Chapter 2: The Five Generators

We introduce the five generators of Category τ: α, π, γ, η, and ω, arranged in a strict total order α < π < γ < η < ω. These five objects are the entire primitive vocabulary of the theory. No further constants, function symbols, or relation symbols will be introduced — every subsequent structure is earned from this starting point and the single operator ρ . We state the first kernel axiom (K1: Strict Order) and derive the immediate consequence that all five generators are pairwise distinct.