TMD: The Sigma Law — Local Stability and Structural Saturation of Matter

This work introduces the Sigma Law, a local stabilizing mechanism of the triadic network (TMD) that maintains orientational coherence and prevents the structural decay of matter. In TMD, matter is not an object but a stable orientational configuration that the network continuously regulates through the Sigma operator. The Sigma Law describes how the network returns to its target structural saturation when perturbed by external interaction or local fluctuation. The mechanism is purely local, requires no energy, and does not rely on global geometry. Sigma ensures the stability of matter, the cohesion of space, and the containment of orientational conflicts. This study presents the Sigma Law as a foundational principle of TMD, complementing triadic dynamics, orientational deficit, and the Flip Freeze mechanism.