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I think there's some way of setting up Levels 1, 6, and 7 to get some sort of cycle on the gravity block or otherwise break it. I have no idea how to actually do it though.

Finally figured it out, so sneaky and so much fun!

Here are some hints (in rot13) because this is a tough one!

1. Gb jva, lbh arrq gb erghea gb gur fgnegvat cbvag naq pbaarpg lbhe genpxf vagb n ybbc.

2. Jura svyyvat bhg gur svefg svir fgngvbaf (jvgu rkpynzngvba znex uvagf), tvir lbhefrys nf zhpu fcnpr ba gur vafvqr nf lbh pna znantr. Lbh’yy arrq vg yngre.

3. Fgngvbaf fvk guebhtu avar ner gur sbhe erznvavat fgngvbaf ba gur gbc unys bs gur znc.

4. Fgngvba gra vf gur bar ba gur sne yrsg.

5. Fgngvbaf ryrira guebhtu guvegrra ner ba gur evtug. Lbh’yy cnff bire gur bar erznvavat fgngvba arne gur fgnegvat cbvag naq erghea gb vg yngre.

6. Gb pybfr gur ybbc, lbh’yy arrq gb jvaq nebhaq gur ybjre yrsg cneg bs gur znc.

You have three rooms to find:

8,11: double teleport from 8,16. Spawn an extra kitten using the flag at the entrance.

6,10: you get there through a wormhole in 8,15, which you access from 8,20. Create an extra kitten there and use it to reach the two lower wormholes. You'll need at least three.

15,8: MetaMetaPuzzle posted a hint below.

You can access 7,20 through either "hole" in the top wall of 7,21. The right hole gets you the star in 7,20 and the left hole helps you get to the star in 7,21.

If the timing is right (which is why MetaMetaPuzzle said you have to "waste" a move), you can push a dead cat through the splitter that would otherwise destroy it. If you've reached 12,13, the mechanic is demonstrated there.

I don't think there's any room built into the game proper that allows you to get to 4,4. My hint is that you'll have to figure out how to make it yourself.

Got it, thanks!

Now to figure out how to get to 13,13.

I'm completely stumped as to how to get the star in 7,20. I've got here (which gets me to 7,21's star) but I can't figure out how to get to the hallway. I feel I should somehow be able to push my way up through the splitter on the top right of the room below, but I can't make it work. Any hints?