Ekadashi, Pradosh, Sankashti and other monthly fasting days.
This page lists the recurring monthly vratas for one month at one place, each dated by the tithi in force at the observance's own prescribed time rather than at sunrise. In a normal month that is Vinayaka Chaturthi, Durgashtami, both Ekadashis with the parana that follows them, a Pradosh Vrat in each fortnight, Purnima Vrat, Sankashti Chaturthi, Masik Shivaratri and Amavasya.
The doctrine is named on the page rather than left in the engine: Kane's History of Dharmasastra V.i, the vrata nirnaya, parana and vedha chapters. Every row carries the selection rule that produced it, so you can see whether the day was chosen because the tithi covered the prescribed window, because it merely existed in that window, or by a named tie-break. Nothing is scored or ranked, because no source weights one selection rule against another.
Ekadashi is emitted once per lineage, because Kane splits it at V.i pp.113-115 and the two reckonings can land on different days. The Smarta date uses suryodaya-vedha alone: the day whose sunrise falls inside the Ekadashi tithi.
The Vaishnava date adds arunodaya-vedha, so if the Dashami runs into the last four ghatikas before that sunrise the Ekadashi is rejected and the fast moves to the next day, the one covered by Dvadashi. On a doubled Ekadashi the earlier day goes to the Smarta reckoning (Narada Purana purvardha 29.45).
The arunodaya here is a fixed four ghatikas, exactly 96 clock minutes before sunrise, not a proportional muhurta, and that distinction is what decides the date. The parana, the breaking of the fast, is emitted with the Ekadashi from Kane V.i p.120 (the Kurma Purana).
Hari-Vasara is not computed: no classical locus for it appears anywhere in Kane Vol V Part I, including the Ekadashi chapter and the parana discussion, so it survives only as a labelled note describing a modern almanac convention.
Kane states the other half of the rule at V.i p.73: "all vratas to be performed in the evening or night have to be performed on the tithi existing in the evening or night even though it may be mixed up (viddha) with another tithi." So Pradosh Vrat is selected against the pradosha window, Masik Shivaratri against the nisitha, and Vinayaka Chaturthi against the madhyahna, which is Kane's own worked example at V.i p.74.
Durgashtami, Purnima and Amavasya are taken at sunrise, because their prescribed time is the day as a whole.
Those windows are proportional: one fifteenth of the actual daylight or night arc, because the day is always fifteen muhurtas however long it is (Mahabharata 13.126.36). They therefore open at different clock times in Delhi and in Chennai on the same date, which is why the page asks for a place before it will give you a month.
The yugmavakya is not implemented as a general engine. It is cited only where a named pair decides a genuine two-candidate tie, as with the Chaturthi pair of the 4th and 5th at Kane V.i p.72. Applying it everywhere would move dates the sources do not move.
The four Brahmavaivarta vedhas of Ekadashi - ativedha, mahavedha and the rest - are likewise not built. Kane names them and expressly passes them over, so they are not reconstructible from the names alone, and a reconstruction would be this app inventing a rule and attributing it to a text. The same discipline explains why no vrat on this page carries an auspiciousness number.
Sankashti Chaturthi is the Krishna Chaturthi, dated from the Smrtikaustubha 171-177 and the Vratarka 180-187. One that falls on a Tuesday is popularly called Angarki, and the page says so and also says that the name is usage rather than a rule from a located text, so the two are never confused.
Pradosh Vrat picks up weekday names the same way, Shani Pradosh on a Saturday and Soma Pradosh on a Monday. Because the pradosha window is an evening window, the weekday attached to it is the weekday of its own civil date. The popular name is printed where one exists and kept separate from the rule that fixed the day.