Ah, I see! In that case, I think "Attribute Clock" is actually perfect. Likening it to a clock definitely feels right to me, especially since there's the cultural context of the "top of the clock" (noon, midnight) being powerful/important, just like how 13 is on your clock. I love this idea btw!

This is such a cool concept!!! Is there a mechanic where you go around the clock somehow? In my TTRPG The Encore playbook can enter a Loop where they can only do certain actions in the defined order of the loop. I almost called it the Cycle, maybe that name's better suited for you!