One to another - For all of them [together] are one mitzvah, and if even one ציצית is missing (ie. missing completely, or is invalid), it's as if you didn't affix any at all and you nullified completely the positive commandment of ציצית.

To a public domain - And to [wear invalid ציצית on Shabbos in] a karmelit (an area that is not a private domain and not a public domain, but conceptually somewhere in between) is forbidden on a rabbinic level. And the same applies to all other invalidations. For example: if the majority of the garment was closed up, or if the ציצית were made/affixed not in the right place - [such as] higher than three finger-widths [from the edge of the garment], or lower than [length of the] thumb from the knuckle to the tip [from the edge of the garment], and all similar cases - or if the four corners (ie. the length and width of the garment itself) was less than the measurement described in siman 16, see there. In all those [cases], it is forbidden to go out [while wearing] them [on Shabbos], even to a karmelit on a rabbinic level. And [regarding] a garment which is open exactly halfway (ie. a tallit katan where the sides under the arms were stitched up so that it was exactly half-open and half-closed (if measured from the top, by the shoulder, to the bottom)), see above in Siman 10 in Mishnah Berurah se'if katan 27.

Is obligated to bring a sin offering - For it is [considered like] carrying due to the remaining ציצית, and they are not nullified to the garment (ie. they are not considered to be part of the garment itself) because the ציצית strings are significant/valuable and [therefore] are not nullified. And even if those [remaining] ציצית are also invalid, nevertheless, as long as they have some valid strings on them, his mind is on them (ie. he will want to use them at some point) and they are [therefore] significant and are not nullified, unless all the four [original] strings were severed and they didn't have enough left over to make a loop [around the other strings], for then it is considered as nullified to the garment. Therefore, if he realizes this (ie. he realizes that all the strings are invalid) on Shabbos as he is walking in the public domain, he is not required to remove the tallit.

It is permitted to go out - Even at night (ie. Friday night), which is not the time [for the fulfillment of the mitzvah] of ציצית, because it is [considered] a beautification of the garment. And even [regarding] a טלית made from other materials, even according to those rabbinic authorities above in siman 9 - se'if 1, [who hold] that the obligation [of those other materials] is only on a rabbinic level, nevertheless [they agree] that it is a beautification of the garment since in any case they (ie. those טליתות) are obligated [in ציצית] based on a certainty (ie. we can say with certainty that they are obligated in ציצית, even if it's only on a rabbinic level). And it's not similar to a garment that is [exactly] half open and half closed (ie. a tallit katan where the sides under the arms were stitched up so that it was exactly half-open and half-closed (if measured from the top, by the shoulder, to the bottom)), which the Shulchan Aruch ruled above in siman 10 - se'if 7, that one may not go out with it on Shabbos, for there the obligation [to affix ציצית on it] is only because of a doubt (ie. it's doubtful whether that half-stitched up garment requires ציצית or not). [Pri Megadim and Orchot Hachaim, who disagree with the Shev Yaakov. Afterwards I found that also the Olat Tamid wrote like them].

Blue-dyed [strings] - For behold, it is established that the blue-dyed [strings] and the white [strings] do not prevent one from the other (ie. they don't prevent the mitzvah from being fulfilled due to the absence of either the blue or white strings - assuming you still have the correct number of strings). For it is written "...and you shall see it" (ie. the word אותו is singular) (Numbers 15:39) - which is understood to mean on each one (ie. the mitzvah of "you shall see it" applies to each one -blue or white- separately, so you can fulfill the mitzvah with either one)....

On his shoulders - [For then] it is not a decoration, rather it is [like] a carried load, because that is not the way it is worn during the week. However, if it covers the majority of his body, that is sufficient. And see below in siman 301 -se'if 30, what we will write there regarding this.

Before he leaves with it - Since he checked it in the morning (ie. Shabbos morning) when he was making the blessing upon wearing it and found them to be intact, it's not common for it to become severed in such a short time, even if he took it off in the meantime [Magen Avraham]. And it's evident from this that also on Shabbos one must check his ציצית. And the Ba"ch wrote like this explicitly in siman 8, but people are not careful with this. And see [further] in Biur Halacha....

On Shabbos - And if he knew from yesterday [that his טלית was invalid] and he forgot to put on [valid] ציצית, it seems that there too we do not penalize him. And a proof [for this] is from [what's written] below in siman 355, se'if 3, in the Rem"a where "...if they forgot and did not make an eiruv...", see there further [from the Chidushei R. Akiva Eiger].

When he was in a karmelit - That is a place where the prohibition to carry [things] is only on a rabbinic level. And therefore, it is not necessary [for him] to remove [his טלית] because human dignity overrides a rabbinic level prohibition. And even though ציצית is a Torah level mitzvah, and a Torah level mitzvah does not get overridden because of human dignity, nevertheless, it is still permitted, because the Torah did not say "Don't wear a garment without ציצית" (ie. in a negative term), rather it's a positive commandment to affix ציצית on it (the garment). And since [here] he can't affix [a valid] ציצית on Shabbos, he's not transgressing a positive commandment, and he's only [violating] a rabbinic level prohibition. And therefore, he is permitted [to carry it in a karmelit] because of human dignity and he is not required to remove the טלית. But [to carry] in a public domain, which is a Torah level [prohibition], he is required to remove it, whether it's a large טלית (that we use for prayers) or a small טלית (that we wear under our clothing throughout the day), and even if he will be left naked (ie. shirtless) by doing that, because human dignity does not override a Torah level prohibition like this in any situation. And below in the [section dealing with the] Laws of Shabbos, G-d willing, we will explain that there is a dispute if nowadays we have a public domain or not. And it appears, that if the tassel (ie. the winded up and knotted part of the ציצית) was intact, and the invalidation was only on the loose strings [that are hanging down past the last knot], we can join with the opinion of the R"i above who permits it (ie. the R"i holds that you measure the minimum length of string needed, if they were severed, from the tassel part. So if the tassel part was intact, then the ציצית are still valid), and one would not be required to remove it immediately, rather he should hurry to go to his home [and remove it there]....

