  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.
