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Mohammad Ghomi answered
Shortest closed curve to inspect a sphere,
in a paper, Shortest closed curve to inspect a sphere, posted to the arXiv (https://arxiv.org/abs/2010.15204),
whose PDF is available here,
verifying the conjecture that the shortest curve is four
consecutive semicircles each of length $\pi$ for a unit sphere.
It sounds like a natural demand. I'm not aware of its existence at the moment. Journals (not colleagues) have this role of reviewing, but the idea (public posting and reviewing) would be an interesting alternative.
There is a practical difficulty. From my observation so far, the majority the posts appearing and which are (explicitly or in disguise) reviewing ...