Imam Ali by his actions
Quran 5:55: Your guardian is only Allah, His Apostle, and the faithful who maintain the prayer and give the zakat while bowing down during prayer.
Quran: Al-Ma'idah (5:55)
Translation: Sarwar

Only God, His Messenger, and the true believers who are steadfast in prayer and pay alms, while they kneel during prayer, are your guardians.

 
Translation: Qarai

Your guardian is only Allah, His Apostle, and the faithful who maintain the prayer and give the zakat while bowing down.

 
Translation: Shakir

Only Allah is your Vali and His Apostle and those who believe, those who keep up prayers and pay the poor-rate while they bow.

 
Translation: Daryabadi

Your friend is but Allah and His apostle and those who have believed- those who establish the prayer and give the poor-rate while they bow down.

‏إِنَّمَا وَلِيُّكُمُ ٱللَّهُ وَرَسُولُهُۥ وَٱلَّذِينَ ءَامَنُوا۟ ٱلَّذِينَ يُقِيمُونَ ٱلصَّلَوٰةَ وَيُؤْتُونَ ٱلزَّكَوٰةَ وَهُمْ رَكِعُونَ
Reference  : Quran: Al-Ma'idah 5:55
 
Abu Dharr narrates that the events that led to the revelation of Quran 5:55, making it clear the verse was revealed specifically about Imam Ali.
Tafsir al-Kabir, Vol 12. Page 28
Narrated Abu Dharr:

It was narrated on the authority of Abu Dharr, may God be pleased with him, that he said: I prayed with the Messenger of God, may God bless him and grant him peace, one day, the noon prayer, and a begger begged in the mosque, but no one gave him anything, so the begger raised his hand to the sky and said: O God, I bear witness that I begged in the mosque of the Messenger, may God bless him and grant him peace, and no one gave me anything. Ali, peace be upon him, was bowing [in prayer], so he gestured to him with his right little finger, and there was a ring on it. So the begger approached until he took the ring in the presence of the Prophet, may God’s prayers and peace be upon him, and the Prophet said:

 

“Oh God, my brother Musa asked you.” He said: "My Lord, expand my chest for me" [Quran 20:25] to the saying "and associate him in my affairs" [Quran 20:30] So Allah (swt) sent down a speaking Qur’an: "We will strengthen you with your brother and grant you both authority." [Quran 28:35] Oh God, I am Muhammad Your Prophet, so expand my chest for me and ease my affairs for me and appoint for me a vizier from my family, strengthen me through him. Abu Dhar said: By God, the Messenger of God did not complete this word until Gabriel descended and said: "O Muhammad, read "Your guardian is only God and His Messenger" [Quran 5:55] to the end, so this is a entirety related to the narratives in this matter.

 

Ataa narrated on the authority of Ibn Abbas that it was revealed about Ali Ibn Abi Talib, peace be upon him.

 

It was narrated that Abdullah bin Salam said: When this verse was revealed, I said, O Messenger, I saw Ali in charity with his ring on a needy person while he was bowing, so we take care of him.

روى عطاء عن ابن عباس أنها نزلت في علي بن أبي طالب عليه السلام . روي أن عبد الله بن سلام قال : لما نزلت هذه الآية قلت يا رسول أنا رأيت عليا تصدق بخاتمه على محتاج وهو راكع ، فنحن نتولاه . وروي عن أبي ذر رضي الله عنه أنه قال : صليت مع رسول الله صلى الله عليه وسلم يوما صلاة الظهر ، فسأل سائل في المسجد فلم يعطه أحد ، فرفع السائل يده إلى السماء وقال : اللهم أشهد أني سألت في مسجد الرسول صلى الله عليه وسلم فما أعطاني أحد شيئا ، وعلي عليه السلام كان راكعا ، فأومأ إليه بخنصره اليمنى وكان فيها خاتم ، فأقبل السائل حتى أخذ الخاتم بمرأى النبي صلى الله عليه وسلم ، فقال :

