Verification package for openai/math family 003, Uniform exclusion of Landau–Siegel zeros: comparator + nanoda replay, Lean formalization of the paper's Lemma 3, rerouted proof, exact small-N checks (preliminary)
Description
PRELIMINARY VERSION. No specialist review of this packet has been received, and nothing in it has been revised in response to expert input.
Independent checks of the paper "Uniform exclusion of Landau–Siegel zeros" (openai/math, family 003, preprint of 1 Oct 2026) and its Lean formalization at openai/math commit adc7f1241b42e322a6451854ab7e4b4c146bf78a. It contains: the official Lean FRO comparator rerun with nanoda as a second kernel, with IP and Unix-domain sockets blocked by a seccomp filter (see the 2026-10-26 network note, NOTE); a Lean formalization of the paper's own proof of Lemma 3; the main theorem rerouted through that Lemma 3 and accepted by the comparator with both kernels; exact small-N checks of Sections 3–5 (these confirm the lemmas at those N only); and a declaration-level overlap between the two Lean routes. It is not a proof of the theorem and does not replace expert reading. Claims are separated into what the paper states, what was computed (each with a results file) and what is inferred.
A separate corpus-wide comparator replay of openai/math is not part of this version.
Notes
Files
jmreilly1113/siegel-zeros-audit-reviewer-packet-v2-preliminary.zip
Additional details
Related works
- Is supplement to
- Software: https://github.com/jmreilly1113/siegel-zeros-audit/tree/reviewer-packet-v2-preliminary (URL)
- References
- https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a (URL)
Software
- Repository URL
- https://github.com/jmreilly1113/siegel-zeros-audit