Vehicle 2D: Complete Multimodal Contractive Experimental Framework and Planar Stability Analysis

This publication presents the internally reviewed and mathematically consolidated formulation of Vehicle 2D as a hybrid discrete–continuous multimodal contractive dynamical system defined on bounded-degree planar graphs.The framework combines finite event selection under compatibility constraints with convex contraction updates. A quadratic global energy functional is introduced and rigorously proven to be monotonically non-increasing.We establish:• Invariance of admissible state sets• Global boundedness of trajectories• Existence of solutions for all discrete time steps• Asymptotic coherence under compatibility constraints• Exponential convergence rate bounds under strict contraction• Fixed-point characterization and fragmentation conditions• Robustness under bounded perturbations• Operator-theoretic interpretation• Structural comparison with Laplacian consensus dynamicsTwelve structured experimental regimes are formalized as controlled instantiations of the same contractive backbone.This document constitutes the definitive planar theoretical layer of the Vehicle research program and formally extends the initial validation note (DOI: 10.5281/zenodo.18777915).