A boundary product–certificate proof of the Riemann Hypothesis
Independent Researcher
Summary
Single‑route boundary proof: a product certificate yields a quantitative boundary wedge (P+), Poisson transport gives a Herglotz interior, Cayley maps to a Schur bound, and a pinch eliminates off‑critical zeros—no adjustable parameters.
Abstract
We prove the Riemann Hypothesis via a single boundary route. A quantitative product certificate on \(\{\Re s>\tfrac12\}\) yields an almost‑everywhere boundary wedge (P+); Poisson transport and a Cayley transform provide Schur/Herglotz control on zero‑free rectangles; a pinch across putative off‑critical zeros then globalizes the bound and eliminates such zeros. The right‑hand side uses only a local Cauchy–Riemann/Green pairing on Whitney boxes with a Carleson \(L^2\) bound for the Poisson extension. All load‑bearing steps are unconditional; diagnostic numerics are gated and do not enter the inequalities that close (P+) and the globalization.