This paper analyzes partial admissibility regimes within the admissibility framework formulated in Spectral Admissibility and the Riemann Hypothesis: A Conditional Equivalence. It establishes unconditional admissibility results in restricted settings, including finite frequency bands and averaged window-energy bounds. A Lyapunov-type slope functional is introduced, yielding a coercive inequality that reduces full admissibility to uniform control of a single local quantity. The analysis isolates the precise remaining arithmetic obstruction to admissibility within the framework of Paper 0. 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

Version 1This paper is a diagnostic companion to Spectral Admissibility and the Riemann Hypothesis: A Conditional Equivalence (https://doi.org/10.5281/zenodo.18277781), identifying all unconditional reductions and isolating the exact obstruction left open by the admissibility formulation.