BU14 Dynamic Completeness and the One-Way Entropy Gradient

Abstract This paper develops Dynamic Completeness and the One-Way Entropy Gradient as the bridge that grounds the arrow of time in fixed ontological boundary coherence. Its central claim is that temporal direction is not an added phenomenological feature, nor the residue of a merely special initial condition, but a structural consequence of dynamic completeness under a single-universe boundary regime. Let D(M) denote the dynamically complete interface on the mother-structure M, let B_U denote global boundary consistency over the total domain U, and let the one-way entropy gradient denote the globally admissible directional standing of irreversible settlement. Within this framework, once D(M) fixes the unique boundary background, admissible evolution no longer permits directionally symmetric global standing. The paper formalizes this result by showing that fixed boundary coherence constrains all admissible large-scale evolution to one non-branching gradient of entropy increase. The arrow of time is therefore reclassified from a puzzling empirical asymmetry into a lawful consequence of boundary fixation. This move simultaneously downgrades several traditional sources of confusion: the appeal to special initial conditions loses explanatory primacy, the tension between microscopic reversibility and macroscopic irreversibility is re-sorted as a resolution-dependent misreading, and multihistory or branch-based temporal pictures lose standing because they presuppose boundary drift. The result is a compact structural account in which irreversible temporal direction is not appended to the universe after the fact, but generated as a necessary consequence of one fixed admissibility background.