Q. We know that “dath Mosha” doesn't require the neck to be covered from the Laws of Hovel u-Mazziq 4:13. There it describes a woman’s neck as being in the category of what is exposed (galuy). According to the Laws of Ishuth 24:9, “dath Mosha” prohibits the woman from going out in public with her head exposed (paruwa). It seems to me that when one takes the Laws of Hovel u-Mazziq 4:13 into account while reading the Laws of Ishuth 24:9, it should be apparent that the neck is not required to be covered by the extra covering that the upper veil (redidh) provides.
A. We do not claim that dath Moshe requires the neck of a woman to be covered. That is a misunderstanding of our views. Rather, we teach that this is a requirement of dath Yehudith (see: Ishuth 24:11).
Also, you write that the Laws of Ishuth 24:9 teaches that dath Moshe prohibits a woman from going out in public with her head exposed. The Laws of Ishuth 24:9, which you reference, only prohibits a woman from going out in a market-place (ie: in public) with the hair of her head revealed (galuy). The emphasis of this halakha is specifically on the hair of the head, not the head itself. What you stated as being taught in 24:9 as a part of dath Moshe is actually what is taught in the Laws of Ishuth 24:11 concerning dath Yehudith - not dath Moshe.
The Laws of Hovel u-Mazziq 4:13 states: "One who injures a married woman [...] if in exposed places, such as her face, neck, hands, or arms..."
Hovel u-Mazziq 4:13 is in reference to parts of a woman's body that are exposed, even if they are exposed only in places other than the market place, such as in her home or courtyards. Otherwise, it would mean that she's allowed to expose her arms in the market place as well, since this same law in Hovel u-Mazziq 4:13 mentions arms along with its mentioning the neck. But we know from the Laws of Ishuth 24:11 that exposing the arms in public is not allowed: "If she does one of these, she transgresses dath Yehudith [...] she sews in the market-place and exposes her arms to people."
So, if Hovel u-Mazziq 4:13 were a valid proof to show that a womon need not cover her neck in the market-place, then we should also use it to show that she need not cover her arms in the market-place either. But we know that this is certainly not the case.
Hovel u-Mazziq 4:13 is in references to those parts of the body that are exposed, whether they are exposed in the market-place or whether they are exposed indoors or in courtyards. It is, therefore, not a proof for showing that a woman can expose her neck in the market-place.
(Laws of Women) Hilkhoth Ishuth 24:9 
(Laws of Women) Hilkhoth Ishuth 24:11 
(Laws of Injury and Damages) Hilkhoth Hovel u-Mazziq 4:13 
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