Spectral-Geometric Program of the Riemann and Grand Riemann Hypotheses

This monograph integrates two prior book-length drafts into a single spectral- geometric work. The first draft (Spectral-Geometric Reduction of the Riemann and Grand Riemann Hypotheses) supplied the finite arithmetic and operator- theoretic architecture: prime-clock spectral flow, Fargues-Fontaine slope packets, Weil positivity, damped trace extraction, zeta spectral triples, screw functions, and de Branges geometry. The second draft (Spectral-Geometric Closure of the Riemann and Grand Riemann Hypotheses) supplied the non-circular closure apparatus: a Sobolev-Suzuki L^2 proof domain, adelic time-frequency concentration, weighted eigenvector convergence, trace-class resolvent convergence, variational uniqueness, regular normalization, and stable L-packet projection.

The integration is deliberately conservative. Finite self-adjointness, distributional trace extraction, closed-form realization, Fredholm determinant continuity, and the Hurwitz implication are stated as ordinary mathematical theorems. Infinite limiting assertions are separated into named estimates and model-specific verification tasks. This distinction is necessary: a rigorous spectral- geometric proof must not smuggle in the positivity of a de Branges space whose positivity is equivalent to Riemann Hypothesis (RH) itself.