Spectral Admissibility and Logarithmic Rigidity for the Generalized Riemann Hypothesis

We extend the Standing–Sitting Band Framework (SSBF), a deterministic arithmetic–spectral construction based on forward divisibility causality and logarithmic scale decomposition,to Dirichlet L–functions. Within this framework, Dirichlet characters actas unit–modulus phase twists on prime–indexed logarithmic translations and do notalter the underlying arithmetic scale or growth structure.We show that admissibility of twisted prime orientations is forced by the classicalanalytic properties of Dirichlet L–functions, namely the existence of an Euler product,a functional equation, and polynomial growth in vertical strips. A twisted self–adjointSSBF Hamiltonian is constructed, and a no–amplification rigidity principle is shownto persist unchanged under character twisting.As a consequence, any admissible twisted Dirichlet collapse is obstructed from vanishingaway from the critical line ℜ(s) = 12 . Applying this result to Dirichlet L–functions yields a proof of the Generalized Riemann Hypothesis. All arguments arecarried out within standard Zermelo–Fraenkel set theory with the axiom of choice,using only classical arithmetic, harmonic analysis, and operator theory.