I'd be curious to hear more about how you do the 2 -> 3 embedding there. In S2 it uses cartesian three space, but points are constrained to be unit magnitude. This has advantage and disadvantages obviously.
I'd like to hear more about the synthetic part of these three spaces, because S2 works exactly as you say, embedding the 2-sphere in three (cartesian) dimensions. S2 points are always three dimensional.
You can do this with [S2](https://s2geometry.io/) as well which has the very nice property that parent cells do indeed always contain their children, and sorting the cell ids puts them into in-order order.
The Box is very frustrating, especially when there's no one handling the other things, yet you're still not allowed to do them because it'd make the wrong people look bad.
This person admits he drove people to quit with his behavior, that goes wayyyyyy beyond trying to get the full details. I've worked with this type before and I can envision the cold sweats in the office as he comes around to hold people hostage explaining every micro-detail of their work until he understands it.
I've worked with this particular kind of toxic personality, they think until they've personally internalized all the details, that its not "right", and will exhaust everyone doing so.
They were also loose powder hand loaded weapons, you could fire three rounds a _minute_ if you were really skilled. Everyone in town had to store their powder in a (secure) communal location because it was, duh, an explosive.