Non Factorizability of Admissibility

This paper establishes a structural constraint on admissibility: admissibility cannot be factorized into independent, locally satisfiable conditions. It proves that reference fixation, scope integrity, and standing preservation form a coupled whole, such that failure in any component renders the entire structure inadmissible. The result is eliminative. The paper does not propose admissibility checklists, modular criteria, or partial compliance schemes. Instead, it shows that treating admissibility as a set of separable requirements permits illicit compensation—allowing success in one dimension to mask failure in another. Such compensation preserves apparent coherence while destroying standing. The analysis blocks a class of approaches in which admissibility is treated as something that can be satisfied “enough,” distributed across subsystems, or repaired by strengthening unaffected components. It demonstrates that these approaches rely on an illicit decomposition of admissibility that admissibility itself forbids. This work is purely boundary-setting. It introduces no operational tests, no enforcement mechanisms, and no governance workflows. Its contribution is to clarify why admissibility is all-or-nothing and globally coupled, and why no part of a structure can remain legitimate once admissibility has failed anywhere within it.