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The attack is needed to get by the enemies on higher difficulties.
The idea is to avoid circumstances that prevent you from being able to run.
You're the second person who said they got soft locked. I would love if you could point me to how that happened, as you should be able to spring jump out of that gap. I assume there is something I'm just not thinking of.

You know, you're absolutely right about the tutorial. I knew that there should be a tutorial but I was told over and over by people that I shouldn't have a tutorial in a platformer, that the level design should teach the mechanics without explanations. And I knew that that there were things that players would want to have explained as the game's mechanics are unique. But I let people convince me not to do it. I'm sorry about that.

You can pretty much get momentum with only a single tile of space. All you do is jump out and back in and jump out and back in. Even falling with the run button held generates momentum. Any air movement does, so you can get it just by jumping around.

I uploaded a clear video since a lot of people seem to be confused by this game, maybe this will show you the intended way if you want it: