It seems well-known among the community that on Level 1, hopping at the start of the level consistently saves 1 frame (4.17) compared to simply holding right (4.20). After staring at the source code for 3 days last month, I figured out why this works.

The bug: this comes from the code that handles speed limiting. When not burning flow, if you're not at max speed at the start of a jump, then you can accelerate up to 10% faster than the intended max speed while in the air. (This does not work when burning flow, so I don't expect this to be useful outside of Levels 1, 2, and 17.)

The execution: jumping at the start of a level, or slowing down right before a jump. This GIF shows (afaik) the first recorded 4.13 on Level 1, using this trick: https://gfycat.com/barrenunfoldedgnu Here the slowing down was achieved by releasing right for 1 frame, before holding up and right the next frame. However, I later realised that tapping down before jumping is a much easier method; you don't have to release right.

The time savings: after learning this trick, it is fairly easy to get 4.10 or 4.13 consistently on Level 1. It is possible, but rare, to get a 4.07. Using this trick, my individual level PBs on Levels 1, 2, and 17 are 4.03, 7.33, and 6.97 respectively. (For reference, WR splits are 4.20, 7.53, and 7.27.) I estimate that I can get each of these with 1% chance, so realistically this trick might give only a half-second time save throughout the entire run.