«اللهم إن أخي موسى سألك » فقال : { رب اشرح لي صدري } إلى قوله { وأشركه في أمري } فأنزلت قرآنا ناطقا { سنشد عضدك بأخيك ونجعل لكما سلطانا } اللهم وأنا محمد نبيك وصفيك فاشرح لي صدري ويسر لي أمري واجعل لي وزيرا من أهلي عليا أشدد به ظهري . قال أبو ذر : فوالله ما أتم رسول الله هذه الكلمة حتى نزل جبريل فقال : يا محمد إقرأ { إنما وليكم الله ورسوله } إلى أخرها ، فهذا مجموع مع يتعلق بالروايات في هذه المسألة

Book  : Tafsir al-Kabir
Author  : Fakhr al-Din al-Razi (534 AH - 606 AH)
English reference  : 
Arabic reference  : Vol. 12, Page 28
Narrated by: Abu Dharr.
 
Imam Ali by his attributes
Quran 4:59: Obey Allah, Obey the Messenger and those in Authority among you

Reference: Quran: An-Nisa 4:59

Quran: An-Nisa 4:59
Translation: Dr. Mustafa Khattab, the Clear Quran

O believers! Obey Allah and obey the Messenger and those in authority among you. Should you disagree on anything, then refer it to Allah and His Messenger, if you ˹truly˺ believe in Allah and the Last Day. This is the best and fairest resolution.

‏يَٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ أَطِيعُوا۟ ٱللَّهَ وَأَطِيعُوا۟ ٱلرَّسُولَ وَأُو۟لِى ٱلْأَمْرِ مِنكُمْ ۖ فَإِن تَنَزَعْتُمْ فِى شَىْءٍۢ فَرُدُّوهُ إِلَى ٱللَّهِ وَٱلرَّسُولِ إِن كُنتُمْ تُؤْمِنُونَ بِٱللَّهِ وَٱلْيَوْمِ ٱلْءَاخِرِ ۚ ذَلِكَ خَيْرٌۭ وَأَحْسَنُ تَأْوِيلًا
Reference  : Quran: An-Nisa 4:59

Note: 1. Obeying, by definition is unconditional. To obey unconditionally, those in authority among you must be infallible, else we could be committing a sin. Hence, we can conclude that the only types of people this can possibly apply to are the Ahlulbayt, who Allah (swt) has purified in Quran 33:33.

2. Allah (swt) reminds us in Quran 14:22: Be careful of who you take as your leader, if they misguide you, they will not be able to protect you on the day of judgement.

3. It's evident that those in authority of the Muslim ummah did order Muslims to sin, for example, Abd Rabb al-Ka'ba testifies that Mu'awiayh ordered them to unjustly consume wealth and kill one another. Clearly, Allah (swt) cannot be telling us to obey such people unconditionally.

4. The Quran also tells us in Quran 11:113: Do not incline to those who do wrong, and therefore this verse can only refer to those who are infallible, the AhlulBayt.

 
Quran 33:33: Only the Ahlul-Bayt have been purified by Allah (swt), and only they can meet the criteria established by Allah (swt) for leadership and authority.

Reference: Quran: Al-Ahzab 33:33

Quran: Al-Ahzab 33:33
Translation: Pickthall

Allah's wish is but to remove uncleanness far from you, O AhlulBayt (Folk of the Household), and cleanse you with a thorough cleansing.

 
Translation: Dr. Mustafa Khattab, the Clear Quran

Allah only intends to keep ˹the causes of˺ evil away from you and purify you completely, O AhlulBayt (members of the ˹Prophet’s˺ family).

 
Translation: Saheeh International

Allah intends only to remove from you the impurity [of sin], O people of the AhlulBayt (Prophet's household), and to purify you with [extensive] purification.

‏وَقَرْنَ فِى بُيُوتِكُنَّ وَلَا تَبَرَّجْنَ تَبَرُّجَ ٱلْجَهِلِيَّةِ ٱلْأُولَىٰۖ وَأَقِمْنَ ٱلصَّلَوٰةَ وَءَاتِينَ ٱلزَّكَوٰةَ وَأَطِعْنَ ٱللَّهَ وَرَسُولَهُۚۥٓ إِنَّمَا يُرِيدُ ٱللَّهُ لِيُذْهِبَ عَنكُمُ ٱلرِّجْسَ أَهْلَ ٱلْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًۭا
Reference  : Quran: Al-Ahzab 33:33
 
A'isha identifies who the members of the AhlulBayt are, and who was purified in Quran 33:33

