Canonical truncation conjecture for parabolic contractions in type C

Let $\operatorname{\mathfrak{q}}^C$ be a parabolic contraction in type $C$, and let $\operatorname{\mathfrak{q}}^C_\Lambda$ denote its canonical truncation. Write $(\operatorname{\mathfrak{q}}^C)'$ for the derived algebra, and let $(\pi^C)'$ be the corresponding subset of simple roots. Canonical truncation conjecture. One has

$$\operatorname{\mathfrak{q}}^C_\Lambda=(\operatorname{\mathfrak{q}}^C)'.$$

In particular, for a standard parabolic contraction,

$$\operatorname{ind} \operatorname{\mathfrak{q}}^C_\Lambda=\operatorname{ind} \operatorname{\mathfrak{q}}^C+\operatorname{Card}\left((\pi^C)\setminus(\pi^C)'\right).$$

This predicts that canonical truncation is obtained simply by passing to the derived algebra in type $C$, with the stated index correction in the standard case. The supplied text reports this as a conjecture based on recurring results and computations; no resolution is given.