Spectral Entropy Collapse and the Riemann Hypothesis
Résumé
We present a trace-theoretic reformulation of the Riemann Hypothesis (RH) as a condition of spectral entropy collapse. Specifically, we define an analytic functional Θ int (t; σ), constructed from weighted cosine interference over logarithmic prime modes, and show that its asymptotic vanishing uniquely characterizes the critical line. This functional arises as the heat trace of a compact, self-adjoint, trace-class operator A † σ A σ on a weighted L 2 space, with lim t→0 + Θ int (t; σ) = 0 if and only if σ = 1 2 . The reformulation requires no assumptions about zero locations, analytic continuation, or RH-equivalent criteria, and is grounded entirely in real-variable analysis, classical exponential sum estimates, and operator theory. The framework interprets the critical line as the unique thermodynamic fixed point of entropy suppression, revealing a spectral coherence principle in arithmetic phase space and suggesting structural links to noncommutative geometry.