What are the prerequisites to be a caliph (according to Muslim sources)?

There are several requirements that have been delineated that any potential candidate should meet. In his book An Introduction to History, Ibn Khaldun recorded exactly what the prerequisites are for assuming the mantle of the caliph.
Knowledge: the caliph can execute the divine laws only if he knows them, thus he cannot blindly accept tradition but must be capable of independent decision making.
Probity: the caliph must be unimpeachably honest, virtuous and just. He must be able to supervise the ulama' although there is dispute on whether this quality is nullified if the caliph engages in innovations of previously articulated and accepted Shari'a (theologically jurisdictional dogma).
Competence: the caliph must be willing to carry out the punishments fixed by Shari'a and be strong enough to fulfil his political duties. He must be willing to understand warfare, to be able to assume responsibility for engaging the Umma in war and to declare war. He must lead the Umma in the jihad against the enemy while maintaining religious laws and administering for the public good.
Physical fitness: the caliph must be sound in all senses and limbs, be free from any disabilities such as blindness, deafness, insanity or missing limbs or eyes. The requirement for, in essence, physical perfection precludes even physical deformity such as disfiguring features such as missing or extra digits, large facial birthmarks, etc.
A fifth requirement, one which is still debated because it seems to stem from Qureshi origin, is that the caliph must be of Qureshi (preferably of Hashemite) descent. Most jurists accept this but some like Baqilani and Ibn Khaldun do not stipulate this as a requirement.
A sixth requirement, that is unspoken because it is literally incomprehensible for Islam to consider otherwise, is that the caliph will be male.