Proof Of Triadic Minimum

This work presents a formal proof that all universal explanatory frameworks reduce to a triadic structure. By eliminating monadic, dyadic, and tetradic+ models as incomplete or redundant, the paper establishes Pattern × Intent × Presence as the minimal non-arbitrary invariant. The triad is shown to be presupposed in empirical science and instantiated across theology, philosophy, semiotics, physics, mathematics, biology, language, and society. The result positions the triad as a meta-logical law of reality.