Obligations, not theorem solving
Lean is supported as formal proof evidence, not as a promise of arbitrary theorem solving. The obligation is the acceptance target.
Use case — formal math
Proof obligations the kernel actually checks.
Lean is a first-class formal proof evidence backend for FalseGreen Jobs — from single-lemma obligations to research-scale formalizations.
A human or model may write the proof. The Lean kernel checks it. The Job decides whether the exact frozen formal obligation was satisfied by the exact source under the declared trust boundary — and says so with a signed report.
How formal evidence worksA formal Job, end to end
formal obligation · frozen
↓ kernel check
lake build · proof artifacts replayed
↓ authority decision
Accepted / Failed / Insufficient Evidence
Why formal math
The kernel is the referee. The Job is the record.
Lean's value is that a checked proof is a checked proof — no reviewer fatigue, no plausible-but-wrong handwave. FalseGreen adds the layer around the kernel that research and product work both need: the obligation is frozen, the source identity is bound, the proof artifacts are replayed rather than trusted, and the result is signed and re-checkable offline.
Proof artifacts replayed
Prebuilt proof objects are re-verified by the kernel in the checking environment — replay, not trust. Only the challenge code builds fresh.
Independent reference checks
Target theorems can be re-checked by the reference checker with a second, independent Lean kernel, with the axiom baseline audited.
Real evidence
What formal-math work actually produced.
The evidence below is from real Jobs on the 0.4.0 platform — job identifiers, verdicts, and report contents, not illustrations.
The Navier–Stokes work is documented as a four-paper series — the counterexample, the verified formalization, the step-by-step walkthrough, and the Lean code itself. Each post carries the full paper as a PDF.
Research-scale formalization
Job aa1a2a63 — verdict Accepted
The OpenAI Navier–Stokes/Euler Lean formalization, verified as a single six-criterion Job: the full fork compiles with the prebuilt proof artifacts replayed (the Lean kernel re-verifies every proof), the independent reference checker re-checks the target theorems with two different Lean kernels, and the axiom and proof-hole audits pass.
Real 0.4.0 Job
Job f1a4b61d — verdict Accepted
A Lean workspace through the 0.4.0 platform: lake build plus the workspace's own test runner (5/5). The signed report binds the criteria to the exact source identity.
End-to-end, through the live Internet
Lean lane: green
The hosted end-to-end world ran the Lean lane over the real network path — real git, real CI, the combined job image — with the acceptance and blocking outcomes both exercised.