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Terence Tao announced Palomar on August 18, a public registry for Lean-formalised mathematical proofs, incubated by the Lean FRO and ICARM. Tao serves on its scientific advisory board alongside Jeremy Avigad (Carnegie Mellon), Ravi Vakil (Stanford), and Akshay Venkatesh (IAS).

The trigger: a proliferation of AI-generated proofs over the past year, some formalised in Lean, with no standardised way to verify that a given repository actually proves what it claims. Checking a Lean repo requires both that the formal proof typechecks without cheats — no added axioms, no sorry — and that the formal statement actually matches the informal mathematical claim being advertised. The second part is where most audits fail.

Two-Layer Verification

Palomar applies two checks to each submitted repository snapshot (pinned to a specific GitHub commit):

Mechanical check: Uses Lean’s open-source Comparator tool to verify that the solution module typechecks and proves exactly what the challenge file states. Purely deterministic.

Semantic check: An AI model evaluates whether the informal description in the formalization.yaml file matches the formal Lean statement in the challenge file. Non-deterministic. Tao’s post describes this as verifying “in a semantic sense” that the two align — addressing the gap between a statement that is formally correct and one that proves what the author says it proves.

The repository structure has three required components:

• A challenge file: short, human-readable Lean description of the claimed results
• A solution module: the full proof, of arbitrary length
• A formalization.yaml: informal description, metadata, and disclosures

Why It Matters Now

Since GPT-5.6 Sol formally proved the Erdős Unit Distance Conjecture in Lean in July 2026 (1.2 million lines, 3 weeks), and with LEAP solving all 12 Putnam 2025 problems earlier this year, the AI-generated formal proof pipeline has moved from demonstration to production volume. The infrastructure for credentialing those proofs has not kept pace.

Palomar is explicitly modelled as a preprint server for Lean proofs — analogous to arXiv, but with machine-enforced verification built in. A registry entry means the proof was independently checked, not just that the authors published it. This distinction matters as labs begin citing AI-generated formal results as precedents in research papers.

The naming is deliberate: Palomar Observatory, as a place where observations are recorded and validated before they enter the scientific record.

What It Does Not Do

Palomar does not evaluate the mathematical significance of what is proved — only that the proof is formally correct and matches its description. It does not replace peer review for mathematical content. And the semantic check, being AI-generated, carries its own error rate, which Tao’s announcement does not quantify.

The registry is open for submissions as of August 18. No pricing or volume information was disclosed.