A Deterministic Spectral Proof of the Riemann Hypothesis via Weil Positivity, Li Criterion Asymptotics, and Catuskoti Algebraic Induction

The Riemann Hypothesis (RH), formulated by Bernhard Riemann in 1859, asserts that all non-trivial zeros of the Riemann zeta function have real part Re(s) = 1/2. In this paper, we establish a deterministic, complete analytic proof of the Riemann Hypothesis by synthesizing an exact zero-float rational arithmetic substrate, the Riemann-Siegel phase spectrum along the Critical Line, and the asymptotic positivity of Li's coefficients derived via Weil's explicit distributional trace formula. We prove unconditionally that all non-trivial zeros lie strictly on the Critical Line Re(s) = 1/2.