The Geometric Operator (L): The Spectral Basis of Prime Distribution and Informational Physics

Abstract This document formally introduces the Geometric Operator L, a self-adjoint Hamiltonian acting on the Hilbert space of the number line. We propose that the distribution of prime numbers is not pseudo-random, but is the deterministic result of Constructive Interference patterns generated by the vibrations of L. By defining the spectrum of L as equivalent to the squared imaginary parts of the non-trivial Riemann zeros (n^2), we provide a physical and geometric basis for the Riemann Hypothesis. Furthermore, this operator serves as the "Function F" within Informational Physics, linking the abstract laws of the 7D Bulk to the manifest constants of the 3D Universe via the unified equation R = E + I.