I'm Jude Gomila and I've been exploring the zeta function in private since 2025. This post is part of a series on discoveries from human/ai collaboration. It concerns the de Bruijn–Newman constant Λ, a single real number with this property: the Riemann hypothesis holds exactly when Λ ≤ 0. Nobody can prove that yet, but its known ceiling can be lowered, and this is my computer-assisted proof taking it from 0.2 to 0.1787854, unconditionally, with no unproved conjecture anywhere in the chain.

The proof walks through every step, with each claim linking back to my audit repository and the independent review record. The method uses the Polymath 15 criterion and interval certificates. Special thanks to Dan Romik and Max Atkin. The result is an exact rational: 129/800 + 87677/5,000,000, obtained by exact arithmetic from 3,149,013 + 883 + 1 machine-checked interval certificates.

Previous bounds include Λ ≤ 0.2 via Platt–Trudgian, 2021, and Λ ≤ 0.22 via Polymath 15 (Tao et al.), 2019. This work rules out values above 0.1787854. The proof combines three finite checks: machine-verified RH below the barrier, 3.1 million windows certified zero-free, and a wall no zero can cross.

The proof was checked four layers deep, and the method cannot reach Λ ≤ 0, as explained in the full post.