[gambler]

> I'll cheat by making my "large file" the output of a PRNG, meaning I don't have to store any of it, but other people do because they don't know the seed.

This will work, but only until the file is sufficicently changed/expanded by the networks as the result of transactions.

(I probably should have said it explicitly: the file would be shared by all participants.)

You can also generate the file by recording something random everyone can observe, like records of a stock market, temperature of some location, etc. I don't see any reason it would have to be perfectly, cryptograhically random.

And yes, a single participant could "help" other nodes by responding to challenges instead of them. But think about the economics of how that would work over time.

I'm not saying that what I described is a full, working, tamper-proof protocol, but I think something interesting can be built based on the core idea.