Theorem XII — Theorem of Stability This paper completes the formal corpus of Complex Binarity Theory by proving the Axiom of Stability as a mathematical theorem. The system is modeled in triadic state spaces (t) = (ρ (t), p (t), τ (t) ) s (t) = ( (t), p (t), (t) ) s (t) = (ρ (t), p (t), τ (t) ), where spectral radius ρρ, accumulated load ppp, and temporal resource ττ define the admissible stability region. Under three structural conditions — existence of a Lyapunov function, a positive compensation index, and monotonic spectral non-growth — the system converges to a unique asymptotically stable equilibrium within the admissible region. The convergence time is bounded. The proof proceeds through region preservation, contraction mapping, Banach fixed point existence, and asymptotic stability. This theorem closes the axiomatic gap of the theory: stability is not assumed but derived from the triadic coordinate structure. The document also states the foundational geometric formulation: Principle of ThreeOne forms a point. Two form a line. Three form a plane.
ANDREY STANKO (Mon,) studied this question.