What is the strong evidence from the Sunnah for a menstruating woman to break her fast in Ramadan? Is it confirmed that one of the Prophet's wives broke her fast? What is the wisdom behind her breaking the fast, despite the possibility of fasting without prayer, and that there is no evidence for breaking the fast in the Quran?

Islamic rulings are not derived solely from the Quran, but from the Quran, Sunnah, Ijma (consensus), and Qiyas (analogy). Whoever denies the Sunnah has denied the Quran, because the Sunnah clarifies the manner of prayer, zakat, Hajj, and other acts of worship. The authentic Prophetic Sunnah indicates that a menstruating woman is prohibited from fasting. In Sahih Al-Bukhari, the Prophet, peace and blessings be upon him, said regarding the deficiency in a woman's religious commitment: "Is it not that when she menstruates, she neither prays nor fasts?" They said, "Yes." He said, "That is from the deficiency in her religious commitment." Furthermore, Aisha, may Allah be pleased with her, mentioned that a menstruating woman was commanded to make up for missed fasts but not for missed prayers, and the Ummah has reached a consensus on this matter.