I'm guessing it's kickflip, heelflip, bs shuv, and fs shuv.

Your definition leaves out varial heels and inward heels.

Edit: On second thought I'm still not sure, I saw this in the paper, and I'm guessing they're classifying both direction shuvs as the same, and kick/heelflip as the same

Below we list these four tricks with their corresponding residue class in Z/4Z.

0 ↔ Ollie

1 ↔ 180 Shove-it

2 ↔ 360 Shove-it

3 ↔ 540 Shove-it

Another interesting choice of representatives is given by a combination of the shove-it and the kickflip.

0 ↔ Ollie

1 ↔ 180 Shove-it

2 ↔ Kickflip

3 ↔ Varial Kickflip