Superseded result · C-0108
Certified de Bruijn-Newman upper bound Lambda <= 0.175
In the standard Polymath15 normalization of the de Bruijn-Newman heat family, Lambda <= 7/40 = 0.175. The release package verifies every numerical, tail, canopy, barrier, manifest, runtime, and parser gate and includes a complete abstract pattern-space regression covering all 142 reachable zero- through three-prime state sequences, including all 104 three-prime patterns.
A certified de Bruijn–Newman upper bound of 0.1729
In the standard Polymath15 normalization, the de Bruijn–Newman constant satisfies $\Lambda\le 1729/10000=0.1729$. The certificate combines the published verified zeta-zero height, a cutoff-uniform sparse four-prime finite canopy, complementary analytic tails, and an 844-rectangle argument-principle barrier. It improves the established bound $\Lambda\le 11/50=0.22$ by exactly $471/10000=0.0471$ and replaces the earlier under-audit $0.175$ target.