UV-Complete Gravity Amplitudes and the Triple Product

We construct an infinite class of new ultraviolet-complete four-graviton scattering amplitudes that reduce to Einstein gravity at low energies, vanish at high energies, are meromorphic, and exhibit a triple-product structure ${\cal A}(s){\cal A}(t){\cal A}(u)$. The spectrum invariantly exhibits accumulation points in the form of infinite towers of states on each mass pole, whose residue can be positively expanded on tree-level exchanges of irreducible representations of the Lorentz group.