3 problems

Fundamental limitation conjecture. This is a fundamental limitation of all methods using cheap linear bounds and branching.

Optimal-row conjecture. The row used for the optimal partition should be of a form similar to

Strict-decrease partitioning conjecture. If $l_k<l_k^{(i)}$, $u_k^{(i)}<u_k$, $l\le l^{(i)}$, and $u^{(i)}\le u$ for every $i\in\{1,2,\dots,p\}$, then the $k$th coordinate of the…