There is evidence that originally the Ten Commandments used to be recited with the three paragraphs of the Sh'ma in the Temple.
Some regard the ten turns to represent the Ten Commandments.
There was a difference of opinion between Rashi and his grandson Rabbenu Tam as to the order of the four quotations.
This seems to reflect different traditions as examples of both kinds were found at Qumran.
The four arms of the letter presumably represent the four quotations.
While the shin is mentioned in the talmudic discussions, the shin with four arms is first spoken of by later (c. The Shin is thought to stand for Shaddai, one of the names of God.
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The box for the arm has the four quotations written one after the other on a long strip.