BU20 Path Admissibility, Boundary Rejection, and Structural Pruning under Dynamic Boundary Fixation

Abstract This paper develops Path Admissibility, Boundary Rejection, and Structural Pruning under Dynamic Boundary Fixation as a dynamic governance platform for coherent paths under a fixed boundary regime. Its central claim is that admissible evolution is not determined by path writability alone. Under dynamic boundary fixation, a path must pass through layered structural selection: boundary admissibility, rejection of irreducible drift, and pruning of high-cost trajectories. Let B_0 denote the unique fixed boundary set. A path \gamma is admissible only if it remains within the B_0-consistent path space and does not exceed the tolerated boundary deviation at the generation instant. Paths that fail this condition are not merely disfavored; they are structurally rejected and lose ontological standing. The paper then strengthens this minimal criterion by introducing structural pruning as a dynamic operator coupled directly to the information-update cost functional. This move upgrades path selection from a static accept/reject judgment into a governed transition architecture in which only boundary-consistent and cost-acceptable trajectories contribute to lawful advancement. The framework is explicitly two-layered: an invariant kernel fixes the non-negotiable logic of admissibility, rejection, and pruning, while a refresh layer allows thresholds, tolerances, and pruning intensity to be synchronously updated as admissible resolution increases. The result is a harder account of path governance in which not every formally writable trajectory qualifies for reality-network participation. Dynamic boundary fixation therefore yields not a passive path catalog, but an active constitutional regime for admissible evolution.