Half–Spacing Windows and the Riemann Hypothesis a Single–Stream Analytic Proof with a Finite Computational Seed

We develop a quantitative Fejér–transport framework that certifies zero–freeness for the Riemann zeta function in thin rectangles to the right of the critical line. The method combines: (i) a localized cubic mean bound at the quadratic scale with effective constants; (ii) a quantitative de–mollifier bridge that transfers this to an unmollified cubic bound on Fejér windows; and (iii) a bandlimited Jensen/Poisson transport with positive per–zero harmonic measures. Together these ingredients yield an explicit Fejér–Transport Mechanism (FTM) budget that becomes positive beyond a computable crossing height under the locked baseline (α, κ, c) = (1.0, 0.08, 0.01). With a finite low–height seed, the band pipeline excludes off–line zeros in all such thin rectangles, while a half–spacing transfer inequality supplies local, auditable certificate for critical–line windows. A curvature remainder gives strict barrier against any uniform “one per window for all large T” rule, so certification is necessarily pointwise/bandwise in T.