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Whether these correlations form a self-consistent quantum theory on that sphere is unknown.","posed_since":"2016","precise":"Celestial holography maps the 4D asymptotically flat S-matrix, via a Mellin transform in energy, to correlators on the celestial sphere. Determine whether for Einstein gravity beyond tree level these correlators form a CFT with a local operator algebra, OPE and state-operator map, and find an intrinsic definition independent of the bulk.","problem_ref":"bd665f6512a075226bcf3e486f6b8fee99baff2e09feb7c38044c62257b92f34","references":"","settled_by":"An intrinsic 2D construction reproducing loop-level gravitational amplitudes, or a proof that the required CFT axioms fail.","status_note":"A top-down dual, a 2D chiral algebra, exists for a self-dual-type theory (Mabuchi gravity coupled to a 4D WZW model) on Burns space (Costello, Paquette, Sharma 2022-2023); full Einstein gravity remains open.","title":"Is there a consistent celestial CFT for four-dimensional 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