Harmonic Vortex Theory (HVT): Topological Emergence of the Standard Model via Faddeev-Skyrme-Niemi Hopfions (v3)

Harmonic Vortex Theory (HVT) v3 – Full Topological Expansion & Numerical Validation Original v1 deposited: March 11, 2026 (DOI: 10. 5281/zenodo. 18948463) v2 added the full March 14, 2026 topological paper. This v3 adds live relaxation animations and reproducible code: - Vacuum as compressible superfluid governed by extended Faddeev-Skyrme-Niemi Lagrangian + geometric pressure potential V (πⁿ) - Particles as stable Hopfion knots with acoustic phase-locks - n=5 proton with Bogomolny saturation, 1: 5 Dark Matter halo entrainment, and Finkelstein-Rubinstein spin-1/2 - n=44 non-singular black-hole core - Full spectrum from n=−13 (neutrino) to universal-scale vacuum Supplementary files: • protonₕvtᵣelaxation. mp4 — live animation of the n=5 proton vortex forming in real time • HVTSimulationCore. py — reproducible relaxation code • HVTRelaxedSpectrum. csv — complete numerical table A closely related preprint appeared on rxiVerse the same day as v1 under a different author name (Antoine Van Hoof). This deposit establishes priority for the original HVT concept and all subsequent topological developments, including the −4. 5 proton boundary condition and 1: 5 halo mechanism. Keywords: Harmonic Vortex Theory, Hopfions, Faddeev-Skyrme-Niemi, topological solitons, non-singular black holes, gravitational-wave echoes, Dark Matter halo, acoustic phase-lock, Finkelstein-Rubinstein