Invalid - Meaning, whether one corner [of the garment itself] became severed and now it only has three [corners], or whether the [entire] ציצית from one corner was severed alone. And even if it was already invalid when he left his house, since at the time that he wore it, he was not aware of it, we do not penalize him, for human dignity is paramount. And even [in regards to] our large טלית that we are not accustomed to wear all day, except for during prayers for the sake of the mitzvah, and [therefore] there is no shame by removing it (ie. he won't be left shirtless), there also there is no requirement to remove it. For the sages did not distinguish between one טלית and another (ie. small vs. large). And R. Akiva Eiger in his Novellae questions this.

That's under his clothes - And it wouldn't be obvious [to other people] afterwards (when he removed it) that he's walking without a tallit katan. Nevertheless, the [act of] removing it [in public] is an even bigger shame.

One of the ציצית - Meaning, whether he came to the synagogue and wants to wear his טלית, and before he put it on he found the ציצית to be invalid and he's embarrassed to sit in public without a טלית; it's permitted for him to wear it without a blessing. Or whether he noticed, while already wearing it, that the ציצית became severed; there too he does not need to remove it [Birchei Yosef and Artzot Hachaim and the other later rabbinic authorities]. And see further in the later rabbinic authorities who agreed that it all depends on the man who is wearing it - if he will be embarrassed, he may wear it without a blessing, but if he won't be embarrassed, there is no permission due to human dignity.

That he is able to wear it - And [this is referring to] specifically if he found out today (ie. on Shabbos). But if he knew from Friday evening (before Shabbos) that the ציצית were invalid, then it is forbidden for him to wear it on Shabbos because he should have fixed it yesterday. But if he forgot, then he can be lenient [Chiddushei R. Akiva Eiger].

Because of human dignity - And [this is] specifically if he's not able to borrow a טלית in the synagogue.

And [this is] specifically on Shabbos - Meaning, since on Shabbos it's only a rabbinic level prohibition [to wear a garment without ציצית] as we mentioned above. But during the week, he is transgressing a Torah level prohibition at every moment [that he's wearing it] of "get up and make for yourself ציצית". And a Torah level prohibition, even just a prohibition of "sit and don't do" like this, where he is [passively] preventing himself from performing the mitzvah, is not overridden because of human dignity, unless it's a very big embarrassment [for him]. Therefore, it is forbidden for him to wear the טלית גדול when he sees that it has no ציצית, because to sit [in public] without a טלית, according to the Rem"a, is only minor embarrassment. And similarly, if he became aware when out in public while wearing a טלית גדול that one of the ציצית was severed, he would also [in that case] need to remove it immediately, because nowadays, removing a טלית גדול in the marketplace/street is also only a minor embarrassment. However, if he became aware in the synagogue, after he was already wearing the טלית, that one of the ציצית was invalid, many of the later rabbinic authorities are lenient [to say] that he is not required to remove it immediately, because they hold that since he's amongst many people in the synagogue, removing it would be the biggest embarrassment. Instead, he should hurry home or to the room before the synagogue, and remove it there. And the Chayei Adam is stringent regarding this and he holds that removing a טלית גדול is only a minor embarrassment, because even when it's not a case like this, it's the way of people to always remove their טלית amongst others in the synagogue. Afterwards, I found in the Pri Megadim, in the beginning of the Laws of ציצית, that he also holds like the Chayei Adam. Therefore, it is proper to follow the suggestion of the Artzot Hachaim: that he should disown it, for then he is exempt from making ציצית for it. And when he gets home, he then reclaims it [as his own].

Is forbidden - See in Magen Avraham where he concludes that this that the Rem"a is stringent [regarding] during the week, is not referring to what he wrote at the beginning "Even [regarding] a טלית קטן...", because [regarding] a טלית קטן, if it became known to him that the ציצית were invalid, which would be a big embarrassment for him to remove it from under his clothing, whether he's in the synagogue or in public, he is not required to remove them, for [we say] that where there is a big embarrassment, human dignity overrides even a Torah level prohibition which has [an element of] "sit and don't do"(ie. he is passively transgressing). But he [still] needs to hurry home or to the room before the synagogue and remove it there, even if he's involved in a mitzvah in the synagogue, since it's a Torah level prohibition. But on Shabbos, he does not need to hurry out of the synagogue as long as he's still busy with the mitzvah. And if one sees that his friend's ציצית are severed, he shouldn't tell him until he gets home, meaning, he should call him over to his house and then tell him to remove it. the Magen Avraham wrote further that if there are no ציצית in the city, the law during the week is the same as on Shabbos. And the same applies regarding a טלית that requires ציצית only on a Rabbinic level, for example: a borrowed טלית after 30 days [have passed], it's law is the same during the week as on Shabbos.