K-jdt and Buch insertion equivalence for increasing tableaux

Let $S,T$ be increasing tableaux of shape $\Lambda_1$ with entries in $[n]$. The K-jdt rule given by Equation~ to rectify $T \ast S$ agrees with the Buch insertion $S \xleftarrow{B} T$.

K-jdt–Buch insertion conjecture. The K-jdt rectification of $T \ast S$ is the same tableau as the Buch insertion of $T$ into $S$.

This conjecture identifies the K-jdt operation with Buch insertion in the two-tableau setting. The supplied text does not state whether the claim has been proved or remains open.