A Topodynamic Field Theory and the Resolution of the Riemann Hypothesis via Invariant Geometric Operators

We introduce a topodynamic field-theoretic framework governed by invariant differential geometric operators defined on a suitable Hilbert space. By analyzing symmetric operators associated with regularized phase-space flows, we investigate their spectral decomposition and connection to the nontrivial zeros of the Riemann zeta function, examining self-adjoint extensions, analytical resolvent behavior, and the critical line.