Chapter 5: The Omega Readout and the Lemniscate

Book I’s ABCD chart handles ω as a degenerate case: the point at infinity lies outside the scope of the four-coordinate readout Φ(X) = (A, B, C, D), because its coordinates diverge. This chapter gives ω a meaningful coordinate readout by computing the limit of ABCD readouts along the primorial tower P₁, P₂, P₃, … as n → ∞. The result is a sharp dichotomy: in base coordinates (D, A), the omega readout collapses to a single point (Ω, Ω); in fiber coordinates (B, C), the omega readout has one-dimensional structure — the algebraic lemniscate 𝕃. The lemniscate is not imported; it is the fiber readout of the point at infinity. This is the precise mechanism by which the fibered product τ³ = τ¹ ×_f T² manifests: the fiber T² degenerates to 𝕃 at the boundary point ω.