4D HOPF VORTEX & HASIMOTO sech(u) BREATHER vs. FLAT-JET BLOWUP

Doubly-Ruled Clifford Torus (S³ → ℝ³) · Projective Rake · Hawking Kelvin-Ring Radiation

χ-Fluid Regime: Good Vibrations

Waist Clearance (0⁻‖0⁺):0.28 (Open)
Helicity I = l · r (Hopf Link):+1.42 (Conserved)
Hasimoto Soliton V = sech(u):2ν·sech(ν(s−2τ₀t))
Anisotropy Debt (−2h):Paid via Kelvin Rings
As radial compression tightens the doubly-ruled hyperboloid waist, non-zero chiral torsion τ converts the pinch into travelling Hasimoto sech(u) breather waves along the vortex core and sheds linked Hawking/Kelvin vortex rings across the seam.