(Beraisa): If foods (that are Avos ha'Tum'ah, e.g. Neveilos) are joined through liquids, they are considered joined (to complete the Shi'ur) to be Metamei food and drink, but not for severe Tum'ah (to be people and Kelim.)

Eruvin 80b (Mishnah - R. Yehoshua): An Eruv must be a full loaf.

81a (R. Yochanan ben Sha'ul): He requires a full loaf to avoid strife (those who give full loaves might resent those who give pieces).

(R. Yochanan ben Sha'ul): If one removed from a loaf the Shi'ur for Chalah, it may be used.

Question (Beraisa): If the Shi'ur for Chalah was removed, it may not be used.

Answer: R. Yochanan permits a baker's Shi'ur of Chalah. The Beraisa forbids a regular person's Shi'ur:

(Mishnah): The Shi'ur of Chalah (for a regular person) is one part in 24, whether it is for himself or his son's wedding feast. If a baker or woman makes bread to sell it, the Shi'ur is one part in 48.

(Rav Chisda): If a loaf was Nifresah (sliced) and one connected the ends together using a chip, one may use it to make an Eruv.

Question (Beraisa): One may not be Me'arev with it.

Answer: One may be Me'arev with it if it is not evident that it was Nifresah.

Ohalos 2:7 (Mishnah - R. Yochanan ben Nuri): If a bone the size of a barley seed was split, it is Tahor.

Ohalos 3:4 (Mishnah): If two half k'Zeisim of flesh (of a Mes) were brought into a house, it is Tamei. If they were inserted through people, they are Tahor, for what is connected through man is not connected.

Rambam (Hilchos Tum'as Mes 4:9): If there was half a k'Zayis of flesh on each of two bones, and the bones were partially entered into a house, it is Tamei. If a man stuck the flesh on the bones, the house is Tahor, for something connected through man is not considered connected.

Kesef Mishneh: This is from a Tosefta (cited below by R. Shimshon).

Perush ha'Mishnayos (Ohalos 3:4): A man stuck the two half k'Zeisim on a bone of the Mes. It is Tamei only if they were was naturally on the bone.

R. Shimshon (3:4): A Tosefta (Ohalos 4:3/4) teaches that if Chelev of a Mes was disconnected, and Chitcho, it is Tahor, for connection through man is not a connection. 'Chitcho' is like Hitcho, i.e. he melted it.

Perush ha'Rosh (Ohalos 2:7): It is Tahor even if one joined them again, for something connected through man is not considered connected.

Rashi (105b DH Chiburei, DH v'Ein): There are two half-k'Zeisim of Neveilah, and Mashkeh Tofe'ach (it is wet enough to wet something that touches it) in the middle joins them. I do not know why they are not connected for severe Tum'ah.

Tosfos (105b DH Chiburei): Rashi explained similarly in Menachos 24a regarding connection through a Keli or water. (If two half-Isaronim (an Isaron is the volume of 43.2 eggs) did not touch, but they were in one Keli, or water connected them, and Tum'ah touched one half, both of them become Tamei.) It is astounding to say that liquids can connect food to become Tamei or be Metamei others. Even skin does not join meat (Chulin 117b)! Rashi said that Nitzuk (falling water) can connect. Nitzuk does not connect even water itself! However, Taharos 8:8 is like Rashi. A Tosefta (Ohalos 4:3/4) says that if an Esrog was split and one connected it through a needle or chip, it is not connected to be Yotzei the Mitzvah, for something connected through man is not considered connected. A dough kneaded with fruit juice is Tahor, for only the seven liquids join foods. This is astounding to say that kneading with fruit (juice) does not (Halachically) join the flour. Perhaps it does not truly refer to a kneaded dough. Rather, it is common that when one kneads with fruit juice, sometimes the fruit juice connects two half k'Zeisim.

Rosh (Eruvin 7:12): If one removed from a loaf the Shi'ur for Chalah of a baker, it may be used for an Eruv. This is if it was removed to be Chalah. If not, there will be enmity. The Beraisa said 'if the amount for Chalah was removed, and not 'if Chalah was removed', to teach that even if only Chalah was removed, if it was more than the (minimal) Shi'ur, it may not to be used, due to enmity. Logically, it seems that since the concern is for enmity, it makes no difference whether or not it was removed for Chalah. The neighbors do not know why it was removed! Up to the amount for Chalah, they will assume that it was removed for Chalah, so there is no enmity.

Roke'ach (329 DH b'Perek): If one has two half-loaves, and he does not have a whole loaf, he joins the halves on a piece of wood or something so it will not be evident (that it is not one loaf). One may do so even on Shabbos, like it says in Eruvin.

