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I tried to do something like that (http://proofpeer.net), but got lost in the details. Learnt a lot from it, but implementing your own cloud versioning system is probably more appropriate for a project with 100 million dollars funding, not 600000 pounds, half of which goes to university bureaucracy ;-)

I think formal abstracts (https://formalabstracts.github.io) is promising in principle (it doesn't focus on proofs though).

The Archive of formal proofs (https://www.isa-afp.org) is the biggest effort I know, but the logic (Isabelle/HOL) is not powerful enough for doing advanced mathematics comfortably, and the process of contributing is quite arcane.

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