An explicit failure of complex affine-space cancellation

We construct an explicit integral complex affine fourfold X with $X\times {\mathbb{A}}^1\cong {\mathbb{A}}^5$ but $X\ncong {\mathbb{A}}^4$. This gives a negative answer to Zariski's affine-space cancellation problem over ℂ in dimension four. The same construction disproves the Stable Coordinate Conjecture in ambient dimension five and yields smooth 𝔸${}^3$-fibrations over 𝔸${}^1$ and 𝔸${}^2$ that are not Zariski-locally trivial. These fibrations disprove the Dolgachev–Weisfeiler affine-fibration conjecture over these bases.