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.