The cat isn’t going up or down. It’s judging you from a higher dimension.
And truth be told, it doesn't matter. The cat has already decided you’re wrong.
Direction was never the question.
The edge of the stair tread, often called the nose, overhangs the riser a nominal 1 1/4 inch (I did that from memory after building three houses by myself.) The puzzle may have been unsolvable had if it had been a typical cement staircase, where the tread does not have a nose.
Up the stairs. Very easy to see, by concentrating on the edge of the stairs. No way the cat is going down. If the cat was going down, he/she would be going in the opposite direction.
I've done "extensive research" on this. When questioned Erwin Schrodinger said he didn't know if there was a cat or not, but Sandy Dennis did confirm there was a cat and without question, the cat was walking down the up staircase.
Down...I would like to think that cat would have enough sense to turn around if it was going up the steps.Besides the way it's paw are placed says down to me.