Behind the observance sits a piece of arithmetic. A tithi is the time the Moon takes to open a further twelve degrees of separation from the Sun. Krishna Chaturdashi occupies the arc from 336 to 348 degrees of that separation. The Moon does not move at a fixed rate, and the same twelve degrees may take a little over nineteen hours near perigee or close to twenty six near apogee. A calendar has to name whole days, so the rule is that whichever tithi is current at sunrise gives the day its name. A tithi shorter than the interval between two sunrises can therefore be skipped entirely, which the tradition calls a kshaya tithi, and one longer than that interval can carry its name over two civil days, an adhika or vriddhi tithi. Both occur in the ordinary course of a year, and both are why an observance can appear on two dates in the same almanac.
Each tithi is halved again, and each half carries a karana, so the first half of Krishna Chaturdashi carries Vishti, the karana also called Bhadra, and the second Shakuni, first of the three fixed karanas that close the month. Vishti is the one karana the muhurta literature marks as unfit for beginnings, and its presence in the first half is why this tithi is read with more care than its neighbours. Seven of the eleven karanas repeat, cycling eight times through the month, while four are fixed to particular half tithis at the month's opening and close.
The Moon is waning through this arc, rising later each night and showing about 2 per cent of the disc lit, a thread visible only in twilight. The phase follows from the elongation and not the other way round, so the tithi and the shape of the disc are two readings of one measurement.