Closure_Requires_Exhaustion

This paper proves that genuine closure can only be achieved by exhaustion, not by construction, synthesis, or accumulation of explanatory structures. It shows that any claim of closure that leaves unexamined alternatives, repair paths, or scope-shift strategies is structurally incomplete and non-auditable. By systematically eliminating all admissible alternatives, the paper establishes exhaustion as a necessary condition for maximal, brittle closure across physics, mathematics, and epistemology. No constructive methods, algorithms, or procedural frameworks are provided; the result is a necessity theorem about what closure must be, not how to build it.