Discrete Exterior Calculus, Transverse Hodge Decomposition, and Non-Hamiltonian Vorton Dynamics

This work establishes a non-Hamiltonian fluid dynamics framework by coupling discrete exterior calculus on the Johnson association scheme with singular solenoidal vorton mechanics. The oriented cell complex exhibits metric-free coboundary nilpotency, a vanishing first Betti number, and an exact orthogonal Hodge decomposition into longitudinal and transverse subspaces, confirming that the two-thirds transverse polarization fraction is an exact topological property of every elementary triangular simplex. The line tension of an equilibrium vortex sponge generates a macroscopic shear modulus that sustains propagating transverse shear waves without empirical elasticity parameters. Mutual hydrodynamic strain tension drives anti-parallel filaments to finite-time kinematic Leray collapse without requiring added mass. During reconnection, singular energy dissipation and non-invertible topological surgery destroy phase-space volume, driving the system asymptotically onto an invariant survivor attractor composed of ballistic solenoidal dipoles and knotted solitons. In addition, hydrodynamic spinor mappings identify the quantum potential with osmotic enstrophy, while cosmological expansion enforces dynamical freeze-out once the reconnection rate drops below the Hubble expansion rate, preserving stable relic topological solitons.