All we _ever_ have is an idea of the correct solution. There's no point at which we can ever say "this is the correct solution", at least not for any moderately sized software problem.

That being said, we can say

- Given the implementation options we've found, this solution/direction is what we think is the best

- We have enough information now that it is unlikely anything we find out is going to change the solution

- We know enough about the solution that it is extremely unlikely that there are any more real "problems/puzzles" to be solved

At that point, we can consider the solution "found" and actually implementing it is no more a part of solving it. Could the implemented solution wind up having to deal with an off-by-one error that we need to fix? Sure... but that's not "puzzle solving". And, for a lot of people, it's just not the interesting part.