Structural Energy: Energy as a Necessary Consequence of Admissible Persistence Architecture

This structure is not introduced here. It is already implicit in the Foundation Series and is isolated in the present paper. Papers D001–D004 derived structural time, information, causality, and decision as necessary consequences of LP admissibility restriction. This paper derives structural energy as the fifth necessary consequence: the required expenditure for maintaining admissible persistence trajectories under transformation load. The central claim: energy is not a primitive physical substance or a separately postulated resource. At the structural level, energy is the integration cost — the required expenditure of integration capacity IK = F·M·K for executing admissible transformations while maintaining IR ≤ 1. Any LP-admissible system that persists under real transformation necessarily expends structural energy. Persistence is never free. Three theorems are proven. Theorem D5.1 — Non-Zero Integration Cost: every admissible transformation under real transformation load requires a non-zero expenditure of integration capacity. Theorem D5.2 — Persistence Cost Scaling: the required integration expenditure scales monotonically with transformation load R and with proximity to the persistence boundary. Theorem D5.3 — Depletion and Recovery Asymmetry: integration capacity depletes faster under transformation load than it recovers — the depletion-recovery asymmetry is a structural necessity, not a contingent property. Corollary D5.4 (Class C) identifies thermodynamic free energy, biological metabolic expenditure, organizational resource consumption, and psychological effort as domain instantiations of structural energy. Persistence is not a passive state. It is a structural expenditure — continuously required, never free, and asymmetrically costly to recover.