B1 Replacement Mathematics Is Impossible Closure by Exhaustion

This paper establishes a foundational impossibility result for replacement mathematics within a closed admissible framework. It proves that once closure is achieved by exhaustion, no alternative mathematical system, reformulation, or foundational replacement can recover admissibility or standing. Any attempt to substitute the closed structure with a different mathematics is shown to rely on illicit scope transport, hidden parameterization, or external authority injection, collapsing admissibility. The analysis is strictly eliminative and non-constructive: it introduces no new primitives, specifies no procedures, and provides no alternative formalisms. The result functions as a boundary theorem, fixing closure by exhaustion as terminal and ruling out mathematical replacement as an admissible move.