Sharpness of Irrationality after One Stabilization for Cubic Threefolds

The theorem that every smooth complex cubic threefold remains irrational after multiplication by P^1 is sharp. For each of two explicit smooth cubic threefolds X over Q, this preprint proves that the least m for which X times P^m is rational is exactly two, over both Q and C. The reusable theorem proves 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. Applied to both Tschinkel–Zhang series of smooth cubic hypersurfaces, it 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 and generated manuscript values for the tangent-incidence calculation; the new rationality theorem is not formalized in Lean.