Proposition 3.1 (Turbulence Classification)

The nine turbulence levels correspond to increasing topological complexity:

τ = 1: Isometric (all invariants preserved)

τ = 2: Conformal (angles preserved)

τ = 3: Quasi-conformal (bounded distortion)

τ = 4: Shear (metric violated)

τ = 5: Homology perturbation (rank change)

τ = 6: Handle addition (genus increase)

τ = 7: Cross-cap insertion (non-orientable)

τ = 8: Multiple punctures (H₂ trivialized)

τ = 9: Complete ungluing (all structure lost)