Verification package for openai/math family 003, Uniform exclusion of Landau–Siegel zeros: machine-checked complement to existing human write-ups (comparator + nanoda, Lean Lemma 3, explicit constant)

A machine-checked complement to the existing human write-ups of the OpenAI argument for the uniform exclusion of Landau–Siegel zeros (OpenAI, manuscript dated October 1, 2026; openai/math family 003). Human write-ups: W. D. Banks, arXiv:2610.15483; B. Kerr, arXiv:2610.21099; B. Green, Hexagon 2610.00311v2 (2026-10-17). Not refereed; not a proof of the theorem.

 Contents: (1) the official Lean FRO comparator with nanoda as a second kernel accepts the family's Lean statements with standard axioms only (IP and Unix-domain sockets blocked by a seccomp filter; see the 2026-10-26 network note, NOTE); (2) a Lean proof of the paper's Lemma 3, whose hypotheses equal Banks's Proposition 3.4, condition (3.1), and which certifies a step of OpenAI's and Banks's route; (3) the challenge theorem rerouted through that Lemma 3 and accepted by the comparator with both kernels; (4) an Arb-certified explicit constant, conditional on the paper's proof: (1 − β) log q > 4.467×10⁻³ with Lu–Zaman–Zhao (q ≤ 10¹⁰), or > 3.399×10⁻³ with Platt (q ≤ 4×10⁵) only, compared term by term with Banks's 3.0696×10⁻³; (5) exact small-N checks. Release notes: docs/packet-v3/release-notes-v3.md, including corrections to the v1 methods text.