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What is the law if a Tzitzis string tore within the braid [i.e. Gdil], or beneath the braid [Gdil] by the hole?[1]

If even one string tore from its root, it is invalid.[2] This means that if even one string tore near the hole, within the area that precedes the braid[3], or within any area of the braid[4], the Tzitzis is invalid. [Thus, any tear that occurs beneath the loose area called Anaf is invalid.]

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[1] Siddur Admur; Shlah Chulin 112a in interpretation of Rav in Menachos 39a; Elya Raba 8:10 in name of Taz and Shlah; Emek Haberacha 2:13; Soles Belula 12:2

Background:

The Gemara states that if a string tore in the “Ikkur” or root of the Tzitzis, the Tzitzis is invalid. There are various interpretations of this word “Ikkur”. Does it mean the “Anaf”, the loose strings; does it mean the Gdil, the braided area; does it mean the area below the braid, which is the strings that pass through the hole? Admur in the Siddur, as well as the other Poskim listed above, take the approach that it refers to the braid and below the braid.  In the Shulchan Aruch however Admur takes the last approach, as will be explained. 

[2] Admur ibid; Rav in Menachos ibid

[3] Admur 8:13; Siddur Admur; Taz 8:8; Poskim ibid and in addition so also rule: Kitzur SHU”A 9:13; M”B 8:21; Biur Halacha 12:1 “Yeish Lismoch”; Tehila Ledavid 12:2; Chazon Ish 3:6; Kaf Hachaim 8:37; See Piskeiy Teshuvos 12:3

The reason: As when the tear occurs beneath the Gdil, by the holes, it is considered as if both sides have been cut off, and hence an entire string is missing. [Tehila Ledavid ibid]

[4] Siddur Admur; Shlah Chulin 112a in interpretation of Rav in Menachos 39a; Elya Raba 8:10 in name of Taz and Shlah; Emek Haberacha 2:13; Soles Belula 12:2

The reason: As whenever it tears beneath the Anaf, it is viewed that the entire string has torn and one hence only has three whole strings remaining. [Shalah ibid]

Ruling of Admur in Shulchan Aruch and other Poskim: In the Shulchan Aruch 12:6 Admur rules that only when a string requires a minimum length of 4 cm, is there a difference of opinion regarding if the string tore in the braided area. This implies that if the string does not require 4 cm, such as if the other side of the string still maintains a 4 cm length, then according to all [even Rashi] it does not invalidate the Tzitzis even if it tore within the braid. So rules also Biur Halacha 12:1 “Yeish Lismoch”; Kitzur SHU”A 9:13; Tehila Ledavid 12:2. This is all regarding if the tear occurred within the Gedil. If however the tear occurred below the Gedil, by the hole, then it is invalid according to all. [Admur 8:13; Poskim ibid]

Ruling of Mishneh Berurah: In Biur Halacha ibid, the M”B rules that if the tear occurred within the first set of loops, it is invalid. If it occurred after the first two knots made on top of the first set of loops, and there is 4 cm of string that protrudes, it is valid. [See Piskeiy Teshuvos ibid]

[5] As the last two knots are still considered part of the Gdil from which the Anaf extends, and hence when a tear occurs in that area, the Anaf is considered to have lost one whole string.

[6] As the knots separate between the Anaf and the Gedil, and hence if the string is now extending from beneath the knots, within the Gedil, it is now invalid as it is considered as if its root is torn, and hence both sides are now considered torn. However, according to this understanding, even if a string did not tear but simply unraveled from the knots, and now extends below the knots, it would be invalid, and this is preposterous to even ponder.