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Whether a smooth temperature pattern can form an infinitely sharp front in finite time is unknown.","posed_since":"1994","precise":"Inviscid SQG: $\\mathrm{d}\\theta/\\mathrm{d}t + u . \\mathrm{grad}\\,\\theta = 0$, $u = (-R_2 \\theta, R_1 \\theta)$ with $R_j$ the Riesz transforms, on $R^2$ or $T^2$, smooth (e.g. $C_c^\\infty$) initial $\\theta$, no forcing. Prove global regularity, or give smooth data with $\\int_{0}^{T} ||\\mathrm{grad}\\,\\theta(t)||_{\\mathrm{inf}}\\,\\mathrm{d}t = \\infty$ at finite T. Answer: yes or no with proof.","problem_ref":"12bac92a004b75eefb9a746d6ca32c9f5e10d2704d0c9401a137872fc72dc7d1","references":"","settled_by":"A proof of global regularity or a verified finite-time singularity from smooth finite-energy data without forcing.","status_note":"Frontal blowup was proposed by Constantin, Majda and Tabak (1994); blowup from smooth compactly supported data with a suitable time-dependent force, inside the Sobolev well-posedness regime, was proven for generalized SQG with $\\gamma \\text{ in } (0,1)$ (Cordoba, Dominguez, Lucas-Manchon and Martinez-Zoroa, arXiv 2608.17192, 2026), not for unforced SQG.","title":"Finite-time singularity of the inviscid surface quasi-geostrophic 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