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Why a driven, dissipative flow should have this symmetry is unexplained.","posed_since":"2006","precise":"Forced 2D incompressible Navier-Stokes turbulence with large-scale friction, inverse-cascade range $\\ell_f \\ll r \\ll L$. Zero-vorticity isolines are statistically consistent with Schramm-Loewner evolution $\\mathrm{SLE}_{\\kappa}$ with $\\kappa = 6$ (Bernard, Boffetta, Celani, Falkovich 2006), the class of critical percolation cluster boundaries. Is this conformal invariance exact as $L/\\ell_f \\to \\infty$, and which property of the dynamics implies it? Answer: a derivation, or a measured deviation of $\\kappa$ beyond error bars.","problem_ref":null,"references":"","settled_by":"An analytic derivation from the $2\\mathrm{D}$ Navier-Stokes dynamics, or a high-precision numerical test of $\\kappa$ and of the conformal covariance of multipoint observables.","status_note":"Evidence is numerical and experimental; a 2025 theoretical proposal models the cascade as constant-flux domains whose boundaries carry a Liouville conformal field theory (Eling, arXiv:2505.09657), without derivation from the Navier-Stokes equations.","title":"Are inverse-cascade vorticity isolines exactly conformally 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