The phantom-category conjecture for Sarkisov conic bundles

Let $X$ be the smooth threefold conic bundle constructed from the Sarkisov example, with discriminant curve as described in the source. Let $D^b(X)$ denote its bounded derived category, and let a phantom category mean a nontrivial category with trivial $K^0$ group.

Sarkisov phantom-category conjecture. The semiorthogonal decomposition of $D^b(X)$ contains a phantom category.

The conjecture is motivated by the nonrationality of Sarkisov's conic bundle and by the moving scheme arising from conifold transitions; the source further suggests a relation between the phantom and the absence of spectral gaps.