Time in a Bottle

If I could make days last forever

If words could make wishes come true

I'd save every day like a treasure and then

I'd play sudoku with you

Enough of that. This puzzle was made as a tribute to one of my favorite musicians, Jim Croce. The song can be found here. The inspiration for this puzzle comes from everyone's favorite setter, Richard. His original clock sudoku can be found here.

This is the third in a series of puzzles that are played on a Klein Bottle.

Ordinary sudoku rules apply. This puzzle takes place on a klein bottle. The top and bottom of the grid are glued together--they obey periodic boundary conditions (see the example on the left). The left and right side are twisted and then glued together (see the right side). The circles in the grid represent clocks. The four digits surrounding a white clock must strictly increase in a clockwise fashion starting from any of the four cells. The four digits surrounding a black clock must strictly increase in an anti-clockwise fashion starting from any of the four cells. All possible clocks are marked. (Don't forget the negative constraint!) Let me know if anything is unclear in the comments :)

Here is the puzzle. Enjoy! :)

Here is a penpa link courtesy of panthchesh. Thank you!