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It is intentional that cheats disable saving and there is no intended way around that. Editing the save file also is not allowed and the game detects if you have tampered with it. Obviously you could get around that, given the game is open source, but let’s try to not cheat and see if we can get you past the part another way.

The good news is, you don’t need to beat this part. From The Anti-Hub there are three sections - you need to beat just one of them so you can beat the game.

However, all three ways from The Anti-Hub are only open if you have completed all three ways from The Hub (and gotten all three abilities). The two alternate routes are:

• Pushing Onwards, Multi Party Authorization, Tower of Impossible: all this is really easy once you have all three abilities from The Hub. In MPA you do need to be rather careful though, but it’s basically just a matter of patience here.
• Butterfly Effect, Kaizo, Kaaaart Race, Taking Out The Trash: apart from Kaaaart Race, it’s all rather easy, and Kaizo is a room intended to teach what you need to do to beat the race.

Now, as for beating Higher, Higher, Higher… the first half is really easy, so I assume you don’t have trouble with that part. The second half contains rows of blocks where half only let you through, and the other half only let the platform through. What one does here is stand on the platform so you’ll barely get through the part that lets you through and destroys platform, while being off center on the platform so that if you press the action button, the platform will move to the parts that would block you but let the platform through. Then you get close, and press both jump and action at the same time. The platform will move away from you, and you will jump through. At the apex of the jump, you release action (and jump, doesn’t matter if you do or not) and move towards the platform again to land on it. It’s a bit tricky, but once you know the trick, it’s easy even on a smartphone display.