Chapter 4: τ

Book I built the ABCD coordinate chart Φ : Obj(τ) → τ-Idx⁴ as a total, injective address system for every finite object. This chapter extends the chart beyond finite objects to define the full point set τ³. The key insight: τ³ is not defined by importing an ambient space or invoking Hartogs extension. It is defined purely algebraically as the set of τ-admissible ABCD quadruples — those quadruples satisfying the constraints forced by the normal-form structure. The profinite completion of the finite ABCD space adds limit points, including the omega boundary.