Is it permissible for a man to return to his wife, whom he divorced with an irrevocable triple divorce using the words "You are thrice divorced," after an unregistered marriage, and this being before the expiry of her 'iddah and without documentation or witnesses?

The husband's statement to his wife, "You are divorced by three," effects three divorces according to the majority of scholars, including the four Imams, and this is the established practice. With this, the woman becomes irrevocably divorced (baynunah kubra), and she is not permissible for him again until she marries another man, he consummates the marriage with her, and then he separates from her and her waiting period (iddah) from him ends. Some scholars, like Ibn Taymiyyah, held the view that a divorce pronounced with the phrase "by three" counts as a single divorce. Furthermore, documenting marriages in courts serves significant interests.