CE_4 Admissibility Is Not Gradual

This paper establishes that admissibility is strictly binary and fail-closed, and cannot be meaningfully treated as graded, approximate, or probabilistic. Any attempt to introduce degrees of admissibility is shown to rely on illicit parameterization, hidden smoothing, or retrospective justification that undermines standing preservation. The argument proceeds by exhaustion. All apparent notions of partial admissibility—confidence levels, tolerance bands, soft constraints, or asymptotic convergence—are demonstrated to either collapse into full admissibility or to constitute outright inadmissibility once their assumptions are made explicit. There is no intermediate regime that remains coherent under enforced standing. The result clarifies why error, uncertainty, and approximation must be handled within admissible representations rather than by weakening admissibility itself. The paper introduces no new primitives and provides no procedures or metrics. It places on record the necessity of binary admissibility as a structural boundary condition for any coherent system of reasoning.