No, I'm proving that Bitcoin doesn't function at all like the PDF states. Words used like "trustless" are obviously not correct because a second layer of abstraction was added (pools) that invalidates much of what he says about voting. You're not participating in democracy, you're participating in a republic. If it was trustless, it would be a democracy. This is why PoW is a less efficient, worse scaling, resource wasting form of DPoS.
Your idea of a proof is something that I don't recognise. I'm not entirely sure what kind of government you have where you live, but where I live, you have to trust politicians, and that trust is abused on a regular basis.
POW is nothing like DPOS. DPOS is just plain POS turned on its head with a deterministic block production order. It is a reactive design subject to all kinds of social engineering attacks on top of the regular nothing at stake attacks. Producing a block costs nothing, therefore neither does attacking the chain.