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The Kashrus status of purchased Tzitzis:
Purchasing from a Jew: One who purchases a pair of Tzitzis from a Jew can assume that the Tzitzis is Kosher [without doing any further inquiry]. [Nevertheless, in today’s times one can no longer rely on an unfamiliar Jew, even if he is observant, as Halachic mistakes and forgery are very common. Thus, one is to only buy Tzitzis with a reliable Hashgacha.]
Purchasing from a gentile: One who purchases a pair of Tzitzis from a gentile merchant, and the gentile states that he purchased the Tallis together with its Tzitzis from a Jew, one can assume that the Tzitzis is Kosher. This applies even if the gentile’s main business is not in selling Tzitzis, but in selling other merchandise. However, this only applies if one purchased a Tallis with Tzitzis that are properly tied to its corners, however plain Tzitzis strings [without a double Chosem] that are not attached to a Tallis may not be purchased from a gentile, even if he is a merchant, as perhaps he made them himself.
Found Tzitzis in the open: One who finds Tzitzis strings in the marketplace, the Tzitzis can be assumed to be Kosher if they are interwoven and cut into four long strings, as certainly they have been made for the sake of Tzitzis.
All Tzitzis that are purchased from a Jew, or found in the open, are assumed to be Kosher. [In today’s times however one can no longer rely on an unfamiliar Jew, even if he is Torah observant, as Halachic mistakes and forgery are very common. Thus, one is to only buy Tzitzis with a reliable Hashgacha. The same applies regarding one who finds Tzitzis strings, that they should not be used unless they contain a reliable Hashgacha.] One may not purchase Tzitzis strings from a gentile unless they [contain two signs and a Hashgacha, or contain a Hashgacha and] are already properly tied to the Tallis.
 20/1; Michaber 20/1
 The reason: The Tzitzis are held in Chezkas Kashrus, being that every Jew is an expert in the proper making of Tzitzis. [ibid]
 See Chasam Sofer 6; Shulchan Hatahor 20/1; Shemen Rokeiach 2; Birchas Habayis 37/33; Levushei Mordechai 3/1; Biur Halacha 11/2 “Vetzerichin”; Kaf Hachaim 20/6; Piskeiy Teshuvos 20/1
 20/2; Michaber and Rama ibid
 The reason: The gentile merchant is assumed not to lie, as if he is discovered to be lying regarding one issue people will no longer believe him about anything relating to business. [ibid]
 Pashut, see next Halacha!
 Admur ibid; M”A 20/1
The reason: Regarding loose strings, we do not believe a gentiles word to say he purchased it from a Jew, as although he is believed in the case of a Tallis with tied strings, this is because in addition to the fact that he risks ruining his business, there is also another reason to assume that he is speaking the truth. It is not common for a gentile to know how to tie the Tzitzis to the corners with all of its loops and knots, and one can thus assume he purchased it from a Jew. [ibid]
 20/5; Olas Tamid 20/3
Other opinions: Some Poskim rule one may not use Tzitzis that were found in the open. [See Kaf Hachaim 20/17]