[firechickenbird]

> That is not entirely true

what are you referring to?

Obviously x^4 != x^10, but noone has ever proven that "if SAT is P, then it would have the lowest (or highest) polynomial complexity among the other problems", or anything similar

[Hendrikto]

I was referring to this:

> [All NP-hard problems] have equivalent difficulty.

I get what OP meant, but there can still be some NP-hard problems that are more difficult than others.

As I said, x^4 and x^10 are both polynomials. I wouldn‘t call them "equivalent" though.