This is not the edges. The paper is about a simulation, not actual time travel. Simulated time travel, following typical rules, is just a regular ol' quantum system that you assign extra meaning to. It was provable that this would work - though still a technical challenge to make it happen.
Except - and apologies if I'm wrong, since I don't completely understand the article - it seems like they first proved that this was equivalent (under current understanding of QM) to a system that includes a CTC.
So it looks like it's proving "If quantum mechanics works, this describes a CTC."
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