Structure Before Time: Perpetuity, Registration, and the Origin of Duality

This paper re-examines the concept of perpetuity by separating it from time-based operation. It argues that the historical rejection of perpetuity in physics arises from a category error: perpetuity is evaluated within time, despite being a structural property that exists only outside time. Perpetuity is defined as structural consistency in the absence of loss, not as indefinite operation or energy extraction. Phase change may occur outside time without entropy so long as no record is retained. Time is shown to arise only when structural stability permits registration, forcing ordering, differentiation, and irreversibility. Duality and entropy are therefore consequences of registration, not fundamental features of structure. Within this framework, entropy and heat are bookkeeping measures of unrecoverable differentiation, not causal drivers of change. Perpetual machines fail not because perpetuity is forbidden, but because they attempt to instantiate perpetuity after time, registration, and entropy have already entered. This work establishes a correct conceptual hierarchy in which structure precedes phase change, registration, time, duality, and entropy. Time is not the stage on which reality unfolds, but the record of where structural consistency can no longer be perfectly maintained.