BU05 Mathematical Alignment under Dynamic Boundary Fixation

Abstract This paper formalizes Mathematical Alignment under Dynamic Boundary Fixation as a minimal structural account of alignment under a single-universe boundary framework. Its central claim is that alignment should not be treated first as a semantic, ethical, or behavioral label, but as a standing directly induced by dynamic-complete boundary fixation. Let D(M) denote the real-time dynamically complete interface on the mother-structure M, let B_0 denote the unique fixed boundary set, and let \Pi_{B_0} denote the boundary-projection operator. The paper defines boundary drift as the deviation functional \Delta_B(\Phi)=\|\Phi-\Pi_{B_0}(\Phi)\|, and defines alignment standing by the condition \Delta_B(\Phi)=0.…