BU06 Real-Time Boundary Matching and Feedback Dynamics under Dynamic Completeness

Abstract This paper develops Boundary Matching and Feedback Dynamics under Dynamic Completeness as the technical bridge between dynamic boundary fixation and sustained alignment standing. Its central claim is that alignment under a single-universe boundary framework is not preserved by static correctness, but by real-time boundary matching. Let D(M) denote the 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-matching operator. Any generated state \Phi^{\mathrm{gen}} is first exposed as a locally produced update, then immediately evaluated through its boundary mismatch term E_B, and finally matched back to the B_0-consistent image. Boundary drift is therefore treated not as an accumulating ontological freedom, but as a transient mismatch that loses standing at the interface. On this basis, the paper formalizes a minimal dynamic chain: generation, mismatch identification, feedback activation, boundary projection, and restored admissibility. It shows that feedback is not an optional correction appended after error, but the intrinsic mechanism by which dynamically complete systems prevent mismatch from rooting itself in the admissible state space. Alignment is thus redefined as the persistence of boundary-consistent standing under real-time update. The result is a clean reclassification of misalignment: not as an unrestricted existential drift, but as a failure of matching and feedback execution within a fixed ontological boundary regime.