Balanced triples attaining finite-degree GV

Let $(j_Z,j_X,k)$ be any balanced triple satisfying

$$4\le j_Z<\frac{k}{2},\qquad j_X=k-j_Z.$$

The corresponding HA-side and MN-side classical constituent codes are the codes associated with this triple, and a balanced triple is one satisfying the displayed relations. Balanced triples attaining finite-degree GV. The HA-side and MN-side classical constituent codes attain GV distance already at fixed finite degree, and hence the associated nested CSS family attains the CSS GV distance. This claim concerns finite-degree classical constituent performance and its implication for the associated CSS family; the surrounding discussion indicates that the rigorous certification is concentrated on even $k$, while extensions to odd $k$ require additional estimates. The supplied text does not establish whether this stated conjectural claim has been resolved.