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

Abstract

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.