I skimmed the article and saved it for later reading.

Just wanted to point out that continued fractions are also interesting for those trying to encode hierarchical data into SQL tables: https://arxiv.org/pdf/cs/0402051.pdf

Yeah, that's a good paper -- Vadim's nested-interval tree method is quite clever. For more related references, see...

Using rational numbers to key nested sets https://news.ycombinator.com/item?id=13517490

Gap keys are generally good enough.

On a related note, if you’re interested in clockmaking, the amazing YouTuber ClickSpring has an entire series where he builds a beautiful clock from scratch.