One possible way to incentivize the existence of more Bitcoin network nodes
is by paying peers when they provide data in the blokcchain. One of the
problems is that it is not easy to tell if the peer is really providing a
useful service by storing the blockchain or it is just relying the request
to some other peers as a proxy.

In this post I review the use of asymmetric-time functions to be able to
prove unique (IP-tied) blockchain storage and propose improvements to make
it fully practical.

Full post here:
https://bitslog.wordpress.com/2015/09/16/proof-of-unique-blockchain-storage-revised/

Best regards, Sergio.