Vehicle 2D: Experimental Validation of Multimodal Contractive Dynamics in Two Dimensions

This work presents the initial formal development and experimental validation of a multimodal contractive dynamical system defined on a two-dimensional discrete structure. The framework models distributed systems in which each node selects locally optimal states from finite event libraries and updates through a convex contractive rule governed by compatibility constraints.The 2D formulation establishes monotonic energy behavior under spectral and compressed–expanded dynamics, providing the foundational mathematical structure for subsequent higher-dimensional extensions.The results demonstrate boundedness, structural stability, and compatibility-driven coherence formation in a planar setting. This document represents the foundational formal layer of the Vehicle framework.