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Whether this is a law of all quantum gravity theories is unproven.","posed_since":"2006","precise":"Weak gravity conjecture (Arkani-Hamed, Motl, Nicolis, Vafa 2006): every U(1) gauge theory coupled to gravity has a state with charge-to-mass ratio at least that of extremal black holes. Determine whether this holds in every consistent quantum gravity theory, and whether the sublattice or tower versions hold.","problem_ref":null,"references":"","settled_by":"A derivation from general principles (black hole thermodynamics, unitarity, holography), or a consistent theory violating it.","status_note":"Shown in perturbative string settings and supported by black-hole arguments; the strongest lattice version fails in some compactifications (2016), leaving sublattice and tower versions.","title":"Does the weak gravity conjecture hold in all quantum gravity 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