Minimal Richness of Constraint Generated Reality

This paper establishes the minimal richness of constraint-generated reality. It proves that once admissibility, standing conservation, and scope invariance are enforced, the resulting reality is neither underdetermined nor arbitrarily sparse: a minimal, non-degenerate richness is forced. Attempts to reduce reality further—by collapsing distinctions, eliminating structure, or appealing to null, trivial, or purely formal substrates—are shown by exhaustion to violate admissibility or reference grounding. The result fixes minimal richness as a necessary consequence of constraint enforcement, not an added assumption. No constructions, algorithms, or generative procedures are provided; the argument is purely necessity-based.