[doormatt]

Thanks so much for being so open and willing to discuss this!

Just to be clear though, if that lemma isn’t yet explicitly proven, then the core claim (that Algphys cannot simulate certain NP-complete solutions in polynomial time) has not been established. I agree the components may suggest difficulty in high-rigidity regions, but unless you formally prove that no polynomial-time Turing machine’s trajectory enters those regions, the P != NP conclusion doesn’t follow.

[LaghZen]

Thanks for the help! It will take at least a week to fix the gap. During the addition, I came across a more serious problem: there was a contradiction between the "hard" function (ε = 2^(—n)) and the statement Algphys ⊆ P. I'm dealing with this now, and I'll need additional verification.