Nonrationality conjecture for conic bundles with phantom decompositions

Let $X$ be a conic bundle of dimension $3$. Let $D^b(X)$ denote its bounded derived category, and suppose

$$D^b(X)=(\mathcal A,E_1,\ldots,E_n)$$

is a semiorthogonal decomposition into a phantom category $\mathcal A$ and an exceptional sequence $E_1,\ldots,E_n$. The conic-bundle nonrationality conjecture. Then $X$ is not rational. This proposes a categorical nonrationality criterion for three-dimensional conic bundles; the source gives no resolution.