Causal Dynamics: A Field-Based Framework for Structural Stability, Collapse, and Emergence

This paper introduces a formal framework for causal dynamics, treating causality not merely as event succession but as a structured field with recursive stability, feedback tension, and emergent geometry. Drawing on thermodynamics, systems theory, and topology, we develop a general causal field model \Psi_c whose behavior governs structural coherence, adaptive memory, and phase transitions across physical, biological, and symbolic systems. Recursive closure and loop attractors are shown to underlie the stability and transformation of systems, while causal tension \vec{T}_c mediates rupture, collapse, and reformation. We define a set of mathematical operators—such as the coherence coefficient \kappa, loop density \rho_L, and causal order parameter \Omega_c—to characterize the dynamic state of systems under perturbation. Phase transitions are reinterpreted as topological rewrites of causal manifolds, producing novel attractor structures that enable emergence and re-stabilization. This unifying framework sets the stage for cross-disciplinary application, ranging from crystalline lattice collapse to neural plasticity, ecological resilience, and institutional breakdown. The resulting model offers a comprehensive paradigm for understanding not only how systems function, but how they endure, adapt, and evolve under recursive causation.