Structural Sufficiency, Sacrificial Pruning, and Minimal Throughput

This paper formalizes the principle of "Sacrificial Pruning" as a fundamental mechanism for systemic coherence, arguing that functional integrity depends on protecting a minimal structural core rather than maintaining material mass. By unifying the Theory of Axiomatic Necessity (TNA) with nonequilibrium thermodynamics and information theory, we demonstrate that systems achieve stability through the active rejection of redundant substructures. We introduce Negentropic Throughput ($\Psi$) as an operational metric to quantify the efficiency of this minimal core, showing how both extreme biological cases (hydrocephalus) and artificial architectures converge toward a threshold of Minimal Structural Sufficiency (F_{min}). Unlike standard optimization, sacrificial pruning is presented as a survival imperative: reduction succeeds only when it reveals the "trunk" of the system while discarding the "leaves" of optional complexity. This framework provides a non-materialist account of cognition and inference, where throughput—not volume—is the primary predictor of sustained functional presence. Unlike consumerist or materialist interpretations that mistake convenience for quality, this framework distinguishes between perceived coherence and structural necessity, proving that cutting into the 'trunk'—whether in audio hardware, neural architectures, or biological brains—inevitably leads to systemic collapse, regardless of user consensus. Diagram https://drive.google.com/file/d/1K3Mg9sQEIL5bi0f0-PrA9NMEV8wTa3pH/view?usp=sharing