So verification time alone is always less than trying candidates AND verifying.
That holds only if you verify a single number
again and again.
I'm not sure I'm following. My base is this:
So, I can check for correctness pretty easily, but to solve the problem it could take generating, inputting and verifying 10.000 tries max (or if I was looking for a DES 8-char password, a lot more) versus just checking for correctness.
On one hand I must have a process to increase the counter loop, input something, check something, restart the loop, on the other hand I only have a process of inputting / checking for the one final answer.
Say if the pin is 6666, or even 0000, in one process I've gone through many more steps to start generating and checking candidates, on the other hand I already know that the pin is 6666 or 0000 and I'm just checking it to see if the computational problem (cracking the pin) is solved.
The process of solving the computational problem (=finding the right pin) takes more time than simply verifying that the problem is solved with the right answer (=checking the pin). If that happens
for even one problem, then how can P=NP as a broader "rule"? It can't.