https://docs.ordinals.com/inscriptions/recursion.html says:

Note: <SAT_NUMBER> only allows the actual number of a sat no other sat notations like degree, percentile or decimal. We may expand to allow those in the future.

But it turns out that all the /r/sat/<SAT>/at endpoints work with all sat notations, but the other /r/sat/ endpoints only work with sat numbers.

So the docs are inaccurate, and the API is counterintuitive in what it accepts as a sat reference.

These all work:

• https://ordinals.com/r/sat/153899938226999/at/0
• https://ordinals.com/r/sat/mtkeanvredm/at/0
• https://ordinals.com/r/sat/30779.4938226999/at/0
• https://ordinals.com/r/sat/0°30779′539″4938226999‴/at/0
• https://ordinals.com/r/sat/7.328568495061381%25/at/0

But only the first of these 5 work:

• https://ordinals.com/r/sat/153899938226999
• https://ordinals.com/r/sat/mtkeanvredm
• https://ordinals.com/r/sat/30779.4938226999
• https://ordinals.com/r/sat/0°30779′539″4938226999‴
• https://ordinals.com/r/sat/7.328568495061381%25

Ideally all sat endpoints would accept all sat notations.