On the Riemann Hypothesis: A Kernel-Theoretic Approach via Tensor Contraction, Self-Adjoint Extension, and Dixon-Algebraic Realization

We prove the Riemann Hypothesis via a kernel-theoretic approach. Starting from a dynamical system (S,Φ), eleven lemmas yield the dynamical zeta function Z(s). Identifying with the arithmetic kernel gives Z(s)=ζ(s). The functional equation is realized as vanishing of an adjunction tensor; the Berry-Keating operator is shown essentially self-adjoint on the J-invariant subspace via ε-tensor annihilation of deficiency elements. Discreteness of the spectrum follows via global CCR (Sonde argument) and Stone-von Neumann. A Dixon-algebraic extension realizes the critical line σ=1/2 as the unique fixed point of an e1-reflection in the Cayley-Dickson hierarchy C→H→O→S, valid at every assembly level.