On the Limits of Admissibility-Based Stabilization Failure Modes, Non-Admissible Systems, and Falsifiability

This paper analyzes the limits of admissibility-based stabilization, a mechanism by which bounded or contractive behavior can arise through restriction of allowable trajectories rather than modification of underlying dynamics. Building on prior work establishing existence results, constructive realizations, and non-equivalence with regularization, the present study adopts a failure-first perspective. We identify structural conditions under which admissibility-based stabilization is impossible or necessarily degenerate, and classify common failure modes arising from absence of invariant admissible sets, intrinsic expansion, parameter-dependent constraints, and insufficient internal structure. Necessary conditions are restated as gates that must be satisfied for admissibility-based stabilization to be applicable at all. Explicit diagnostic criteria are provided to distinguish genuine falsification from misapplication, and conditions for structural disconfirmation are articulated. The results emphasize that admissibility is a selective structural mechanism, not a universal stabilizer. Making these limits explicit sharpens falsifiability, prevents invalid testing regimes, and clarifies the domain in which admissibility-based approaches can meaningfully operate. This paper is part of a series developing admissibility as a constraint-based stability framework independent of physical ontology or microscopic completion.