Dimensionless Constants as Emergent Fixed Points of Cascading Interactions

This manuscript develops a testable framework for understanding whether some dimensionless constants can emerge as stable fixed points of cascading interactions between systems and their environments, rather than being treated only as externally assigned values. The paper formalizes coupled state–environment dynamics, defines emergent constants through fixed-point and basin-of-attraction criteria, and provides a worked discrete model with explicit stability conditions. It then connects this framework to dimensional analysis and renormalization-group reasoning, while clarifying key conceptual and methodological limits. A central contribution is falsifiability: the manuscript specifies concrete empirical signatures (recovery under topology-preserving perturbations, drift under topology-changing interventions, critical slowing near stability boundaries, and motif-level behavioral homology), along with explicit rejection criteria and a staged validation program. Overall, the work is positioned as a rigorous research program rather than a final derivation of fundamental constants: it offers mathematical structure, intervention-based predictions, and practical pathways for testing emergent explanations of dimensionless regularities across physical systems.