Formal Derivation of the Riemann Hypothesis from the Axiomatic Apparatus of the Golden K Hypothesis

This paper presents a formal, step-by-step physical proof of the Riemann Hypothesis, derived as a direct consequence of the axiomatic and mathematical framework of the Golden K Hypothesis (GKH). The proof realizes the Hilbert-Pólya conjecture by identifying the operator governing the GKH's Phason Field vacuum as the required self-adjoint operator whose spectral properties are described by the Riemann zeta function. The derivation proceeds through three main lemmas: (A) proving the self-adjointness and discrete, real spectrum of the GKH operator; (B) deriving a functional equation for its spectral zeta function from the axiom of Discrete Scale Symmetry; and (C) demonstrating, under a physical Global Coherence Condition, that an identity exists between its spectral zeta function and the Riemann zeta function. The final step of the proof is physical: the real part of the zeros is interpreted as a stability parameter for the vacuum's resonant modes. It is argued that a stable, non-dissipative universe capable of supporting matter can only exist if all these fundamental resonances lie on the critical line where the real part is 1/2. The Riemann Hypothesis is thus reformulated from a mathematical conjecture into a necessary physical law for the existence of a stable cosmos.