The Commutation Deficit Formula Hierarchical Encapsulation in Affine 0-Hecke Monoids

We introduce the Commutation Deficit Formula C(K) = K(K−3)/2, which characterizes the number of commuting generator pairs in the affine 0-Hecke monoid H₀(Ã_{K-1}). This formula reveals a hierarchical encapsulation structure: K=3 (total confinement, C=0) generates matter and mass; K=4 (partial factorization, C=2) generates spacetime and causality; K=5 (golden attractor, C=5) generates coherence and information stability. The lexical ratio 42/33 ≈ 1.2727 converges to √φ ≈ 1.2720 with precision ε < 10⁻³, establishing the golden ratio as the universal attractor of algebraic coherence.