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The evidence comes from approximate calculations whose reliability is debated.","posed_since":"1979","precise":"For the renormalization group flow of 4D gravity coupled to Standard Model matter, determine whether a non-Gaussian fixed point exists with finitely many UV-relevant directions, beyond truncations of the effective action, in Lorentzian signature and without ghosts in the full graviton propagator. An answer is a controlled demonstration (for example convergence across systematically enlarged truncations, or a lattice continuum limit) or a no-go result.","problem_ref":null,"references":"","settled_by":"Convergence of fixed-point properties under systematic enlargement of truncations, confirmed by an independent non-perturbative method.","status_note":"Truncated functional renormalization group studies since Reuter (1998) find a fixed point; convergence, Lorentzian formulation and unitarity remain disputed as of 2026.","title":"Does 4D quantum gravity with matter have an ultraviolet fixed 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