From Fascia to Fields: A Recursive Operator Model Bridging Soma–Noēsis Mechanics and the Riemann Hypothesis

We present a novel operator-theoretic formulation of the Riemann Hypothesis within the framework of Soma–Noēsis Mechanics — a symbolic–somatic model of coherence dynamics grounded in Hilbert space geometry. At its core is the Noēsis operator HNHN, defined as a self-adjoint operator on L2 (R) L2 (R) with a compact, Hilbert–Schmidt memory kernel. Using the analytic Fredholm theorem and Birman–Krein trace formula, we demonstrate that e−itHNe−itHNevolves unitarily and remains trace-class under Hilbert–Schmidt perturbations, yielding a discrete spectrum confined to the critical line ℜ (s) =12ℜ (s) =21. This spectrum aligns numerically with the nontrivial zeros of the Riemann zeta function, embedding arithmetic structure into spectral evolution. The operator is further embedded into the 248-dimensional root lattice of the exceptional Lie group E8E8, enabling curvature-based diagnostics for coherence anomalies via geodesic deviation. This formulation interprets the Riemann zeta function as a spectral trace over symbolic–somatic coherence and suggests a physically grounded interpretation of prime structure as recursive alignment in signal dynamics. Simulation results support spectral convergence and reveal geodesic deformation under perturbations. This paper provides a self-contained, first-principles theoretical model bridging analytic number theory, operator algebra, and geometric cognition, offering a new lens through which the Riemann Hypothesis can be examined.