Bardakov–Etingof–Sosnovsky conjecture on idempotents in integral latin quandle rings

Let $X$ be a finite latin quandle, and let $u\in\mathbb{Z}[X]$ be a nonzero idempotent, so $u^2=u$. An element of $X$ is called a trivial idempotent, and $\varepsilon$ denotes the augmentation map. Bardakov–Etingof–Sosnovsky's conjecture. The element $u$ is a trivial idempotent and

$$\varepsilon(u)=1.$$

This conjecture concerns the classification of idempotents in integral quandle rings; it is stated here as a known conjecture for finite latin quandles, and its resolution is not indicated in the supplied text.