The resolution of global regularity for three-dimensional incompressible fluid dynamics presents
dual analytical challenges: establishing the existence of smooth mappings for a priori unknown
evolving free boundaries, and preventing the finite-time vortex stretching singularities inherent
to continuum Navier-Stokes formulations. We present a fully deterministic, geometrically closed
synthesis resolving both analytical obstructions. The continuous fluid domains are mapped using
the conjugate homeomorphisms of the Free Boundary Neural Operator (FBNO), rigorously
integrated via a differentiable Kolmogorov-Arnold Network (KAN) projection. The temporal
evolution of the fluid is subsequently constrained to a finite spectral manifold, designated as the
DSM-861—a rigid 861-node triangular simplicial vorton lattice endowed with a periodic 3-torus
topology. By establishing an exact discrete Graph-Hodge orthogonal decomposition and
bounded pseudo-inverse Biot-Savart operators, we prove that the finite spectral capacity of the
manifold induces a universal Euler-Maclaurin trace anomaly, |ε| = 1/12. This residue operates as
a strictly geometric Casimir damping parameter, arresting nonlinear vortex stretching and
enforcing a global bound on the discrete enstrophy. The continuous-to-discrete transformation is
realized computationally through quantization to exact Apéry polynomial states and phasematched routing governed by the imaginary quadratic field Q(√-163).
Publication Date: 2026-06-05