Shulchan Aruch (OC 168:2): If one has two half-loaves, and he does not have a whole loaf, he joins the halves on a piece of wood or something so it will not be evident. One may do so even on Shabbos.

Magen Avraham (4): Perhaps during the week there is no need to connect them. This is the custom. On Shabbos, one must be careful not to use a Muktzah piece of wood to connect them.

Kaf ha'Chayim (14): One may use a Kli she'Melachto l'Isur (it is used for something forbidden on Shabbos), for one may move it if he needs the Keli itself or its place.

Mishnah Berurah (7): Eliyahu Rabah leans like the Shulchan Aruch, that one should do so even during the week.

Mishnah Berurah (8): If it is evident that it is not one loaf, it does not help, like we say in OC 366:6.

Mishnah Berurah (9): On Shabbos, if one has a truly full loaf, he should not bless ha'Motzi on two half-loaves joined together.

Kaf ha'Chayim (13): This is because some say that it is considered whole only regarding Eruvin (R. Zalman, Eliyahu Rabah).

Kaf ha'Chayim (10): If one removed from it at most the Shi'ur of Chalah, i.e. one part in 48, Minchas Yakov (12) says that it is as if it is whole, like regarding Eruv. Eliyahu Rabah (167:2) says that he proved in a Teshuvah that it is like a piece, even if just Chalah was removed.

Shulchan Aruch (366:6): We use only whole loaves to make an Eruv. If one removed from it at most the Shi'ur of Chalah for a baker, i.e. one part in 48, one may use it, even if there was no Chiyuv to take Chalah from it.

Beis Yosef (DH u'Mah): The Ri permits only if Chalah needed to be removed. If not, there will be enmity. The Rosh and Tur permit even if there was no need to take Chalah.

Shulchan Aruch (ibid.): If a slice was cut, and he inserted a chip in the loaf and the slice to reconnect them, if it is not evident that it was sliced, he may use it for an Eruv.

Mishnah Berurah (40): Even though it is not whole, since this is not evident, there will not be enmity.

Shulchan Aruch (OC 274:1): On Shabbos, one blesses on two full loaves.

Sha'arei Teshuvah (1): Chacham Tzvi (62,63) says that if a loaf is missing less than one part in 48, the Rosh permits and the Ri disqualifies it for Lechem Mishneh. If it was not yet removed, but it was burnt and it is destined to be cut off, Sha'ar Efrayim (1) is Machshir. It is not it is as if it was already cut, even if it is more than a finger. It seems that Chacham Tzvi agrees. Mekom Shmuel agrees, for some people eat it even if it is charred, so it is not considered destined to be cut, for one can use it for Muryas (fish oil). I disagree. Since it is abnormal to eat charred bread, it is destined to be cut from this edible loaf! Minchas Yakov (b'Sof ha'Sefer 12) says that if one forgot to take Chalah until after the loaves were baked, or if due to Isur one needed to remove or peel off part of the loaf, since it is a small amount and it is due to necessity, and not because the Mitzvah is disgraced in his eyes, it may be used. He proved this from Eruvin. Others including Har ha'Karmel disputed this. Magen Avraham discusses saying ha'Motzi on cake when he fixes his meal on it, but it should not be used for Lechem Mishneh.

Mishnah Berurah (2): If one does not have whole loaves, it is not Me'akev. One may make Kidush even on a k'Zayis of bread.

Kaf ha'Chayim (4): Poskim argue about a loaf from which less than the Shi'ur for Chalah was removed. If one does not have a full loaf, it is better to used it than to use another loaf (missing more than this).

Kaf ha'Chayim (5): If mice nibbled on a loaf, surely it is invalid for Lechem Mishneh, for it is evident that it was not taken for Chalah, and it is despised. Even if one cut off more, so it is not evident that mice ate from it, this does not help, for it came from a Pasul loaf.

Aruch ha'Shulchan (5): The loaves must be whole, for a deficient loaf is not honorable. Therefore, if mice bit it, it is not proper for Lechem Mishneh. If the Torah requires something complete, e.g. an Esrog, surely connection through man is not a connection. Lechem Mishneh is not explicit in the Torah. Also a slice is called Lechem. If something is missing, it is not whole. Some say that up to the Shi'ur of Chalah is not a problem, like regarding Eruv. Here is different. There, the concern is enmity. Here, it is not called whole. However, if one has nothing whole, he should take two slices. It is Lechem Mishneh, just it is not honorable.