Kala vyapini is the single concept that separates a correct Hindu festival calendar from a plausible one. It translates roughly as "pervading the time period", and it is a question about overlap.
The question it asks
A tithi is a lunar day: the period during which the angular separation between Sun and Moon advances through twelve degrees. Because the Moon does not move at a constant rate, tithis vary in length — roughly 19 to 26 hours. They begin and end at arbitrary clock times, and they routinely span midnight.
A festival rule names a target tithi and a window of the day. Vyapti asks: does the tithi prevail during that window? Not "was it running at some reference instant", but "does it cover this interval, and by how much".
The windows
The windows are fractions of the local day and night, not clock times. Dinamana is sunset minus sunrise; ratrimana is next sunrise minus sunset. Everything is derived from those two quantities.
- Madhyahna — the day divided in fifths, taking the third fifth. Used by Ganesh Chaturthi.
- Aparahna — the fourth fifth of the day. Used by Vijayadashami.
- Pradosha — sunset to sunset plus two-fifteenths of the night, about 96 minutes. Used by Diwali and Dhanteras.
- Nishita — the eighth of fifteen night muhurtas, the midnight muhurta. Used by Maha Shivaratri and Janmashtami.
Because these scale with day length, the same festival can resolve to different days in Chennai and Kathmandu in the same year. An engine that stores muhurat windows as fixed clock times cannot represent that and will quietly serve one of those cities the wrong date.
Why different festivals use different windows
The window is not arbitrary — it reflects when the observance actually happens. Lakshmi Puja is performed in the evening, so the relevant question is which tithi is present in the evening. Shivaratri is observed at midnight, so nishita is the test. Ganesh Chaturthi centres on the midday installation, so madhyahna governs.
Once you see that, the apparent inconsistency between festivals dissolves. They are all applying the same rule to a different time of day.
When the answer is not clean
Two awkward cases arise constantly. Vriddhi is when a tithi is long enough to touch the required window on two consecutive days. Kshaya is when a tithi is short enough that it touches the window on neither.
The resolution order is fixed: full overlap on exactly one day wins outright; otherwise the larger overlap in minutes wins; otherwise the rule's declared strategy decides; and if the tithi never met the window at all, a classical fallback applies. Each branch produces a different confidence score, so you can always tell which one fired.