Sharpness of Irrationality after One Stabilization for Cubic Threefolds

The irrationality of X times P^1 for every smooth complex cubic threefold X is sharp: two explicit smooth cubic threefolds over Q become rational after product with P^2. For these examples, the least m for which X times P^m is rational is exactly two, over both Q and C. We prove more generally that if k has characteristic zero and S/k is a smooth quartic del Pezzo surface with a rational point and stably permutation geometric Picard lattice, then S times A^2, equivalently S times P^2, is k-rational. Applying this theorem to both Tschinkel–Zhang series of smooth cubic hypersurfaces gives a uniform P^2 rationality bound. Consequently there are smooth projective nonrational fourfolds Y over Q for which Y times A^1 is rational, answering the affine-line stabilization question raised there. The release includes an exact-arithmetic certificate, retained empty-branch identities, and generated manuscript values for the tangent-incidence calculation; the new rationality theorem is not formalized in Lean.