How does Palomar stop a Lean proof from cheating?

Palomar requires the Solution module to depend only on the three standard Lean axioms — propext, Classical.choice and Quot.sound — and rejects anything reaching for sorryAx or Lean.ofReduceBool. Proofs are replayed through Lean's own kernel and the independent NanoDa kernel using the Comparator tool, so a single tampered kernel cannot wave a bad proof through.

Is Palomar peer reviewed?

Palomar does not perform peer review and states plainly that it is not a journal. Registration means a submission passed automated checks — kernel verification, declaration matching, import validation and a language-model fidelity review — not that a human expert endorsed the mathematics. The registry publishes the review comments so readers can judge for themselves.

Can I submit an AI-generated proof to Palomar?

Yes. Palomar accepts submissions whether they are human-generated, AI-generated or a mixture, and requires structured disclosure of authorship, sources, methods and limitations. The disclosure requirement is the point: the registry does not care who wrote the proof, only that the claim is stated clearly and the machine check passes.

What does a Palomar submission have to contain?

A Palomar submission needs a Lean project with one lakefile, a pinned lean-toolchain, a short Challenge module stating the result, a Solution module proving it, a comparator.json naming every theorem to compare, a formalization.yaml with metadata, and a licence file. The Challenge module is capped at 1,000 lines and 100 KiB so a reader can audit the claim quickly.

Palomar was initially developed by the Lean FRO and ICARM. Day-to-day work splits across three groups: technical maintainers — Terence Tao, Matthew Ballard, Nestor Guillen and Jaume de Dios — who run the repositories and services; moderators who can retract or restore a registered version; and a scientific advisory board that sets policy without reviewing individual submissions.

Lean FRO · 2026-08-18 · major

Palomar — a registry that machine-checks Lean proofs, human or AI

Palomar is a public registry of Lean formalizations whose proofs have been machine-checked. Submissions are open to human-written, AI-written or mixed proofs, and every entry must clear a dual-kernel check plus a language-model review.

Lean theorem prover banner, the language Palomar registers verified proofs for — Lean FRO

A searchable registry of Lean formalizations whose proofs are replayed through two independent kernels before they are listed.

Key specs

Challenge file cap	1,000 lines

Quick facts

Maker	Lean FRO and ICARM
What it is	Registry of machine-checked Lean proofs
Accepts	Human, AI or mixed authorship
Mechanical check	Lean kernel + NanoDa kernel via Comparator
Non-mechanical check	Language-model review of statement fidelity
Peer review	None — Palomar is not a journal
Required files	Challenge.lean, Solution.lean, comparator.json, formalization.yaml

What is it?

Palomar opened for submissions as a public, searchable registry of Lean formalizations whose proofs have been machine-checked. Results are organised by the mathematical claim itself rather than scattered across GitHub repositories, so a reader can look up a theorem instead of hunting for the repo that proves it. Human-written, AI-written and mixed submissions are all welcome.

How does it work?

Every submission clears three gates. The mechanical one replays the proof through Lean's kernel and the independent NanoDa kernel with the Comparator tool, checks that Challenge and Solution declarations share names and types, and rejects any dependency beyond the three standard axioms. A language model then judges whether the formal statement fairly represents the informal claim and meets a research-interest floor. Structured disclosure of authorship, sources and methods is the third requirement.

Why does it matter?

Checking that a Lean repository proves what its README says is slow work even for experts, and the flow of machine-generated proofs has made that bottleneck acute. A registry that replays the kernel, blocks axiom smuggling and publishes the review comments turns 'someone claims a proof' into something a non-Lean reader can check in one place. Palomar is explicit that this is not peer review — it is a floor, not a seal of approval.

Who is it for?

mathematicians and researchers working with Lean formalizations

Frequently asked questions

How does Palomar stop a Lean proof from cheating?: Palomar requires the Solution module to depend only on the three standard Lean axioms — propext, Classical.choice and Quot.sound — and rejects anything reaching for sorryAx or Lean.ofReduceBool. Proofs are replayed through Lean's own kernel and the independent NanoDa kernel using the Comparator tool, so a single tampered kernel cannot wave a bad proof through.
Is Palomar peer reviewed?: Palomar does not perform peer review and states plainly that it is not a journal. Registration means a submission passed automated checks — kernel verification, declaration matching, import validation and a language-model fidelity review — not that a human expert endorsed the mathematics. The registry publishes the review comments so readers can judge for themselves.
Can I submit an AI-generated proof to Palomar?: Yes. Palomar accepts submissions whether they are human-generated, AI-generated or a mixture, and requires structured disclosure of authorship, sources, methods and limitations. The disclosure requirement is the point: the registry does not care who wrote the proof, only that the claim is stated clearly and the machine check passes.
What does a Palomar submission have to contain?: A Palomar submission needs a Lean project with one lakefile, a pinned lean-toolchain, a short Challenge module stating the result, a Solution module proving it, a comparator.json naming every theorem to compare, a formalization.yaml with metadata, and a licence file. The Challenge module is capped at 1,000 lines and 100 KiB so a reader can audit the claim quickly.
Who runs Palomar?: Palomar was initially developed by the Lean FRO and ICARM. Day-to-day work splits across three groups: technical maintainers — Terence Tao, Matthew Ballard, Nestor Guillen and Jaume de Dios — who run the repositories and services; moderators who can retract or restore a registered version; and a scientific advisory board that sets policy without reviewing individual submissions.

Try it

https://palomar-registry.org/how-to-submit