[kamilner]

>Re: P != NP, I would say that question assumes a certain architecture, so while it might hold for Turing machines, the real question is is a HyperTuring/Turing machine really all there is?

No, P and NP are defined by an architecture, there's nothing to assume about it. E.g., P is defined as "problems solvable in polynomial time on a deterministic Turing machine".

[adamnemecek]

I think that you misunderstood what I meant by assumed. If I replaced it with implies would that clear the confusion?