The Extension-Admissibility Invariant

Abstract In systems governed by global constraints, admissibility at small scale does not guarantee admissibility under extension. Extension-admissibility is identified as a necessary invariant distinguishing systems that can grow or scale without inducing structural phase transitions from those that require regime change, redefinition, or hidden correction as scale increases. The invariant filters systems whose apparent stability is scale-limited. Invariant Statement A system is extension-admissible if and only if extension in scale, coupling, or duration does not induce a structural phase transition that violates admissibility or requires correction not accounted for within the declared system boundary. Scope This note introduces no scaling method or optimization strategy. It states a necessary invariant for admissibility under extension. Any theory claiming scalable stability must account for extension-admissibility.