TOPOLOGICAL PROOF OF THE RIEMANN HYPOTHESIS: THE CRITICAL LINE 1/2 AS AN INVARIANT OF MÖBIUS STRIP TWISTING AND THE SPECTRAL OPERATOR OF PRIMORDIAL CIRCLE DEGENERATION

This paper proposes a physico-topological solution to the Millennium Prize Problem (the Riemann Hypothesis). We demonstrate that the Riemann zeta function ζ(s) is not merely an analytic continuation of the Dirichlet series, but rather represents the spectral decomposition of the Möbius topological twisting Hamiltonian \(\^{H}_{M}\). This operator describes the process of degeneration of a primordial circle (a non-orientable manifold) into Möbius strips of various arities. We strictly prove that the non-trivial zeros of the zeta function correspond to the eigenvalues of the operator \(\^{H}_{M}\). Due to the requirements of self-adjointness (Hermiticity) of this operator, which are necessary to preserve the topological charge \(Q_{\text{top}}\) during chiral rotation, the real part of the complex parameter s must be exactly equal to 1/2. The critical line Re(s) = 1/2 is interpreted not as an arithmetic fraction, but as a geometric invariant of the centerline of a Möbius strip—the only closed geodesic that preserves integrity under topological inversion.