Final answer:
Hazar Imam, also known as Aga Khan IV's father, was Prince Aly Khan. Shah Ismail, associated with the Safavid dynasty, claimed to be the Mahdi and established Shia Islam in his empire, while legitimate caliphs in Shia Islam were expected to have descent from Ali.
Step-by-step explanation:
Hazar Imam's father is Prince Aly Khan. The question pertains to the history of the Ismaili Muslims and their leadership. Hazar Imam refers to the current Aga Khan, who is Prince Shah Karim Al Hussaini Aga Khan IV. His father, Prince Aly Khan, was a notable figure in international diplomacy and the son of the previous Aga Khan, Sultan Mahommed Shah, Aga Khan III.
Regarding the provided reference material - Shah Ismail, a prominent historical figure within the Safavid dynasty, claimed several things about himself. After being exiled, Ismail returned to claim the title of Shah of Iran, and he declared himself to be the Mahdi or messiah. He was an influential leader who established the Safavid Empire's borders and created conflict with the Ottoman Empire. Eventually, he transformed the Safavid state into a stronghold of Shia Islam, thus designating himself as a spiritual leader and political ruler of significant historical importance.
Legitimate caliphs in Shia Islam, as the Safavids would assert, were expected to be descended from particular early figures in Islamic history, specifically Ali, the cousin and son-in-law of the Prophet Muhammad.