I still believe there is some insight to gleem from the observation (conjecture or proven?) that converting deterministic intractable problems into tractable problems makes them nondeterministic and unbounded in entropy, but I am not seeing yet how to frame it in a way that proves anything. Perhaps proving that the conversion must be unbounded would prove P ≠ NP. I need to contemplate that.
On proving P ≠ NP, I do not understand why it can't be proven that the algorithmic Kolmogorov complexity of the "traveling salesman problem" is at least O(n2(2n-n-1)), i.e. an exponential lower bound, which is just below the O(n22n) of Held-Karp algorithm which is the best known algorithm
My logic is so simple, that I must be missing something.
Say I want to crack your 4 digit pin (0000-9999).
No matter what I do, I have to generate the numbers, try them, verify them.
Simply verifying the answer is just a subset of generating candidates/trying/verifying. So verification time alone is always less than trying candidates AND verifying.
Time spent (cracking + verifying) > (verifying), because verifying alone is (at least) -1 step.
So P ≠ NP.