OPINIONS: The Gemara teaches that a man is believed to make his wife lose her Kesuvah when he claims that he found her to be a Be'ulah ("Pesach Pasu'ach Matzasi"). The Gemara explains that since the institution of Kesuvah is only mid'Rabanan, the Rabanan trust the husband when he says that he found her to be a Be'ulah. They rely on the logic that a man would not put so much effort into preparing the wedding feast only to lose it all by falsely claiming that his marriage was a mistake -- unless he is telling the truth. This implies that if the institution of Kesuvah would have been mid'Oraisa, he would not have been believed.
The Gemara cites a Machlokes Tana'im regarding whether the Kesuvah is d'Oraisa or d'Rabanan. Raban Shimon ben Gamliel says that it is d'Oraisa. Rav Nachman in the name of Shmuel rules that when the husband claims "Pesach Pasu'ach Matzasi," he is believed to make her lose her Kesuvah because the Kesuvah is only d'Rabanan. What is the Halachah regarding the status of the Kesuvah, and is the husband believed to make his wife lose it? (See also Insights to Kesuvos 39:2.)
(a) RABEINU TAM (cited by Tosfos) rules like Raban Shimon ben Gamliel who says that the Kesuvah is d'Oraisa. He follows the general rule that whenever Raban Shimon ben Gamliel is mentioned in a Mishnah, the Halachah follows his view.
Rabeinu Tam further proves that this is the Halachah from the wording of the Kesuvah in which it was customary to write, "I obligate myself to give you two hundred Zuz to which you are entitled by the Torah." Therefore, he rules that the husband is not believed to cause her to lose her Kesuvah with his claim of "Pesach Pasu'ach Matzasi."
(b) The ROSH (1:19) does not rule like Raban Shimon ben Gamliel. Rather, he rules that the Kesuvah is d'Rabanan since that is the view of Rav Nachman. Regarding the custom to write in the Kesuvah that she is entitled to the money "Min ha'Torah," the Rosh cites Rishonim who write that this phrase is intended merely to denote that the type of money that he obligates himself to pay for the Kesuvah is the type of money that the Torah discusses. This is called "Kesef Tzuri," a currency in which the Dinar was worth eight times more than the local currency commonly in use at the time, which was known as "Kesef Medinah." The Kesuvah must be paid with the larger sum.
Similarly, the Ritva writes in the name of RABEINU PINCHAS (brother of the RE'AH) that although the Kesuvah is normally paid in the currency of Kesef Medinah, if one writes the words "to which you are entitled by the Torah" in the Kesuvah he must pay with Kesef Tzuri.
(c) RABEINU CHANANEL (cited by the Rosh) and the GE'ONIM rule like Rav Nachman, that the Kesuvah is d'Rabanan and is paid with in the currency of Kesef Medinah. The HAGAHOS MAIMONIYOS (Hilchos Ishus 10:6) writes in the name of the MAHARAM (see also RITVA) that because the Kesuvah is d'Rabanan, one should not write in the Kesuvah "to which you are entitled by the Torah," as writing so might even invalidate the Kesuvah since the Kesuvah is not d'Oraisa.
The RAMBAM (Hilchos Ishus 10:7, 11:14) apparently follows the opinion of the Ge'onim and rules that the Kesuvah is d'Rabanan. However, when the Rambam lists the Mitzvos d'Oraisa that pertain to marriage and Ishus in the beginning of Hilchos Ishus, he writes that it is a Mitzvah "to marry a woman with a Kesuvah and Kidushin," and he also writes that "one may not have relations without a Kesuvah and Kidushin." He repeats this in Sefer ha'Mitzvos (Lo Ta'aseh #355) where he writes that there is an Isur against having relations with a woman without a Kesuvah and Kidushin. The RAMBAN there asks that since the institution of Kesuvah is d'Rabanan (as the Rambam himself rules in chapters 10 and 11 of Hilchos Ishus), how can there be an Isur d'Oraisa to have relations without a Kesuvah?
This question is compounded by the fact that even according to those who say that the Kesuvah is d'Oraisa, it certainly is not part of the Kidushin. The Kesuvah is a monetary obligation; not having a Kesuvah cannot create an Isur Be'ilah! (The Isur Be'ilah without a Kesuvah is certainly only an Isur d'Rabanan; see Kesuvos 54b.)
The answer seems to be that the Rambam uses the term "Kesuvah" as a sign of the type of relationship between a man and woman. "Kesuvah" represents a permanent, committed relationship, as opposed to a transient relationship of Z'nus (since the expense of divorce makes a person think twice before sending away his wife). When a Kesuvah is written, it shows that the man and woman are living together as husband and wife with a relationship of Ishus, and not a union of Z'nus.
When the Rambam writes that there is an Isur against having relations without a Kesuvah and without Kidushin, he means that the Isur (the Lo Ta'aseh) applies only when there is no Kidushin and the act is performed in the manner of Z'nus (that is, as a temporary, transient relationship). When a man lives with a woman in the manner of Ishus (that is, "with a Kesuvah," in the Rambam's words) but without Kidushin, he transgresses only a Mitzvas Aseh (of "Ki Yikach Ish Ishah...") and not the Lo Ta'aseh. This Isur Aseh is the source for the Isur against living with a Pilegesh according to the Rambam (as mentioned earlier in Insights to 8:2:b). (See Rambam, Hilchos Ishus 1:4. The Girsa of the Rambam in Sanhedrin 21a seems to have been that a Pilegesh is betrothed without Kidushin, but with a Kesuvah; see Ramban, Bereishis 25:6.)
When the Rambam writes that the Mitzvas Aseh is to marry a woman with a Kesuvah and Kidushin, he means that one does not transgress the Mitzvas Aseh by having Be'ilas Z'nus without Kidushin (he does transgress the Lo Ta'aseh, though). The Mitzvas Aseh is to "marry" a woman, which means to initiate the permanent relationship of husband and wife through Kidushin. (M. Kornfeld. See the similar explanation of ha'Gaon Rav Aharon Kotler on this matter in the Sefer Zikaron printed in his memory.)