5 problems

Scaling conjecture. For all $k,m,s\in\mathbb{N}$,

Reduced-pair conjecture. If $s_t>(v-1)s_v$ and $b^*=2s_v/r_v$ is not an integer, then there exists an optimal solution in which all maximal inseparable pairs are either $\hat b$-pa…

Type-2 zero-problem lower-bound conjecture. If $(v-1)t-v>0$ and $s_t>(v-1)s_v$, then

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 optim…

One-third lower-bound conjecture. For all $m>s\geq 2$,