Topological Connement of Riemann and Dirichlet Zeros via PT -Symmetric Non-Commutative Geometry at EP∞

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We demonstrate the topological connement of non-trivial zeros of he Riemann zeta function and generalized Dirichlet L-functions on the critical line Re(s) = 1/2. By constructing a uctuated Dirac operator DA within a real spectral triplet (A, H, D, J, γ) linked to the Bost-Connes KMS state, we show that the modular ow enforces an exact PT -symmetry. At the asymptotic exceptional point EP∞, the transfer matrix becomes strictly nilpotent for any mode o the critical line. By introducing modulated arithmetic isometries µχ n = χ(n)µn, we extend this barrier to Dirichlet L-functions L(s, χ). The non-commutative Chern invariant ν = 1/2 is invariant under character phase rotations, guaranteeing that the Generalized Riemann Hypothesis (GRH) is protected by the same topological winding mechanism and quantum Fisher-Rao geodesic barrier against stochastic and thermal environmental uctuations.