ECA Critical Transition Framework

This work introduces a preliminary nonlinear framework based on ECA-driven critical dynamics and effective geometric modulation. The model explores the emergence of bounded complex geometric regimes from nonlinear critical transitions without manually imposing external regularization mechanisms. A key result of the framework is the appearance of an invariant amplitude structure: |ρ| = 1/α suggesting a transition from divergent collapse behavior toward phase-rotational dynamics. This publication represents an initial public fragment and conceptual timestamp of a larger ongoing theoretical framework focused on: nonlinear geometry, emergent temporal structures, critical ECA dynamics, and phase-regulated gravitational behavior. The framework is presented as a formal mathematical extension and not as a replacement for established physical theories.