Must the tefillin housing be perfectly square, and does squareness become invalid if the housing loses its square shape over time?

Synopsis

It is a halacha l'Moshe miSinai that tefillin must be perfectly square in their stitching and diagonal. If the squareness is ruined over time, some say it must be resquared. The Rema adds that the height of compartments need not equal the length and width.

Early Acharonim
Lenient
Strict
Lesser cited
Major authority

Discussion

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