As a one-time mathematician, this was a really fascinating article. The similarities seem to be entirely coincidental, but what would have been my doctoral dissertation was also about generalizing some concepts from smooth manifolds to a "non-smooth" setting, and the crux of my work also hinged on optimal transport.
Actually I feel optimal transport is a pretty underrated concept in both pure and applied math, and I would have loved to explore it had I continued in academia. But oh well, one must make choices in life...
Small world. My graduate research was precisely on this topic as well. I was going in a more algebraic direction, though. My master's thesis was essentially about different discrete analogues of curvature using cooked-up cohomological constructions.
I really wish academia consistently provided as much security as industry. Would have loved to continue this line of research.