Chapter 15: The Denotational Order and the Road Ahead

The strict order K1 governs the five generators. With the full arithmetic of τ-Idx now available, we extend this order to all of Obj(τ), producing a well-ordering that respects the orbit structure. This denotational order is the canonical linear order on τ: it determines the position of every object in the universe. We prove that the denotational order is a well-ordering and sketch the Hasse diagram of Obj(τ). The chapter closes with a forward look to Parts IV–XV, outlining the road from these bare-metal foundations to the full edifice of mathematics.