Stable-category invariance of codimension for geometric complete intersections

Let $(A,\mathfrak{m})$ and $(B,\mathfrak{n})$ be geometric complete intersections of codimensions $m,n$, respectively, with algebraically closed residue fields. For an integer $r$ satisfying

$$r \leq \min\{m,n\},$$

write $\operatorname{\underline{CM}}_{\leq r}(A)$ for the thick subcategory generated by maximal Cohen–Macaulay $A$-modules of complexity at most $r$, and similarly for $B$.

Stable-category codimension conjecture. If $\operatorname{\underline{CM}}_{\leq r}(A)$ is triangle equivalent to $\operatorname{\underline{CM}}_{\leq r}(B)$, then $m=n$.

This proposes that the codimension of geometric complete intersections is detected by suitable subcategories of their stable categories of maximal Cohen–Macaulay modules. The surrounding results establish related invariance statements for abstract complete intersections, but the supplied text does not state whether this conjecture has been resolved.