Ottoman Empire
The highest position in Islam, caliphate, was claimed by the sultans starting since Murad I, which was established as Ottoman Caliphate. The Ottoman sultan, pâdişâh or "lord of kings", served as the Empire's sole regent and was considered to be the embodiment of its government, though he did not always exercise complete control. The Imperial Harem was one of the most important powers of the Ottoman court. It was ruled by the Valide Sultan. On occasion, the Valide Sultan would become involved in state politics. For a time, the women of the Harem effectively controlled the state in what was termed the "Sultanate of Women". New sultans were always chosen from the sons of the previous sultan. The strong educational system of the palace school was geared towards eliminating the unfit potential heirs, and establishing support among the ruling elite for a successor. The palace schools, which would also educate the future administrators of the state, were not a single track. First, the Madrasa (Ottoman Turkish: Medrese‎) was designated for the Muslims, and educated scholars and state officials according to Islamic tradition. The financial burden of the Medrese was supported by vakifs, allowing children of poor families to move to higher social levels and income. The second track was a free boarding school for the Christians, the Enderûn, which recruited 3,000 students annually from Christian boys between eight and twenty years old from one in forty families among the communities settled in Rumelia or the Balkans, a process known as Devshirme (Devşirme).

Q: The Ottoman Caliphate claimed by Murad Ir epresented what in Islam?
The highest position