Is it permissible to wear clothes with writing on the back? Has this been mentioned in the widely transmitted (mutawatir) hadiths? And if it is an independent juristic reasoning (ijtihad), what is the proof?

It is not necessary for the establishment of rulings to have a mutawatir hadith (a continuously recited hadith) or a specific report from the Prophet, peace and blessings be upon him. Rather, scholars exert their efforts to deduce rulings for matters not explicitly mentioned by analogizing them with those that are. There is no specific evidence regarding wearing clothes with writing on them. However, if the writing is something that Sharia holds in high esteem, such as the Qur'an or the names of Allah, then it must be safeguarded from anything that contradicts its veneration. It is disliked to mention the name of Allah except in a state of purity. Some scholars consider letters to be inherently sacred, whether written in Arabic or another language, especially if they are among the names of Allah. Wearing clothes with writing on them and sweating in them, or lying down in dirty places while wearing them, contradicts the veneration of what is written on them. Therefore, one should avoid wearing clothes that bear writing that is sacred in Sharia, and it is safer to avoid other types of writing as well.