Polishing the heart through repentance

It is narrated from Sayyiduna Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "When the servant commits a sin, a black spot is placed upon his heart. Then, if he repents, his heart is polished clean; and if he sins again, that spot grows until it overcomes his heart. That is the 'ran' (rust) which Allah, the Mighty and Majestic, has mentioned: 'No! Rather, the rust (of their evil deeds) has covered their hearts.' [Surah al-Mutaffifin: 14]"
This is a hadith that has not been recorded in the "Two Sahihs", although Imam Muslim used the hadiths of al-Qa'qa' bin Hakim from Abu Salih as evidence.

It is narrated from Sayyidah Aishah (may Allah be pleased with her) that the Messenger of Allah (peace and blessings be upon him) was continually asked (by the people) about the Hour, until Allah Almighty revealed these verses: "What have you to do with the mention of it? To your Lord is its finality." [al-Nazi'at: 43, 44]
This is a hadith that has not been recorded in the "Two Sahihs", although it is preserved (mahfuz) and sahih on the condition of both of them (Imam Bukhari and Muslim), and both of them used the hadiths of Sufyan bin Uyaynah from al-Zuhri from Urwah from Aishah as evidence.

It is narrated from Sayyiduna Abu Hurayrah and Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with them both) that they both bore witness about the Messenger of Allah (peace and blessings be upon him) that he (peace and blessings be upon him) said: "When the servant says: 'La ilaha illallahu wallahu akbar' (There is no god but Allah, and Allah is the Greatest), his Lord affirms him and says: 'My servant has spoken the truth; there is no god but Me, and I am alone.' And when he says: 'La ilaha illallahu wahdahu la sharika lahu' (There is no god but Allah, alone, without any partner), his Lord affirms him and says: 'My servant has spoken the truth; there is no god but Me, and I have no partner.' And when he says: 'La ilaha illallahu lahul-mulku wa lahul-hamd' (There is no god but Allah; His is the dominion and His is all praise), Allah says: 'My servant has spoken the truth; there is no god but Me; the dominion is Mine and the praise is Mine.' And when he says: 'La ilaha illallahu wa la hawla wa la quwwata illa billah' (There is no god but Allah, and there is no ability (to turn away from sin) and no strength (to do good) except through Allah), Allah says: 'My servant has spoken the truth; the ability (to avoid evil) and the strength (to do good) are only through Me.'"
This is a hadith that has not been recorded in the "Two Sahihs", although both of them used the hadith of Abu Ishaq from al-Agharr from Abu Hurayrah and Abu Sa'id as evidence, and they are agreed on taking the hadiths of Isra'il bin Yunus from Abu Ishaq as proof.