In caller months location has been a proliferation of AI-generated proofs of various aged and caller results, immoderate of which person been formalized successful the impervious adjunct connection Lean. However, checking that a fixed Lean repository really proves the claimed connection is somewhat non-trivial, particularly for an assemblage which is not master successful the usage of Lean: 1 has to first cheque that the claimed general Lean statements person proofs that typecheck, that the proofs do not incorporate immoderate “cheats” specified arsenic adding further axioms, and that the general statements besides lucifer (in a semantic sense) the informal explanation of the claimed results.
To thief bring immoderate clarity to this situation, I americium happy to denote that Palomar registry of Lean verified mathematics, which is an inaugural incubated by the Lean FRO and by ICARM, is now unfastened for submissions. I americium serving successful respective roles connected this registry, including connected the technological advisory board, together pinch Jeremy Avigad, Matthew Ballard, Jaume de Dios, Nestor Guillen, Bryna Kra, Kim Morrison, Ravi Vakil, and Akshay Venkatesh.
A elaborate information for Palomar tin beryllium recovered here, and further accusation astir Palomar tin beryllium recovered here. A zeroth approximation of what Palomar intends to beryllium is the analogue of a preprint server for Lean proofs. More precisely, Palomar (which is named aft the astronomical observatory) is simply a registry of outer Github repositories (or much precisely, “snapshots” of specified repositories, arsenic represented by a circumstantial Github commit) containing Lean codification adhering to the existent champion practices for specified formalizations, successful peculiar containing
- A “challenge file” containing a short, quality readable explanation successful Lean of the results claimed.
- A “solution module” containing an (arbitrarily long) impervious of the results claimed successful the situation file.
- A “formalization.yaml” record describing the results successful informal language, and besides containing a number of different applicable metadata and disclosures.
(There are besides immoderate further method requirements for the repository which I will omit here.) If a snapshot of a repository is submitted to Palomar, it will cheque some (a) that the solution module typechecks and proves precisely the results claimed successful the situation file, and that (b) the informal explanation of the consequence successful the formalization.yaml record appears to lucifer the consequence claimed successful the situation file, and that the repository meets various minimal standards required for a registry entry. The first cheque (a) is purely mechanical, utilizing the Lean instrumentality Comparator; the 2nd cheque (b) is non-deterministic, being performed by a ample connection model. If a repository passes some checks, it tin beryllium registered connected Palomar. It is worthy stressing that the checks successful (a) and (b) autumn good short of what a due quality adjacent reappraisal of a submission for novelty, interest, and accuracy would give; successful particular, Palomar is not a peer-reviewed journal.
The submission process is thorough, but achievable: arsenic a test, I successfully managed to taxable my ain recent formalization of the impervious of Sendov’s conjecture to Palomar, and besides scheme to taxable immoderate older formalizations to the registry soon.
In immoderate event, the registry is now unfastened for formalizations of some aged and caller results. Submissions (whether human-generated, AI-generated, aliases immoderate substance of both) are welcome; please publication the (somewhat detailed) instructions here earlier starting a submission. (I will nevertheless statement that modern AI agents are rather adjuvant successful assisting pinch the mechanical specifications of the submission, though a quality reappraisal is still powerfully recommended.)
Discussion and feedback connected Palomar will hap connected this Zulip channel.
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