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Is there some sort of discord or a place where you can share your times?

I've been thinking about opening a Discord server, but until then, the best place is probably here: https://www.speedrun.com/mobility. They also have leaderboards for individual levels, and some people who are currently actively speedrunning the game!

thank you!

I know you asked this five months ago, but there is actually a  discord server for this game where you can share level times or full game times. Here is the link.