The paper is deeply flawed. The most important flaw is admitted by the authors in the paper in the final paragraph of Part 1.:

"Until we reach the point we can formally establish that users are incentivized to broadcast their transactions to multiple nodes, we ask readers to treat this assumption as a design parameter as well."

To put it simply, the proof requires behavior by users which is neither incentivised or enforced. Other egregious flaws are that the "proof" insists that sybil actors do things not required of non-sybil actors, i.e. add unnecessary routing hops, and that sybil actors are arbitrarily excluded from being the orgin node.