Table-locus equations conjecture for all entries of Zhao's table

Fix $Q=(u,u-r)$ with $u>r\ge2$, put $B=J_Q$, and let $E(\mu,\nu)$ and $X_s(k_1,k_2)$ be the coordinate expressions defined in the source. All-table loci equations conjecture. For $k,\ell\in\mathbb N$ with $1\le k\le r-1$ and $1\le\ell\le u-r-1$, the ideal $\mathcal I(\mathfrak Z(P_{k,\ell}))$ is given as follows: if $(k,\ell)\in A_t$, it is generated by $E(k-t-1,t+\ell-1)$ when $k+\ell\le r$, and by $E(k_1,k_2),X_1(k_1,k_2),\ldots,X_s(k_1,k_2)$ when $k+\ell>r$, with $k_1=k-t-1$, $k_2=t+(r-k)-1$, and $s=k+\ell-r$; if $(k,\ell)\in B_t\cup C_t$, it is generated by $E(k+\ell-t-2,t)$ when $k+\ell\le r$, and by $E(k_1,k_2),X_1(k_1,k_2),\ldots,X_s(k_1,k_2)$ when $k+\ell>r$, with $k_1=r-t-2$, $k_2=t$, and $s=k+\ell-r$. The source provides no resolution.