Admissible Trajectories and Constraint Filtering: A Structural Account of Path Selection Under Admissibility

This paper defines admissible trajectories as paths through state space that satisfy constraint conditions at every step of continuation. While systems may generate multiple possible trajectories, only those that remain admissible persist. Constraint filtering is introduced as the mechanism by which non-admissible paths terminate. This provides a minimal structural account of observed path selection, showing that persistence is not a result of active choice but of constraint-compatible continuation. Positioned within the Paton System, this work links Tier 3 admissibility, Tier 5 continuation, and Tier 6 structural path space into a unified account of trajectory persistence and selection.