A Fourier–Lévy Normal Form for Localized Weil Positivity: Finite-Rank Boundary Terms, Scalar Resolvents, and a Certified Finite Block and Continuum Fourier Tail
A Fourier–Lévy Normal Form for Localized Weil Positivity: Finite-Rank Boundary Terms, Scalar Resolvents, and a Certified Finite Block and Continuum Fourier Tail
This manuscript develops a Fourier–Lévy operator framework for localized Weil positivity. It derives the normal form A_X = L_X - c_X I + M_X^* J M_X, isolates the finite-rank boundary contribution, and reduces the parity sectors to scalar Herglotz-type resolvents. For the certified parameter choice X = 4 and N = 32, the relevant finite Fourier blocks are verified using interval arithmetic, while the high-frequency continuum Fourier tail is shown to be strictly positive for all Fourier modes |n| > 160. The remaining finite low-frequency Feshbach core is unresolved. Accordingly, this manuscript does not claim a proof of the Riemann Hypothesis. It provides a structural reduction and computer-assisted positivity certificates for the components stated above.
Operator theory, Feshbach reduction, Explicit formula, Computer-assisted verification, Spectral analysis, Finite-rank perturbations, Riemann Hypothesis, Fourier analysis, Weil criterion, Positive operators, Herglotz functions, Weil positivity, Lévy–Khintchine representation, Interval arithmetic, Analytic number theory
Operator theory, Feshbach reduction, Explicit formula, Computer-assisted verification, Spectral analysis, Finite-rank perturbations, Riemann Hypothesis, Fourier analysis, Weil criterion, Positive operators, Herglotz functions, Weil positivity, Lévy–Khintchine representation, Interval arithmetic, Analytic number theory
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