Additive–Multiplicative Windows with a Gauss–Cauchy (Voigt) Kernel: Density One and an Effective Reduction of the Riemann Hypothesis to Finite Verification

We present an explicit and self-contained framework that combines additive/multiplicativewindows and a Gauss–Cauchy (Voigt) kernel to build a functional ∆ whose negativity certifieswindows free of off-line zeros. We prove unconditionally: (i) density one of negative windowsand (ii) a quantitative mixing implying local coverage. We deduce a Reduction Theorem to finiteverification: with effective constants and an implementation in interval arithmetic, it sufficesto certify all windows in [80, T1) to exclude zeros with ℜs > 12 at all heights. We do not claima complete proof of RH : we offer an explicit reduction + a verifiable protocol, and a constantssheet for public instantiation.