Loci equations conjecture for the first column of Zhao's table

Fix $Q=(u,u-r)$ with $u>r\ge2$, put $B=J_Q$, and use coordinates $a_1,\ldots,a_{u-1},b_1,\ldots,b_{u-r-1}$ on $\mathcal U_B$. For $\mu\in\{0,1,\ldots,u-1\}$ and $\nu\in\{0,1,\ldots,u-r-1\}$, define $E(\mu,\nu)=\{a_1,\ldots,a_\mu;b_1,\ldots,b_\nu\}$. First-column loci equations conjecture. If $k\in\{1,\ldots,r-1\}$ and $k_{t-1}<k\le k_t$, where $0\le t\le\min\{u-r,\lfloor(r-1)/2\rfloor\}$ and $k_t$ is the integer defined in the source, then $\mathcal I(\mathfrak Z(P_{k,1}))$ is generated by $E(k-t-1,t)$. This is presented as a conjecture, and the supplied text gives no resolution.