Spectral Realization of the Riemann Zeta Function on the Bounded Logarithmic Manifold [1, 2]

This paper presents a formal physical solution to the Riemann Hypothesis by demonstrating that the non-trivial zeros of the Zeta function correspond to the eigenvalues of a self-adjoint Hamiltonian operator. The central innovation lies in defining the system on a Fundamental Compact Domain Ω = [1, 2], which acts as a generating cell for the set of natural numbers. By introducing a unique singular measure and a holographic projection mechanism, we demonstrate that the energy spectrum is purely real and symmetric, implying that the zeros are positioned strictly on the critical line Re(s) = 1/2.