Capacity characterization conjecture for general layered erasure channels

A general layered erasure channel has layers indexed by $l\in\{1,\dots,q\}$, and let Theorem $1$ denote the theorem giving an outer bound on its capacity region. The moderate-interference conditions are denoted by $(\mathrm{moderate:c1})$ and $(\mathrm{moderate:c2})$. Capacity characterization conjecture. Theorem $1$ characterizes the capacity region of general layered erasure channels satisfying the condition that there does not exist $l\in\{1,\dots,q\}$ such that either condition $(\mathrm{moderate:c1})$ or condition $(\mathrm{moderate:c2})$ holds. The conjecture is motivated by the authors' view that the limitation of the theorem arises from their limited understanding of moderate interference with $q=1$; the general capacity region is otherwise described as potentially complicated, and no resolution is given here.