The tithi is the oldest of the five limbs of the panchanga and the least intuitive, because it is defined by an angle in the sky and not by a sunrise. Krishna Dashami occupies the arc from 288 to 300 degrees of that separation. Because the Moon travels an elliptical orbit its angular speed is not constant, so that twelve degree arc is crossed in anywhere from roughly nineteen to roughly twenty six hours. The convention that resolves this is simple and consequential: the civil day takes the name of the tithi that is running at sunrise. 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 Dashami carries Vanija, the merchant's karana, and the second Vishti, the karana also called Bhadra. Vishti is the one karana the muhurta literature marks as unfit for beginnings, and its presence in the second 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 30 per cent of the disc lit. 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.