TOPOLOGICAL IRREVERSIBILITY AND THE HYDRODYNAMIC ARROW OF TIME

We develop a unified mathematical framework in which the physical vacuum is modeled as a dense ensemble of interacting solenoidal dipoles (vortons) embedded within a Kolmogorov–Arnold Network (KAN) functional architecture on a fixed simplicial complex of size N = 861. We demonstrate that the macroscopic Arrow
of Time is not fundamentally a viscous dissipative effect, but a representationtheoretic phase transition. As vortex stretching drives the system, the admissible C2 spline basis reaches a rigorous curvature limit defined by approximation theory.
At this saturation threshold, the system undergoes a non-invertible projection into a singular sector. This topological reconnection induces an irreversible transfer of phase information into dispersive degrees of freedom, producing a deterministic arrow of time. By defining the singularity strictly as an unresolved scale of information, we show this projection acts as a generalized Rankine-Hugoniot boundary condition, perfectly accounting for the macroscopic inviscid dissipation previously established in 1980s vorton mechanics.

Time flows forward because representational limits force a basis swap. Post-projection, the surviving singular structures are stabilized by an infinitesimally symplectic Jacobian, yielding non-dissipative, force-free coherent cores.