  Combining recent results on noetherianity of twisted commutative algebras by
Draisma and the resolution of Stillman's conjecture by Ananyan-Hochster, we
prove a broad generalization of Stillman's conjecture. Our theorem yields an
array of boundedness results in commutative algebra that only depend on the
degrees of the generators of an ideal, and not the number of variables in the
ambient polynomial ring.
