A certified unconditional upper bound Λ ≤ 0.1875 for the de Bruijn–Newman constant

Let Λ denote the de Bruijn–Newman constant. The recorded state of the art is Λ ≤ 0.2: when Platt–Trudgian verified the Riemann hypothesis to the exact height T = 3,000,175,332,800 (≈ 3.0002×10^12), it was noted at once that this improves the Polymath15 bound Λ ≤ 0.22 to Λ ≤ 0.2. A sharper, essentially 0.197-class computation at the same barrier site was publicly reported in a May 2020 comment on T. Tao's blog by Rudolph [Dwars] — uncertified, unrefereed, and never independently verified. This paper supplies the certified, theorem-grade version of that bound and goes beyond it. Subject to the published Polymath15 criterion and the published Platt–Trudgian verification, the attached certificates prove, unconditionally, Λ ≤ 3/16 = 0.1875 exactly, the deepest rung of a certified assembly ladder 0.1965 → 0.1891 → 0.1875 at the same barrier site, every rung a certified improvement below the recorded Λ ≤ 0.2 and below the uncertified 0.1972624050 sighting of 2020, with every numerical ingredient backed by interval-arithmetic certificates (explicit ball enclosures, exact-rational endpoint comparisons, exit-0 standalone verifiers) and every theorem-grade claim verified on two mechanically independent code lines sharing zero code. The route to the 0.1965 rung runs through a certified Euler-3 mollifier bound, certifiably beyond the reach of the Euler-2-class mollifier underlying the 2020 computation; its assembly binds a certified Euler-3 selection chain, gap-free finite sweeps, a box-uniform tail bound, a three-stage normalization-conversion lemma chain, the y-quantifier transfer, and the site bookkeeping lemmas, with an independent second-line sign-off on the assembled statement. The two deeper rungs are closed by a certified window-tiling assembly route: the integer window range is partitioned at certified split points, each piece closed by an independently certified finite-window or tail certificate, and every joint gated in exact rational or outward-rounded interval arithmetic by a standalone assembly verifier (58 checks per assembly; independent dual second-line sign-off with 76 gates, zero shared code, which re-proves the live tail leg on its own engine). The same certificate chain certifies the intermediate record Λ ≤ 0.197 and the 2020 comment's exact row, Λ ≤ 0.197262405. To our knowledge no prior sighting, certified or otherwise, exists below 0.1965. Beyond the bound itself we contribute: certified mollifier results, including the first quantitative saturation map of the finite-Euler-product mollifier family at this site; the verification methodology, which addresses the cheap-re-verifiability question raised in the 2020 thread and catches a class of silent rendering defects — three of which we document, with resolutions, in the committed Polymath15 artifacts; and a certified negative/feasibility map for the next rung. This version supersedes the Λ ≤ 0.1965 release (10.5281/zenodo.20724170), which remains citable; the full 0.1965 and 0.197 chains ship unchanged in this bundle. This is a fully AI-derived body of results, as disclosed in the paper. Contact/updates: Mosaic Intelligence (@111111, https://x.com/111111)