Losev's simplicity conjecture for canonical quantizations

Let $X$ be a Poisson variety and let $U$ be its canonical quantization, the preferred quantization associated with Losev's classification. A quantization is simple if it has no nonzero proper two-sided ideals. Losev's conjecture. The canonical quantization is simple. The supplied material gives no resolution status; when $X$ has $\mathbb{Q}$-factorial terminal singularities, uniqueness of the quantization means the conjecture asserts that this unique $U$ is simple.