Perfect network coding solution conjecture for receiver packet-intersection instances

Let $\boldsymbol A$ be an instance of the paper's network-coding problem with $r$ receivers, where each receiver wants $r$ data packets and every pair of receivers wants at most one data packet in common. Perfect network coding solution conjecture. The instance $\boldsymbol A$ has a perfect network-coding solution $\mathcal S_p$. The claim is presented as the corresponding network-coding conjecture arising from the hypergraph-coloring reduction; the supplied source gives no resolution status, so it is recorded as open.