Kuznetsov–Smirnov Grassmannian residual-category conjecture

Let $X=\operatorname{Gr}(k,n)$ be the Grassmannian, and let $\mu(d)$ be the Möbius function. Define

$$R_{k,n}=-\sum_{d\mid\gcd(k,n),\ d>1}\mu(d)\binom{n/d}{k/d}.$$

Kuznetsov–Smirnov Grassmannian residual-category conjecture. The category $\Db(X)$ has a rectangular Lefschetz collection whose residual category is generated by $R_{k,n}$ completely orthogonal objects. Here $\mu(d)=1$ when $d$ is square-free with an even number of prime factors, $\mu(d)=-1$ when it is square-free with an odd number of prime factors, and $\mu(d)=0$ when $d$ has a squared prime factor. The conjecture is known when $\gcd(k,n)=1$, when the residual category vanishes, and when $k$ is prime; the general case remains open.