CLOSURE ONTOLOGY Closure Spectral Flow And Renormalization Stability of Relational Transport Dynamics

We investigate renormalization and scale-flow properties of closure-consistent relationaltransport field theories. Building on closure-consistency formulations of classical field dynamics and spectral stability analysis of closure-consistent transport operators, we analyze how closure spectral structure evolves under coarse-graining and renormalization flow. We construct closure spectral flow functionals defined over effective transport configuration spaces and derive conditions under which low closure spectral cost transport sectors remain stable under scale evolution. Using semiclassical renormalization and toy lattice closure spectral models, we show that closure spectral cost ordering can remain monotonic under scale flow under broad locality and invariance assumptions. While not providing a complete renormalization proof for closureconsistent field theories, the present work establishes a framework for analyzing closure spectral persistence across energy scales and suggests that closure-consistency principles may impose structural constraints on effective transport sector stability under renormalization evolution.