which... I think I understand now.... I was misunderstanding how the serialized path is constructed slightly.
252551111 does not mean start at 25,25 as one might naturally expect.
It instead means start at 25,24 and move as follows.
Move down (5) to 25,25
Move up (1) to 25,24
Move up (1) to 25,23
Move up(1) to 25,22
Move up(1), to 25,21
Furthermore, it's smarter than one might expect for a simple serialized path, and will realize you are already at 25,25 and skip the first move accordingly.