A SPECTRAL-ARITHMETIC FRAMEWORK FOR THE RIEMANN HYPOTHESIS

Description: This paper develops a self‑contained spectral-arithmetic framework in which the Riemann Hypothesis follows from four explicitly verified axioms (H1)-(H4). The axioms encode a φ‑ladder block decomposition with unitary renormalization shift, a block‑diagonal center with φ⁻¹ contraction and exponentially decaying off‑diagonal couplings, the existence of an even log‑additive observable with square‑integrable kernel, and multiplicative Dirichlet coefficients satisfying Ramanujan‑type bounds. From these, the argument constructs both spectral and arithmetic completions, calibrates local factors, and identifies them via a trace-kernel correspondence. Applying the degree‑1 Hamburger-Hecke converse theorem yields exact agreement with the completed Riemann zeta function, placing all nontrivial zeros on the critical line. The proof is unconditional, purely functional‑analytic and number‑theoretic, and independent of any physical model; a concrete dynamical example satisfying the axioms is given in an appendix.