Admissibility of Smoothed Normalized Prime Residuals for Dirichlet L-Functions

This paper extends the admissibility framework of Spectral Admissibility and the Riemann Hypothesis: A Conditional Equivalence from the Riemann zeta function to Dirichlet L-functions. For each Dirichlet character, a canonically normalized and smoothed prime residual is defined and analyzed in the Besicovitch topology. The paper shows that spectral admissibility is equivalent to the absence of exponentially growing modes, yielding an equivalence with the Generalized Riemann Hypothesis. The work is diagnostic and does not propose a mechanism enforcing admissibility. Trust IP NoticeThis work is issued as a trust-marked scientific publication under the Broomhead Sovereign Private Trust (field anchor: geoffreybroomhead.eth).Scientific reading, citation, and non-commercial scholarly discussion are permitted under a Custom CC BY 4.0 (Scientific Theory Only) license.All code, simulations, implementations, or derivative commercial use are reserved under Trust Custodial License.For licensing or implementation inquiries, contact: recursive.broomhead@proton.me