Deterministic Arithmetic–Spectral Correspondence and the Critical-Line Constraint

We establish a deterministic correspondence between prime-generated arithmeticdata and the spectrum of a canonical self-adjoint Hamiltonian constructed via logarithmictranslation operators. The correspondence is shown to be faithful, rigidityenforcing,and independent of analytic continuation or probabilistic models.As a consequence, any Dirichlet generating function compatible with this correspondenceis forced to satisfy a critical-line constraint. When the Riemann zeta function isintroduced as such a compatible object, the Riemann Hypothesis follows as a structuralcorollary.