Minimal Structural Sufficiency and the Pruning Paradox in Neural Networks

This paper establishes the Structural Existence Boundary (F_{min}) as the fundamental limit for intelligence, contrasting the "Winning Ticket" in Machine Learning with extreme biological adaptation. By analyzing cases of extreme hydrocephalus—where consciousness persists despite a 90% reduction in brain volume—we demonstrate that system coherence is governed by a "Plateau + Cliff" topology rather than linear parameter scaling. While traditional AI relies on post hoc pruning to find efficient subgraphs, biological evidence reveals a "Single Ticket" configuration where the system operates continuously at the threshold of structural necessity. We show that systems remain functionally invariant on a stability plateau as long as the axiomatic core is preserved, but suffer an irreversible spectral breakdown once the F_{min} boundary is breached. At this critical cliff, re-training becomes impossible as the underlying structural support for information throughput (Psi) collapses. These findings suggest that true efficiency in both neural and biological networks is achieved not by removing excess, but by a system’s intrinsic ability to maintain coherence within a minimal, non-reducible structural configuration.