Taitila तैतिल

Taitila is one of the seven movable karanas, which cycle eight times across half-tithis 2 to 57 of every lunar month. It therefore comes round roughly every four days, at any hour — its position is set by the Moon's elongation from the Sun, not by the calendar.

A karana is six degrees of the Moon's elongation from the Sun — exactly half a tithi. Every tithi therefore contains two karanas, and every tithi boundary is also a karana boundary. Our engine computes the two independently and asserts they land on the same instant, which is how we know the boundary search is right.