Diwali is a sequence, not a day. Kane's summary is that it spreads over about five days, and each of those days is fixed by its own rule anchored to its own division of the day - the trayodashi at dusk, the fourteenth at daybreak, the amavasya at night, the pratipada at night again, the second in the afternoon. This page dates each one for your city, states the rule and the text behind it, and where the rule is satisfied on two civil days it shows both rather than choosing.
Dates computed for New Delhi. A festival day is fixed by which tithi is running at a particular moment of the local day, so the civil date can move with the city - change it above if you are observing elsewhere.
Divali is not one day. Kane's summary of the sequence is that it spreads over about five days, so the trayodashi, the fourteenth, the amavasya night, the pratipada and the second are each dated here under their own rule. Where a rule is satisfied on two civil days and no tie-break for that observance is located in the sources, both days are shown and marked contested. Kane names the digests that would settle those cases and passes over them; those pages were not opened, so no rule is invented here to close the gap.
The days of Divali are not variations on one observance, and they are not decided the same way. Dhanteras falls on the thirteenth of the dark fortnight and is a dusk observance. Naraka Chaturdashi is the oil bath on the fourteenth, whose prescribed time is arunodaya - four fixed ghatikas, ninety-six minutes, before sunrise, which is not a proportional muhurta and does not stretch with the season.
The Lakshmi Puja falls on the night of the amavasya; the Krtyatattva describes a day whose earlier portion holds the fourteenth and whose night holds the amavasya, and names that night Sukharatrika. Bali Pratipada, or Govardhan Puja, is on the pratipada of the bright fortnight and its proper time is night. Bhai Dooj is on the second and is kept in the afternoon.
Because the anchors differ, the days do not always sit one after another on the civil calendar, and two of them can even land on the same date. That is a property of the rules, not an error in the arithmetic, and the page shows the anchor on every row so you can see which rule produced which day.
A tithi rarely lines up with a civil day. When the fourteenth is mixed with the thirteenth on one day and with the amavasya on the next, the rule for the oil bath can be satisfied twice, and something has to break the tie. Kane names the digests that address exactly this - the Nirnaya Sindhu, the Purushartha-cintamani and the Dharma Sindhu - and then says the matter is passed over. Those pages were never opened here.
So the engine does not break the tie. It renders both candidate days, marks the row contested, and prints the reason. Every other almanac silently picks one; what you gain from the honest version is the ability to see that there was a choice at all, and to make it the way your family makes it.
One tie-break IS implemented, because a verse names it. The Padma verse Hemadri quotes says that Shivaratri and Bali's day are to be observed on the day when the tithi is mixed with the preceding tithi. That verse names those two observances and no others, so the rule is applied to Bali Pratipada and to Maha Shivaratri, and nowhere else.
Dhanteras, Naraka Chaturdashi and the Lakshmi Puja amavasya all fall in a dark fortnight, and dark fortnights carry different month names in the two reckonings. In the amanta scheme used across the south and west, that fortnight belongs to Ashvina. In the purnimanta scheme of the north, the same days are Kartik. Bali Pratipada and Bhai Dooj are in the bright fortnight, where the two schemes agree, so both name them Kartik.
There is one place where Bali Pratipada nevertheless prints amanta Ashvina beside purnimanta Kartik, and it is worth knowing rather than being surprised by. The month label on each row is the month running at that civil day's SUNRISE, while Bali Pratipada is decided at night: in many years the amavasya is still running at sunrise and ends during the day, so the pratipada only reaches the evening window. The tithi shown on the row is still Shukla 1 and the observance is still Kartik Shukla Pratipada in both reckonings; what has not turned over yet is the sunrise label. The page says so on any row where that happens.
The engine computes in amanta names and prints the purnimanta name beside every date, so the sequence reads correctly whichever convention you were raised with. Nothing about the underlying date changes; only the label does.
Every anchor on this page is a moment of a local day: a dusk, a daybreak ninety-six minutes before a local sunrise, a night. Sunrise and sunset are functions of latitude, longitude and date, so the tithi in force at those moments is too, and the civil day the observance lands on can differ between two cities on the same evening.
Choose your city at the top of the page. The choice is remembered and shared with the daily panchang, the vrat calendar and the Hindu calendar month grid. Positions are computed to sub-arcsecond precision with the Lahiri ayanamsha.
This page will tell you which night the Lakshmi Puja falls on, and on whose authority. It will not give you a puja window, and that is a deliberate limit rather than an oversight: a per-festival ritual muhurat is a separate body of rules with its own loci, and that research has not been done in this engine. Publishing a window we cannot cite would be exactly the failure the rest of the page exists to avoid.
What can be said with a source is said. The Bhavisya, through Hemadri on vrata, has it that no one but children or the ailing should take a meal by day and that Lakshmi is to be worshipped in the evening. Kane also records that in Bengal Kali is worshipped on this day, corroborated by Underhill's The Hindu Religious Year of 1921. Those are statements about the observance, not clock times, and they are shown as such.
For educational purposes. Astrological interpretations are traditional and not a substitute for professional advice.