The Gabriel's Horn Divergence: A 3D Geometric Resolution of the Navier-Stokes Millennium Problem via the Hernández-Valdivia Limit

The Millennium Prize problem regarding the global regularity of Navier-Stokes solutions is traditionally framed as a challenge of analysis within the unconstrained continuous domain (ℝ3). This paper argues that this foundational requirement suffers from the “Continuum Fallacy,” the erroneous assumption of infinite spatial divisibility (C∞). By deploying Torricelli's acute hyperbolic solid (Gabriel's Horn) as a static 3D bounding geometry for incompressible fluid flow, we construct a deterministic model that forces a kinetic blow-up purely through spatial continuous constraints. We resolve this geometric divergence by projecting the Hernández-Valdivia Limit (εHV ≈ 10-70 m2) onto the transverse fluid area, proving that the mathematical singularity is structurally truncated into a saturated state. This demonstrates that the Navier-Stokes finite-time divergence is not a failure of physical fluid mechanics, but a logical impossibility of processing infinite information within a vanishing continuum volume, establishing the fluid domain as a consistent, computable finite-state machine governed by Hydrodynamic Cosmic Censorship.