The Geometric Origin of the Informational Coherence Constant in the Unified Informational Spin Theory (TGU)

This supplementary note provides a fundamental derivation of the coupling constant k ≈ 0.0881 (the Matuchaki Parameter) within the Unified Informational Spin Theory (TGU). We demonstrate that k emerges naturally as the inverse solid- angle normalization factor of a three-dimensional coherent spin field, yielding k ≈ (4π)−1. This geometric interpretation explains its universality across planetary and exoplanetary systems, transforming k from an empirical fitting parameter to a theoretically predicted constant of informational coherence. The derivation resolves the apparent arbitrariness of k and establishes its role as the efficiency of conversion between orbital anisotropy and informational phase accumulation.