I love the puzzling mechanic, and how it requires understanding how the player's "brain" works to solve. I got stuck around level 7, and think I may have found a bug.
the puzzle is tough, but I think with a few more easier puzzles early on to make the behavior of the "player" easier to predict I think it could be a lot more approachable. maybe with some way to indicate what the players next move will be.
Left is previous state, right is error state after moving box down one: