Stable rationality conjecture for smooth projective surfaces

Let $X$ be a smooth projective surface. The surface is stably rational if $X\times\mathbb{P}^1$ is rational. Stable rationality conjecture for surfaces. If

$$X\times\mathbb{P}^1$$

is rational, then $X$ is rational. This is a cancellation-type assertion for rationality of smooth projective surfaces. The source states it as a conjecture and provides no resolution.