Gemara

(Shmuel): If Leah was Mekadesh Leah with a date, even if it sells for much less than a Perutah, we are concerned lest it is worth a Perutah in Madai (elsewhere).

Question: Beis Hillel say that a Perutah or Shavah (the value of a) Perutah is Mekadesh. This implies that less than Shavah Perutah is not Mekadesh!

Answer: A Shavah Perutah makes Vadai (definite) Kidushin. Less than Shavah Perutah creates Safek (doubtful) Kidushin.

53b (R. Yakov): R. Yehudah taught that if a man was Mekadesh unknowingly with Ma'aser Sheni, she is Mekudeshes.

(R. Yirmeyah): She is unhappy, for she must take the money to Yerushalayim to use it. He is happy, for he acquired a woman with money that had limited use;

(R. Yakov): Perhaps also he is unhappy, lest the money be lost on the way!

Bava Kama 97b (Shmuel): If Reuven lent Shimon money, and the currency was disqualified, Shimon can return the same currency, and say 'you can use it in Meishan (a far away place in which it is still accepted).'

Rav Nachman: Presumably, this is only when Reuven must travel to there.

Rishonim

The Rif brings the Sugya on Daf 12 verbatim.

Rambam (Hilchos Ishus 4:19): If one was Mekadesh with a food, Kli, etc. worth less than a Perutah, she is Safek Mekudeshes. She needs a Get, lest it is worth a Perutah elsewhere. If one was Mekadesh with a Shavah Perutah in that land, she is Vadai Mekudeshes. If it was not worth a Perutah, she is Safek Mekudeshes.

Magid Mishneh: The Rambam connotes that even if we know that it is Shavah Perutah elsewhere, she is Safek Mekudeshes.

Ran (DH Omar, citing Tosfos): Shmuel decreed lest someone from Madai think that Kidushin with this item is invalid, and will not be concerned for such Kidushin in Madai. Even if we knew that it is Shavah Perutah elsewhere, it is not real Kidushin. One who returned his theft except for less than Shavah Perutah need not travel to return it; he brings a Korban (if he swore - Bava Kama 105a). We are not concerned lest it is Shavah Perutah elsewhere!

Rebuttal (Ran): Kidushei Safek connotes that it if we knew that it is Shavah Perutah somewhere, she would be Mekudeshes mid'Oraisa. Since she accepted it, and it is Shavah Perutah somewhere, if the witnesses knew that she regularly pays a Perutah for it, it would be as if she said 'to me it is Shavah Perutah', like we say regarding Pidyon ha'Ben (8a).

Rosh (1:17): Shmuel's law is a stringency mid'Rabanan. Mid'Oraisa, for (redemption of) Hekdesh we are concerned only for (the value in) that time and place. The same applies to monetary laws. The Rambam connotes that if we knew that it is worth a Perutah elsewhere, she would be Vadai Mekudeshes, for if she can get there, it is Shavah Perutah for her. It is called Kidushei Safek because we are unsure if it is Shavah Perutah elsewhere. The Ri says that even if we know that it is worth a Perutah elsewhere, Hekdesh depends only on that time and place. We learned a Chidush, that even if we do not know whether it is Shavah Perutah anywhere, Chachamim decreed due to where it is Shavah Perutah. If so, this is even if it is perishable. Presumably, the Ri is correct. A woman does acquire herself to a man for less than a Perutah where she lives.

Tosfos (53b DH Ihu): Rashi says that Ma'aser Sheni is not Shavah Perutah outside of Yerushalayim. One cannot spend it. Even if one sells it, what he gets becomes Kodesh! He did not want to suffer the loss if she will lose it on the way. This connotes that she is not Mekudeshes until she brings it to Yerushalayim. This is difficult, for in Bechoros (9b) we asked why Kidushin works b'Mezid, since the Torah requires Kesef Tzurah (minted) to redeem Ma'aser Sheni. If the Kidushin takes effect only in Yerushalayim, there we do not need Kesef Tzurah. The money may be exchanged for food there! Rather, she is Mekudeshes immediately. He is unhappy, lest she lose it and be upset.

Poskim

Shulchan Aruch (EH 31:3): If one was Mekadesh with a food... less than Shavah Perutah, she is Safek Mekudeshes. Perhaps it is worth a Perutah elsewhere.

Chelkas Mechokek (8): Even if we know that it is Shavah Perutah somewhere, it is only Safek Kidushin. However, if she will be going there, it is Kidushin mid'Oraisa, at least when she gets there. We say similarly about returning a coin that was disqualified. One may do so only if the lender needs to travel to a place where it is still accepted (Bava Kama 97b).

Question (Beis Shmuel (6): Some say that if we know that it is Shavah Perutah elsewhere, she is Vadai Mekudeshes. The witnesses must know that it is worth a Perutah elsewhere. However, Tosfos explains that Kidushin with Ma'aser Sheni takes effect immediately, even though it is Shavah Perutah only in Yerushalayim! The Sugya there proves that it is mid'Oraisa! Perhaps this is only when she is going to Yerushalayim. The words of the Rosh (for Hekdesh we are concerned only for that time and place) suggest that even if she is going there, she is not Mekudeshes. How will he answer this question?

Answer (Korban Nesan'el 10): We can say that he was Mekadesh her with much Ma'aser, and people here would happily pay a Perutah for it. She did not know that it was Ma'aser; she thought that it was worth the full value here.

Bedek ha'Bayis (DH Yesh...): The correct text of the Ramah (cited in the Tur) says that if it is worth a Perutah now, she is Vadai Mekudeshes, unless witnesses say that it was less than a Perutah at the time of Kidushin. If it is possible to verify that it was Shavah Perutah at the time, she is Safek Mekudeshes. Perhaps his first words 'Vadai Kidushin' are not precise. If another was Mekadesh her, we cannot ignore it! Or, perhaps it is Vadai, for we assume that it was worth the same then as it is now. We infer that if it is not worth a Perutah now, she is not Mekudeshes. This is Stam. If there are rumors that witnesses know that it was Shavah Perutah at the time, she is Safek Mekudeshes. If not for the witnesses, we would not be concerned that it was Shavah Perutah. We do forbid her against her Chazakah of being single. The Ramah is not concerned lest it was Shavah Perutah in Madai. He does not hold like Shmuel. Alternatively, he discusses something perishable.

Avnei Milu'im (13 DH ul'Aniyas): The Mordechai (Kesuvos 206) says that we do not assume that prices were the same as they are now. They are prone to fluctuate. The Rema (CM 227:9) rules that one who claims Ona'ah must prove what the value was. We cannot rely on the current value. This is why the Beis Yosef needed the Chazakah that she was single, and explained that if it is now Shavah Perutah, she is only Safek Mekudeshes. The Shulchan Aruch omitted the Ramah's opinion, for we rule like Shmuel, and in any case there is Safek Kidushin.

Question (Shev Shematsa 3:17): Tosfos (79b DH Mi) holds that the current Chazakah does not apply retroactively, even when there is no Chazakah from the beginning. If so, why did Rav Chisda assess the rock? We may not assume that it was worth the same at the time of Kidushin!

Kehilas Yakov (21): Tosfos (12a DH Rav) holds that if it were Shavah Perutah now, Rav Chisda would say that it was Vadai Kidushin, i.e. due to the present Chazakah! We can answer like R. Akiva Eiger (Teshuvah b'Sof Drush v'Chidush 1 DH Al Derech), that Tosfos agrees that the current Chazakah applies retroactively when it is possible to say that it was always this way and never changed.