Irreversible Constraint Pruning as a Physical Condition for Persistent Structure

Persistent structures such as vortices, solitons, and topological defects are typically explainedthrough properties of the governing dynamical equations. This work demonstrates that persistencecannot always be attributed solely to dynamical laws. Instead, persistent structures requireirreversible distinguishability among dynamically admissible alternatives.We formalize this requirement through a monotonic contraction of the admissible state setunder irreversible constraint events. A stochastic lattice field simulation is presented in whichthe dynamical evolution equation remains fixed while a distinguishability parameter controllingtrajectory selection is varied.The system exhibits a sharp persistence transition. When admissible configurations remaininterchangeable, vortex populations decay rapidly. When alternatives become irreversibly distinguishable,vortex populations persist for orders of magnitude longer times.These results indicate that dynamical laws generate possible trajectories, but persistentstructures arise only when structural constraints act on the space of admissible histories. Keywords: quantum foundations, emergent gravity, irreversible processes, mea-surement problem, constraint satisfaction