Skim is amazing, I've never had it crash on large documents or with keyword searches as Preview almost always does. Also has a great note-taking system for scientific / academic work. Not sure why it flies under the radar so much.
That's a fair critique, although I think you could mitigate that by decreasing the desired arclength - reducing Del S to 0.5 from 0.85 in your example mostly fixes the problem.
In the context of the game described in the post, the main variable we were concerned about was u_x, because we scaled difficulty by increasing it over time. This in fact results in flatter parabolas, so I actually had quite the opposite concern of what you outlined and might have over-optimized in that direction!
Thanks for taking the time to read and try out what's described in the post. It's my first time working on a technical blog, and I'm extremely grateful for any constructive feedback / criticism :)
[1] https://arxiv.org/abs/2207.09238