This is a Numberlink puzzle.
(Click for larger size)
I will confess that I am not 100% sure of uniqueness on this puzzle. But be assured that the method I used to convince myself was not “try for awhile to find a different solution”. I did try with success to work out a proof. I’m just not as sure of each step as I would be for proving an ordinary puzzle’s uniqueness.
In my opinion this puzzle is a bit on the easy side for Numberlinks of this size, which means it’s still hard.