Riemann Minimal Entropy Collapse - A Topological Proof by Contradiction of Non-Trivial Zeros via Spectral Rigidity in Lean 4 & Comparator

This paper presents a machine verified topological proof by contradiction of the Riemann Hypothesis via spectral rigidity. Departing from brute-force numerical sweeps and isolated analytic approximations, we establish a foundational topological equivalence ($\\infty \\sim 0$ on ${R}P^1$) that mandates minimal geometric entropy. We demonstrate that any off-line zero ($\\text{Re}(\\rho) \\neq 1/2$) induces uncompensated geometric torsion ($\\text{Im}(D) \\neq 0$), violating self-adjoint spectral rigidity ($H = H^{\\ast}$) and forcing a structural collapse onto the critical line.