Deformation Retraction of the 0-Sphere Embedding Region (TikZ Source: zenodo_18356895)

Summary: This figure (Fig. 2 in the main paper) illustrates the mathematical limit where the internal dynamics of the 0-Sphere model cease. It demonstrates the topological deformation retraction of the embedding region D.Key Visual Components (TikZ Logic):Contracting Region D: Depicted by dashed boundaries, showing the transition from an arcwise connected domain to a single point.Central Point p: The terminal limit of the retraction where kernels p±​ converge.Degenerate Path w(τ): As D contracts to {p}, the thermal geodesic path degenerates into a constant map, physically representing the suppression of radiative energy transport.Formal Notation: D↘{p} emphasizes the topological nature of this extreme limit.Context: This visualization is essential for understanding the conditions under which internal radiative circulation is inhibited, leading to a static energy state.