1.2 Sector-Factor Binding

This paper proves the rigid binding between the three physical sectors ( Matter, Causal, Information) and the three prime factors (2, 3, 5): , , . The binding is rigorously proved by Schur Rigidity and the First Appearance Rule — it is not an artificial assignment, but an inevitable consequence of the Clifford algebra structure. This paper further provides the formal decomposition of the coding map, a complete constructive proof of the First Appearance Rule, a three-step formal proof of the Sector-Factor Binding, the Mutual Exclusivity Lemma, numerical verification of binding stability, and the relation between binding and physical constants.