The Singleton Meta-Necessity Theorem

This paper establishes the Singleton Meta-Necessity Theorem. It proves that any non-degenerate system admitting unrestricted composition and irreversible evaluation requires exactly one meta-level necessity to avoid collapse, proliferation, or ambiguity. All attempts to posit multiple independent meta-necessities, layered foundations, or substitutable meta-constraints are eliminated by exhaustion for violating admissibility or standing conservation. The result fixes the meta-layer as singleton and non-optional, providing closure without construction or hierarchy stacking. No algorithms, constructions, or procedural frameworks are provided; the argument is necessity-based and eliminative.