L3_5 No Minimal Subset Theorems

This paper proves that no proper minimal subset of constraints suffices to generate or preserve the admissible interior of a closed epistemic system. It shows that admissibility is irreducibly global: any attempt to identify a smaller generating set, core axioms, or privileged constraints either collapses into the full constraint set under admissible closure or violates standing by smuggling in hidden dependencies. The argument is strictly eliminative and non-constructive, introduces no new primitives, and provides no procedural or operational content. The result functions as a boundary theorem, ruling out foundational reduction, axiomatic minimalism, or modular generation of admissibility once closure by exhaustion is achieved.