Type-1 zero-problem conjecture for 3M-DAPs

Let $P=(T;U,V)$ be a 3M-DAP. Write $t,u,v$ for the relevant row lengths, $s_t,s_u,s_v$ for the numbers of rows of types $T,U,V$, and $x_t,x_u,x_v$ for their total values. A $(T,V)$-pair consists of subsets of $T$- and $V$-rows with sizes $a$ and $b$.

Type-1 zero-problem conjecture. If $s_t\leq(v-1)s_v$, then the optimal solution consists of $(T,V)$-pairs with $a/b=s_t/s_v$, with $(T,V)$ itself being one such pair, and the optimal value is

$$\frac{s_tx_t-s_vx_v}{s_tt-s_vv}=\frac{x_u}{u},$$

i.e. all values in $U$ must be $x_u/u$.

The source presents this as a conjecture about the structure and value of optimal solutions for this class of 3M-DAPs. No resolution is supplied in the stated context.