Chapter 6: The τ³ Fibration Emerges

The previous chapter established the ABCD peel-order asymmetry: the four coordinate rays of the ABCD chart split into two outer rays (D, A) and two inner rays (B, C), and the coupling between them prevents a Cartesian factorization. This chapter assembles the fibration. The outer pair (D, A) forms the base τ¹, a two-dimensional number-theoretic space capturing radial depth and prime direction. The inner pair (B, C) forms the fiber T², a two-dimensional parameter space capturing exponent structure and tetration height. The full interior is the fibered product τ³ = τ¹ ×_f T²—not a Cartesian product, because the constraint “prime factors of D are bounded by A” couples the base coordinates, which in turn couples the base to the fiber. The chapter closes with an ontological reframe: τ³ is τ viewed through its coordinate chart, and neither τ¹ nor T² exists as an independent category.