What are the explicitly mentioned obligatory Hady sacrifices based on Quranic text?
Chapter on Ransom (Fidyah) and Penalty for Hunting
Al-Mughni
Book of Hajj
Primary text
Obligatory Hady not stipulated by vow is divided into explicitly mentioned and those inferred by analogy. The explicitly mentioned are four: two requiring the easiest available Hady (at least a sheep or one-seventh of a camel), one being the blood sacrifice for Tamattu', as per Quran 2:196, and the second being the blood sacrifice for confinement (Ihsar), also Quran 2:196. Both of these are obligatory in sequence, and if the Hady is not found, the replacement is ten days of fasting, by analogy with the Tamattu' sacrifice.
Supporting text
Two of the mentioned are based on free choice (Takhyeer): the expiation for harm (Fidyat al-Adha), Quran 2:196, which allows for fasting, charity, or sacrifice, and the Jaza' al-Sayd (compensation for hunting), Quran 5:95, which also allows for choice among offering a specific animal judged by two just men, feeding poor people, or fasting for the equivalent number of days. The obligation of sequence for Tamattu' and Ihsar Hady is due to Allah specifying them without giving a choice, implying necessary adherence unless inability intervenes.