See gridcoin, it is a proof of stake currency where you can additionally earn coins via mostly useful scientific computing. It's a neat project, but it gives effective control to the boinc server managers. The users have to sign up to earn that way
my understanding is that gridcoin "rewards" people participating in boinc by incrementing numbers on a blockchain that uses proof of stake. It doesn't use scientific computing, like protein folding, as a proof of work for the chain itself, which is what the parent comment was all about.
I would love to be proven wrong, to see any reference that grc provides algorithmic benefit to boinc, as in "getting rewarded with grc is proof the provided solution for the requested scientific computation is correct", or even a little thing like storing the boinc participation statistics, but those are features of the boinc network independently from grc.
What grc provides to the scientific community is a weird incentive for monkey-brains: monkey brain sees grc number go up, monkey brain releases happy hormones. It is a mirror of the participation statistic on the blockchain, not because that makes sense, but because blockchain. Sure there is some theory that some monkey may give a monkey a banana for making their number go down and its number go up, but that transaction involves no scientific computation and is purely speculative.