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It is shown that (aΛ2+b|H|2)R in a spacetime of curvature R is a natural ultraviolet (UV) completion of (aΛ4+bΛ2|H|2) in the flat-spacetime Standard Model (SM) with Higgs field H, UV scale Λ, and loop factors a and b. This curvature completion rests on the fact that Λ-mass gauge theory in flat spacetime turns, on the cut view R=4Λ2, into a massless gauge theory in curved spacetime. It provides a symmetry reason for curved spacetime, wherein gravity and matter are both low-energy effective phenomena. Gravity arises correctly if new physics exists with at least 63 more bosons than fermions, with no need to interact with the SM and with dark matter as a natural harbinger. It can source various cosmological, astrophysical, and collider phenomena depending on its spectrum and couplings to the SM.