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Whether every such theory appears in the catalog is unknown.","posed_since":"2015","precise":"Heckman, Morrison, Rudelius and Vafa (2015) classified $6\\mathrm{D}\\,(1,0)$ SCFTs realized by F-theory on elliptically fibered Calabi-Yau threefolds with contractible bases. Determine whether every interacting $6\\mathrm{D}\\,(1,0)$ SCFT admits such a realization, including frozen phases with $\\mathrm{O7}+$ planes, by a field-theoretic completeness argument or a counterexample.","problem_ref":"b60d4f6ed743b29c1139e8b8f40b9fdcf9eafcb4bf69183b69d1869e38c08eed","references":"","settled_by":"A field-theoretic proof that consistency (anomaly cancellation and unitarity on the tensor branch) admits only the geometric list, or an explicit theory outside it.","status_note":"Frozen-singularity theories (Bhardwaj, Morrison, Tachikawa, Tomasiello 2018) enlarged the F-theory list; no field-theoretic completeness argument exists.","title":"Do all six-dimensional superconformal theories arise from 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