Non-Hamiltonian Dynamics of Solenoidal Vorton Ensembles, Singular Reconnection Dissipation, and the Emergent Survivor Spectrum of Primordial Turbulence

The non-Hamiltonian solenoidal vorton framework models fluid turbulence as a discrete, divergence-free vortex system punctuated by singular topological surgeries that relax onto a stable relic spectrum: Solenoidal Dipole Invariance: Fluid vorticity is represented by localized closed filament circuits and antiparallel dipole pairs, mathematically enforcing an identically divergence-free field across the entire domain without unphysical source or sink monopoles. Inviscid Singular Dissipation: Approaching vortex cores violate the minimum smoothness threshold required by Onsager's theorem for energy conservation. Every reconnection event extracts an anomalous, non-viscous kinetic energy deficit that evacuates into unresolved acoustic and dispersive radiation. Finite-Time Broadside Collapse: Mutual hydrodynamic induction between antiparallel dipoles produces an attractive transverse force scaling inversely with the fourth power of separation, driving the pair along a deterministic collapse trajectory into collision within a finite time. Non-Hamiltonian Phase-Space Contraction: The topological reconnection operator acts as a non-invertible projection that maps states into a lower-dimensional constraint submanifold. This irreversibly contracts phase-space volume to zero, breaking Liouville's theorem and precluding standard Hamiltonian or action-principle formulations. Finite Reconnection Termination: Because every reconnection consumes a finite, non-zero minimum quantum of energy from a finite-energy initial state, the total number of reconnection events is strictly bounded. The system halts all reconnection activity within a finite relaxation timeframe. The Survivor Attractor: Following the final reconnection, the system settles onto an invariant global attractor containing two non-colliding configurations: ballistically propagating solenoidal dipoles whose spatial dilution prevents further encounters, and topologically locked, knotted solitons whose non-zero helicity prevents self-intersection in the energy ground state. Cosmological Freeze-Out: In an expanding cosmological background, cosmic volume growth dilutes vorton number density faster than mutual hydrodynamic attraction can drive collisions. Reconnection kinetics naturally decouple from the expansion, freezing the survivor population into a stable relic background without arbitrary potentials or hand-tuned parameters.