Tafsir of Al-Hajj 22:56

(The Sovereignty on that Day is for Allah) (The sovereignty: meaning the irresistible authority, complete mastery, and absolute disposal.) (On that day: meaning on the day when the Hour or its torment comes to them. It is also said: the day when their doubt vanishes—though this is not sound—and similar to this is the opinion that it means the day when they believe.) (For Allah: alone, without any partner at all, in such a way that no one has any disposal in any matter, neither in reality nor metaphorically, nor in form nor in meaning, unlike the world where some possess a degree of formal disposal. The tanwin in idhin (that day) serves as a substitute for the mudaf ilayh (the omitted genitive). The attribution of the ‘day’ to it is an attribution of the general to the specific. It is connected to the stability [of sovereignty] acting as the predicate.)

(He will judge between them: This is a new, inaugural sentence that serves as an answer to a question arising from the news that the sovereignty on that day belongs to Allah. The plural pronoun refers to the two groups: the believers and the disbelievers, due to their mention earlier and the fact that the subsequent detailing encompasses them both. Indeed, the mention of the disbelievers immediately preceding it might suggest it is exclusive to them, as if it were said: "What then will He, Glorified be He, do with the two groups at that time?" Thus, it was said: "He will judge between them" by recompensing them. It is also permissible for it to be a circumstantial clause (hal) relating to the Exalted Name [Allah].)

(Then those who believed and did righteous deeds: they are those who have no doubt regarding what was pointed to previously, regardless of how the object of belief is determined.) (In the Gardens of Bliss: meaning they are established in gardens containing abundant blessings.)