Unfortunately, this doesn't appear to be true. So far all proposed proof of stake systems suffer from problem that miners don't consume a resource to attempt to

Unfortunately, this doesn't appear to be true. So far all proposed proof of stake systems suffer from problem that miners don't consume a resource to attempt to contribute to the consensis. In other words, the problem of proof-of-statke is that there is nothing at stake. There is no reason for a miner to not attempt to extend every chain that they can— or at least every that they don't hate— and, in fact, doing so is the solution maximizing behavior. In proof of work, by comparison, miners must choose to expend a resource for every attempt and so an effort to try to mine on one fork requires a choice to not spend that resource on other ones. The best strategy then becomes putting all your effort on one chain which you think most likely to survive. Optimal POS strategy is to mine all forks you can, just in case any survive. This issue seems fundamental, but perhaps someone someday will find a clever way around it be changing assumptions. Peercoin was attacked this way— a miner grinding out alternative histories and finding ones where they were awarded almost every block— _immediately_ when POS mining became possible on it. The attack was thwarted because PPC has a central control mechanism where its developer cryptographically signs blocks to force the network to accept them over longer, otherwise better, chains... and it was later closed off by requiring POW blocks to select the POS blocks that can mine. (But now, the security of that coin reduces to the security of POW and the security of the signing key controlled by its pseudonymous developer). See also section 5 of https://download.wpsoftware.net/bitcoin/asic-faq.pdf https://download.wpsoftware.net/bitcoin/asic-faq.pdf