שולחן ערוך · אורח חיים

The laws of the tsitsit on Chabbat. This siman has 3 seifim:

Seif 1: the four tsitsyot condition one another (מעכבות זו את זו): as long as the four are not all [present], the garment is not מצוייצת כהלכתה; and one who goes out with it into the רשות הרבים on Chabbat — incurs the חטאת. [See further on סי׳ ש״א séif ל״ח.]

Seif 2: if it is מצוייצת כהלכתה — it is permitted to go out with it into the רשות הרבים, whether a טלית קטן or a טלית גדול, even nowadays when we have no תכלת, provided only that it not be merely laid on his shoulders (מונח על כתפיו). [Words of the Ran and the R"i, chap. חבית, folio 108b.] And we presume the talit according to its חזקה that it is מצוייץ כהלכתו, and it is not required to examine it before going out with it.

Seif 3: if one learns on Chabbat, while in a כרמלית, that the talit he is wearing is pasoul — he shall not remove it from himself until he reaches his home, for גדול כבוד הבריות (great is the honour of created beings). [Glose: even a טלית קטן under his clothes — he is not required to remove it; and likewise if one of the threads snapped and he is ashamed to sit without a talit — he may wear it without a blessing by virtue of כבוד הבריות; and this, precisely on Chabbat when it is forbidden to make tsitsyot, but on a weekday, in such a case — it is forbidden.]