Lean's error output is fed back into the run and the code is refined against it, round after round, by HOA and Humanize 1 agents. Nothing about this is clever — it is just that almost nobody does it for hundreds of rounds without a human losing patience.

Seed the hard ones with the easy ones. For the problems that resist, the argument is first turned into a precise, stepwise informal plan, and the run is seeded with reusable Lean proofs from related problems that already closed. The agent then spends its budget formalizing the ideas that are actually missing rather than re-deriving the ones that are not.

What counts as solved

Two independent gates, on two different agents, before anything is accepted:

• the worker runs a comparator check on its own output; and
• the reviewer re-verifies through the AXLE API, which has no access to how the proof was arrived at.

Nothing is accepted with a sorry placeholder or an unproved assumption standing in for a step. That bar is the whole reason a leaderboard position in formal mathematics means anything at all: a proof either has a term the Lean kernel accepts, or it does not exist.

HOA · the flows · the runtime