Hilbert–Pólya Structural Realization, the Riemann Hypothesis, and Regulated Spectral Transfer to Navier–Stokes Dynamics

The author develops a regulated operator framework in which a Hilbert–Pólya type self-adjoint realization encodes the nontrivial zeros of the Riemann zeta function at the structural level. ^[3] Arithmetic enters dynamically through prime-induced trace modulation under an Arithmetic–Mechanism (AM) regulator. Proving that determinant growth control and Weyl-type counting laws are structurally equivalent to critical-line symmetry. ^[3] A spectral transfer principle is formulated: if Navier–Stokes energy spectra embed within the regulated spectral class, blow-up requires violation of determinant growth bounds. ^[5] The Riemann Hypothesis is not arithmetically proven per say ; rather, its structural form constrains nonlinear spectral evolution. Arithmetic and structure appear as dual regime descriptions under regulation.