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Having carefully studied the decisions laid out in the Smrityarthasara original: Smṛtyarthasāra, an influential 12th-century legal digest, the works of Hemadri and Madhava Two of the most prominent medieval scholars of Hindu law and calendar systems, and the Nirnayasindhu A 17th-century authority on religious timing with great respect, I am now composing this work. It is called the Extraction of Decisions original: Nirṇayoddhāra. I have extracted the core essence of these texts for the benefit and pleasure of those with modest knowledge. || 1 ||
In this system, a lunar day Sanskrit: Tithi is of two types: the Pure original: Shuddha and the Mixed original: Viddha, literally "pierced".
A Pure lunar day is one that is complete and fit for performing rituals. A Mixed lunar day is one that is joined or overlapped by another lunar day. This "overlap" original: Vedha is generally considered to last for three muhurtas A muhurta is a traditional unit of time lasting 48 minutes; three muhurtas is roughly 2 hours and 24 minutes in the morning. However, some authorities state it is only two muhurtas. The solar measure should be established to confirm this.
Regarding the specific overlap rules for fasting: "A lunar day is considered 'pierced' or overlapped for the purpose of a fast if the previous day extends into it by a certain number of units." Specifically:
The rule is that one must accept the lunar day that actually covers the specific time required for the intended ritual.
For the Single-Meal Vow original: Ekabhakta, a penance where one eats only once a day, the lunar day prevailing during midday should be accepted.
Midday Sanskrit: Madhyāhna: In this context, it is defined as the third portion of the day when the daylight period is divided into five equal parts.
According to the scholar Madhava, if the required lunar day covers midday on both days, or on neither day, then the first day should be chosen.
For the Evening Vow original: Nakta-vrata, a fast broken only after seeing the stars, the lunar day prevailing during the Pradosha period should be accepted.
Pradosha: This is the period of three muhurtas (approximately 2 hours and 24 minutes) immediately following sunset. Some authorities argue it is only two muhurtas.
If the Pradosha period is covered by the lunar day on both days, or on neither, then the later day is preferred.
For the First Day of the Bright Fortnight original: Shukla Pratipad, the lunar day prevailing in the afternoon should be accepted. Madhava states that if it is not present in the afternoon, the one prevailing in the evening should be taken.
According to Hemadri, the second lunar day should be accepted if it prevails during midday. However, the third lunar day follows different rules, except in the case of the Rambha vow... The text breaks off here; Rambha Tritiya is a specific festival dedicated to the goddess Parvati