Modular Stabilization of Symbolic Fields: Admissibility, Collapse, and Persistent Coherence in KN-Stabilized Dynamics

This work introduces a falsifiable symbolic field framework for modeling quantum-like behaviors under explicit structural constraints. Rather than modifying the formalism of quantum mechanics or proposing a new physical ontology, the paper investigates which behaviors associated with quantum systems persist within a restricted class of admissible dynamics—defined as bounded, well-posed, and stable under perturbation. At the core of the framework is a bounded nonlinear stabilizing function, KN, which constrains symbolic field evolution within a modular phase space. Within this constrained regime, phenomena commonly associated with quantum mechanics—interference, collapse-like transitions, entanglement, memory persistence, and decoherence—emerge as structural consequences of resonance, phase alignment, and admissibility filtering rather than as observer-dependent postulates. Using four simulation-based tests, the paper demonstrates that: Linear superposition fails under KN modulation, producing bounded asymmetry rather than cancellation. Symbolic memory decays without active modular reinforcement and persists only under feedback. Collapse-like transitions propagate synchronously across phase-aligned symbolic fields. Decoherence emerges from stochastic phase drift without invoking measurement or observation. The framework reframes collapse as resonance locking, entanglement as modular phase alignment, and decoherence as admissibility failure induced by phase instability. These mechanisms do not alter the empirical predictions of quantum mechanics, but instead clarify the structural conditions under which quantum-like behavior survives. This work is intended as a structural and methodological contribution, providing a constrained symbolic model that complements existing quantum theory and connects ideas from nonlinear dynamics, decoherence, and constructive field theory. It forms part of a broader research program exploring admissibility as a unifying principle across physical, symbolic, and informational systems.