Computational Explorations of Constrained $SO(3,3)$ Spacetimes: Part I. Visualizing the Curvature Singularity and Topological Solitons

Abstract

Numerical and visual verifications of the constrained SO(3,3) multitemporal spacetime framework are presented in this paper. While heavy lattice simulations are constrained by hardware limitations, this study employs accessible, low-dimensional computational toy models to graphically simulate the core geometric mechanics governing topological particle generation. We first render the 2D kinematic projection of transverse-time rapidity, visually confirming the extrinsic curvature explosion at the strict Wunderlich geometric limit (1/√3). This explicitly visualizes the continuous diffeomorphism breakdown that mandates topological surgery. Next, we reconstruct the 3D spatial structure of the multitemporal Möbius knot, projecting the interactive topological soliton protected by the BPS energy bound. By translating complex tensor mathematics and constraint algebras into reproducible visual models, this computational exploration provides intuitive, concrete evidence for the geometric origin of mass and structural stability in extra-dimensional frameworks.