What is the evidence that there are only four Rightly Guided Caliphs, and is it correct to include 'Umar ibn 'Abd al-'Aziz among them?

Question:
May Allah reward you, Honorable Shaykh. This questioner says: What is the evidence that there are only four caliphs? And is it correct to include 'Umar ibn 'Abd al-'Aziz (may Allah have mercy on him) among them as a caliph specific to him?

Answer:
Yes, the reality, the reality is this: the Messenger (peace and blessings be upon him) specified the caliphate for thirty years, specifying that it is with these four. The reality confirms this, and the consensus of the Companions confirms this. As for 'Umar ibn 'Abd al-'Aziz, he is a renewer (may Allah have mercy on him); he is considered among the renewers because he renewed the caliphate. So he is among the renewers in Islam, not among the Rightly Guided Caliphs. Yes, but he followed the example of the Rightly Guided Caliphs, renewed the matter of the caliphate, and even renewed Islam itself; he renewed in Islam. Yes. Husam. And he renewed. Yes.