Reference: Sahih Muslim 2424

Sahih Muslim 2424
`A'isha reported:

that Allah's Apostle (ﷺ) went out one norning wearing a striped cloak of the black camel's hair that there came Hasan b. 'Ali. He wrapped hitn under it, then came Husain and he wrapped him under it along with the other one (Hasan). Then came Fatima and he took her under it, then came 'Ali and he also took him under it and then said:

Allah only desires to take away any uncleanliness from you, O people of the household (AhlulBayt), and purify you (thorough purifying) - (Quran 33:33)

حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، وَمُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ، - وَاللَّفْظُ لأَبِي بَكْرٍ - قَالاَ حَدَّثَنَا مُحَمَّدُ بْنُ بِشْرٍ، عَنْ زَكَرِيَّاءَ، عَنْ مُصْعَبِ بْنِ شَيْبَةَ، عَنْ صَفِيَّةَ بِنْتِ شَيْبَةَ، قَالَتْ قَالَتْ عَائِشَةُ خَرَجَ النَّبِيُّ صلى الله عليه وسلم غَدَاةً وَعَلَيْهِ مِرْطٌ مُرَحَّلٌ مِنْ شَعْرٍ أَسْوَدَ فَجَاءَ الْحَسَنُ بْنُ عَلِيٍّ فَأَدْخَلَهُ ثُمَّ جَاءَ الْحُسَيْنُ فَدَخَلَ مَعَهُ ثُمَّ جَاءَتْ فَاطِمَةُ فَأَدْخَلَهَا ثُمَّ جَاءَ عَلِيٌّ فَأَدْخَلَهُ ثُمَّ قَالَ ‏{‏ إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا‏}‏‏
Reference  : Sahih Muslim 2424
In-book reference  : Book 44, Hadith 91
Additional References:
 
Imam Ali by name in the Quran
Quran 26:83-84: Ibrahim asks Allah for a "Tongue of Truthfulness" among future generations.
Quran.com: Ash-Shu'ara 26:83-84
Translation: Arberry & Saheeh International

[Abraham says:] My Lord, give me Judgment, and join me with the righteous,

 

and appoint me a tongue of truthfulness among the later generations.

رَبِّ هَبْ لِى حُكْمًۭا وَأَلْحِقْنِى بِٱلصَّلِحِينَ

وَٱجْعَل لِّى لِسَانَ صِدْقٍۢ فِى ٱلْءَاخِرِينَ

Note: Tongue of Truthfulness is a verbatim transation.

 
Quran 19:49-50: Allah responds: and We appointed unto them a tongue of truthfulness, Ali-ya
Quran: Maryam 19:49-50
Translation: Arberry

So when he had left them and those they worshipped other than Allah, We gave him Isaac and Jacob, and each [of them] We made a prophet.

 

and We gave them of Our mercy, and We appointed unto them a tongue of truthfulness, Ali-ya.

فَلَمَّا ٱعْتَزَلَهُمْ وَمَا يَعْبُدُونَ مِن دُونِ ٱللَّهِ وَهَبْنَا لَهُۥٓ إِسْحَقَ وَيَعْقُوبَ ۖ وَكُلًّۭا جَعَلْنَا نَبِيًّۭا

وَوَهَبْنَا لَهُم مِّن رَّحْمَتِنَا وَجَعَلْنَا لَهُمْ لِسَانَ صِدْقٍ عَلِيًّۭا

Reference  : Quran: Maryam 19:49-50

Note: 1. Ali-ya is translated by Arberry as sublime, but we see from the previous verse (19:49) that Allah (swt) mentions Isaac and Jacob by name, and therefore can infer that Ali-ya is indeed the name of Imam Ali.

2. A sublime or high tongue of truthfulness (لِسَانَ صِدْقٍ عَلِيًّۭا) is not an idiom or expression used in vernacular, poetic nor historical Arabic. Therefore, it must be a name.

3. Inventing an idiom could contradict Quran 12:2

4. Why is not more explicit? Mu'awiyah invoked the "Sunnah" of cursing Imam Ali from the pulpit during Jummah prayers every Friday. This sunnah continued for approximately 70 years and would have resulted in the Quran being changed by Banu Ummayah.