Derived Symbolic Collapse Coefficients: A Structured Replacement for Arbitrary Thresholds in Modular Field Dynamics

This paper introduces a mathematically derived method for detecting symbolic collapse in modular field systems using the KN (Kuro Nova) framework. By replacing manually tuned dissonance thresholds with interpretable coefficients grounded in symbolic structure—loop length, amplitude difference, phase alignment, and modular residue—we offer a falsifiable alternative that strengthens the theoretical foundation of KN-based field dynamics. This work serves as a direct refinement of the collapse criteria presented in the prior paper "Modular Stabilization of Symbolic Fields: Falsifiable Tests of the KN Function in Quantum-Like Systems" (DOI: 10.5281/zenodo.15484635). All simulations are reproduced using the new derivation, and collapse behavior is shown to persist with improved coherence and accuracy.