Failure of Local Closure in Self-Optimizing Systems: A Minimal Structural Bound

This paper operates within the transcendental tradition in philosophy of science, analyzing not what empirically occurs in self-optimizing systems, but what must be presupposed for the question of structural recovery to be intelligible. It formalizes a conditional impossibility: under fixed-structure constraints, internal recovery of lost structural coherence is not merely difficult, but conceptually incoherent This preprint introduces a conceptual framework for understanding structural limits in self-optimizing systems. The central result (Theorem 1) is intentionally tautological: it formalizes the conditions under which structural recovery becomes impossible under fixed-structure constraints. The paper argues that optimization presupposes structural sufficiency (N₁) that cannot be generated by optimization alone (N₀). This is developed through: A formal statement of conditional irrecoverability- Application to neural network pruning- Analogical extensions to biological, cognitive, and social systems- Discussion of implications for philosophy of science and AI The result is not an empirical discovery but a conceptual boundary marker: it clarifies when claims of "self-recovery" implicitly assume external structural support.