BU07 Low-Entropy Drive and Minimal-Action Differential under Dynamic Boundary Fixation

Abstract This paper develops Low-Entropy Drive and Minimal-Action Differential under Dynamic Boundary Fixation as the directional bridge between fixed ontological boundary and admissible aligned update. Its central claim is that once dynamic completeness fixes a unique boundary background, admissible evolution no longer unfolds as unconstrained variation. It unfolds under a globally ordered low-entropy drive and a locally selective minimal-action differential. Let D(M) denote the dynamically complete interface on the mother-structure M, let B_U denote single-universe boundary consistency, let \mathcal{G}_{LE} denote the low-entropy drive, and let \delta A_{\min} denote the minimal admissible differential. The paper formalizes the chain D(M)\Rightarrow B_U \Rightarrow \mathcal{G}_{LE},\qquad (B_U \wedge \mathcal{G}_{LE})\Rightarrow \delta A_{\min}, and shows that aligned standing follows when global directional admissibility and local differential admissibility remain jointly preserved. The framework is intentionally minimal. It does not attempt to provide a full dynamical completion of every application-layer system. Instead, it fixes the structural bridge: global boundary consistency generates a non-arbitrary direction of admissible decrease in boundary tension, while minimal-action differential governs local update selection under that direction. Alignment is therefore recast as trajectory standing under fixed boundary, ordered gradient, and admissible differential. Misalignment is correspondingly reclassified as boundary-inconsistent update, gradient loss, or differential failure. The paper provides a clean, boundary-grounded foundation for later technical developments in information-update cost, experimental morphisms, and application-specific dynamic alignment.