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Are the above modestly laws of dress a requirement from the letter of the law or a mere act of piety?
According to Admur  the above modesty laws are an absolute Halachic requirement and not a mere matter of piety, and so rule other Poskim. Nevertheless there are Poskim that learn the above law is a mere act of piety.
 Basra 2/1; 2/6; unlike Kama 2/1 which implies it is not an obligation.
In Basra 2/1 Admur rules that the “Sages commanded to be modest” and therefore a person “needs to act in modesty” and “therefore one may not reveal his flesh”. Likewise in Basra 2/6 Admur rules it is “forbidden to walk or even sit with uncovered head because of modesty”.
Ruling of Kama: In Kama 2/1Admur writes that it is merely proper to beware [“Tov Lizaher”] to dress under the covers.
 Mishneh Halachos 6/2
 Kama 2/1; Igros Moshe Yoreh Deah 3/68-4 and 47: “The laws of modesty by man, to cover the body, is not a complete prohibition but is rather an act of extra piety”; Az Nidbaru 6/40-41; This law is completely omitted from the Rambam; See Piskeiy Teshuvos 2/1 footnote 1
Ruling of M”B: The M”B 2/1 2 writes that one needs to always beware to cover his body.