Comparator and nanoda replay of the openai/math Lean corpus at fd4aeeb, with statement checks for family 003

What this is. A replay and statement check, not a mathematical review. It has not been reviewed by a specialist.

Corpus replay. The 189 Comparator configurations referenced by formalization.yaml in openai/math were replayed with the Lean FRO comparator (d03acab), with the nanoda kernel enabled in addition to Lean's kernel. 187 were replayed at commit fd4aeeb; SiegelZeros and QuasiRiemannHypothesis ran at adc7f12, where their import closures are unchanged. Toolchain: Lean 4.34.1, Mathlib d13f23b, lean4export 076e8e5, landrun 811cfff, nanoda_lib 3a24072, on x86_64 WSL2 in a systemd-run sandbox with IP and Unix-domain sockets blocked by a seccomp filter (see the 2026-10-26 network note, NOTE).. Result: 178 configurations accepted by both kernels; 9 accepted by Lean's kernel while nanoda 3a24072 aborted with a stack overflow; no other failures. A separate, unofficial batch with nanoda f67473b (same 16 MiB stack) accepted all 9. A diagnostic showed that two of the 9 need more than 16 MiB but at most 1 GiB of stack with stock 3a24072.

Statement checks, family 003. The challenge statements QuasiRiemannHypothesis, DirichletSevenEighths and HeckeSevenEighths were compared with Theorem 1.1 of the September 30, 2026 quasi-Riemann manuscript. All three match. The zeta statement also covers s = 1, through Mathlib's nonzero assigned value riemannZeta 1. For the locally defined Hecke L-function, Lean lemmas (importing only the challenge file) prove: the lattice Dirichlet series for Re s > 1; holomorphy on C minus {0, 1}; independence of the auxiliary period; an explicit nontrivial character mod (7); and N(x + yw) = x^2 - xy + y^2. That each nonzero ideal has 6 generators is standard and not formalized. The Dedekind factorization was checked numerically for 5 characters, not proved. All 34 #print axioms outputs are exactly propext, Classical.choice, Quot.sound.

Not checked. Whether the statements of the other configurations match their papers; the papers' mathematics. Agreement of two kernels reduces but does not remove kernel-bug risk: the Lean v4.33.1 release notes (#14807) describe a proof of False that nanoda also accepted.

Relation to other replays. nealmcb/openai-math-lean-tooling ran comparator, as shipped, on all 416 configurations at fd4aeeb and accepted all of them; this covers all 190 configurations here, so the Lean-kernel half of this replay replicates his. His nanoda runs were on exports with a 1 GiB checker stack (his clarification on nanoda_lib #55). davegoldblatt/openai-zeta-proof-check replayed QuasiRiemannHypothesis at adc7f12 with both kernels, with the same result. The contribution here is nanoda run through comparator for the whole scope on a second platform, the stack-size diagnosis, and the statement checks.

Companion record: the Siegel-zero verification packet, concept DOI 10.5281/zenodo.23269527.