Admissibility Certificates: Axiomatic Framework

This document provides an axiomatic classification of the minimal structural conditions under which admissibility-based reductions for arithmetic residuals become unavoidable. It introduces the notion of an admissibility certificate, defined by a finite set of explicit axioms governing monotonicity, non-cancellation, local rigidity, mean dominance, and forward invariance of an admissibility functional. No new arithmetic estimates, zero-location arguments, or analytic bounds are introduced. Instead, the purpose of the document is to fix the logical boundary of disagreement after admissibility-based frameworks and their consequences have been developed across several independent but related works. The axiom set is shown to be minimal: removing or weakening any axiom re-admits a known class of classical escape mechanisms. The framework is coercive rather than reformulative and serves as a structural closure of the admissibility-based program. This note is intended as a classification and boundary specification, not as a proof of admissibility itself. 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