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 (∞ ~ 0 on RP¹) that mandates minimal geometric entropy. We demonstrate that any off-line zero (Re(ρ) ≠ 1/2) induces uncompensated geometric torsion (Im(D) ≠ 0), violating self-adjoint spectral rigidity (H = H^) and forcing a structural collapse onto the critical line.