But I don't see anything about verification and Nash equilibrium. I do not see a complete specification of how the mining and verification works and the game theory thereof.
That's funny - first you criticise Vitalik for being too abstract and "in the clouds" and now you criticise AT for being too practical and grounded.
If you would like to do some mathematical analysis you are most welcome to but you should realise that I didn't have anything to do with either of the two blockchains that AT runs on (and AT isn't a blockchain so your question about mining makes very little sense actually as the two blockchains in question work entirely differently).