Bukhari

Hadith Commentary:
➊
The questioner was from Egypt; his intention was to raise objections against Hazrat Uthman (radi Allahu anhu), but Hazrat Abdullah bin Umar (radi Allahu anhu) gave sufficient and satisfactory answers to those objections.
This clarifies the virtue of Hazrat Uthman (radi Allahu anhu): that fleeing from the Battle of Uhud is mentioned by Allah Ta’ala in the Qur’an, and that they were forgiven and pardoned.
Despite not being present at the Battle of Badr, he was given a share equal to those who were present and attained a reward like theirs, which was not granted to any other absentee.
At the Pledge of Ridwan (Bay‘at al-Ridwan), the Messenger of Allah (sallallahu alayhi wa sallam) pointed to his right hand and said:
“This is the hand of Uthman (radi Allahu anhu).” This is a distinction that was not granted to anyone else.

➋
The person who came from Egypt was among the opponents of Hazrat Uthman (radi Allahu anhu), and out of astonishment, he asked Hazrat Abdullah bin Umar (radi Allahu anhu) three questions.
When he confirmed the answers to these questions, he exclaimed “Allahu Akbar” out of joy, but Hazrat Abdullah bin Umar (radi Allahu anhu) gave detailed answers to all three of his questions and told him:
“Now go, correct your belief, and stop spreading false propaganda.”

➌
Hafiz Ibn Hajar (rahimahullah), referencing Musnad al-Bazzar, has written that once Hazrat Abdur Rahman bin Awf (radi Allahu anhu) also raised these same objections, so Hazrat Uthman (radi Allahu anhu) himself gave him the same answers that Hazrat Abdullah bin Umar (radi Allahu anhu) gave to the objector.
(Fath al-Bari: 7/75)

Hadith Commentary: Imam al-Bukhari rahimahullah has indicated towards the view of the majority (jumhur) that among all the Companions, Abu Bakr al-Siddiq radi Allahu anhu holds superiority. Most of the early scholars (salaf) have held this opinion, and the majority among the later scholars (khalaf) have also said the same. Some researchers state that there is no definitive (qat‘i) text regarding giving preference among the four Rightly Guided Caliphs (khulafa’ al-arba‘a) over one another, therefore all four are superior. Some say that among all the Companions, these four are the most virtuous, and their caliphate, in the order in which it was established, is the correct and true order, and preference among them can only be given in this sequence. In any case, the view of the majority is given precedence. Preference among them can only be given in this sequence. In any case, the view of the majority is given precedence.

Hadith Commentary:
1.
In one narration, it is mentioned that in the presence of the Messenger of Allah (sallallahu alayhi wa sallam), we used to say:
The most virtuous in this Ummah is Abu Bakr (radi Allahu anhu),
then Umar (radi Allahu anhu),
then Uthman (radi Allahu anhu).
(Sunan Abi Dawud, Kitab al-Sunnah, Hadith: 4628)
In al-Tabarani, there is an additional detail that the Messenger of Allah (sallallahu alayhi wa sallam) would hear this but would not object.
(al-Mu’jam al-Kabir by al-Tabarani: 12/221, Hadith: 13132)
Imam al-Bukhari (rahimahullah) has supported the view of the majority in his chapter heading, that among all the Companions (radi Allahu anhum ajma‘in), Abu Bakr (radi Allahu anhu) possesses superiority and excellence. However, some researchers state that regarding giving preference to one over the other among the four Rightly Guided Caliphs, there is no definitive text, therefore all four are virtuous.
But in light of the aforementioned hadith, this position is less preferred, and the view of the majority is the stronger one.
Imam al-Shafi‘i (rahimahullah) says:
There is consensus among the Companions (radi Allahu anhum ajma‘in) and the Followers (tabi‘in, rahimahumullah) on this matter, that the most virtuous in the Ummah is Abu Bakr (rahimahullah), then Umar (rahimahullah),
then Uthman (rahimahullah),
and then the rank of Ali (rahimahullah).
(Fath al-Bari: 7/22)
2.
In the chapter heading, Imam al-Bukhari (rahimahullah) has used the word "ba‘d" (after).
This word is used for both remoteness in rank and status, as well as remoteness in place and time.
In this context, it refers to the first meaning: that after the rank and status of the Messenger of Allah (sallallahu alayhi wa sallam), the rank is that of Abu Bakr (radi Allahu anhu).
It does not refer to remoteness in place or time, because even during the lifetime of the Messenger of Allah (sallallahu alayhi wa sallam), the difference in rank and status between them was established.
(‘Umdat al-Qari: 11/391)