Chapter 24: Navier–Stokes at Macro Level: Regularity from τ³

The Navier–Stokes regularity question has been addressed at two levels in the preceding books. Book III proved the Positive Regularity Theorem (III.T25): blow-up is structurally impossible for τ-admissible data on the enrichment layer E₀. Book IV, Chapter 53, gave the E₁ physical interpretation on the fiber T²: the fluid never develops infinite velocity, because the compact fiber, bounded ABCD extraction, and K5 sector isolation jointly forbid energy concentration.

This chapter completes the story at the macroscopic level. The base τ¹ is a circle—compact, like the fiber. The full fibered product τ³ = τ¹ ×_f T² is therefore compact, and macro-scale transport inherits the regularity of the fiber-level defect dynamics. We derive the macro τ-Navier–Stokes equation as a base-projected budget transport law, prove that the macro velocity readout is bounded for all time, and explain why the base circle eliminates a class of singularity scenarios that do not arise on the fiber alone: those involving temporal blow-up.

Scope: τ-effective (structural regularity); conjectural (bridge to Clay problem).