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Finishing the 4th chapter - with the series of baraitot about the "chaver" - with a focus here on the last one. That is, specifically, a kohen can examine first-borns for blemishes, as long as they are not being given to himself, but he could rule on his own sacrifices, for example. Plus, how many judges are needed for various things, including judging first-borns, one or three? Plus, other examples that require a court of 3, including halitzah. What if you have an expert in blemishes on that court? And starting chapter 5 - with a new mishnah: selling the meat of disqualified consecrated animals at the butcher vs. selling the blemished of first-born animals. They're not weighed precisely in contrast to the regular consecrated animals, and the proceeds go to the owner. Plus, Rav Sheshet and narrowing the focus of the mishnah to orphans...

A new mishnah! A person who is suspected or known to not be careful about the laws of the shemitah year may or may not be careful about tithing, and likewise with regard to the rules of purity/impurity. But once one is suspect, that person can't judge or bear witness, at least with regard to that specific arena. Also, a focus on the "chaver," someone who is known to be careful in all areas of halakhah. Including details that are debated between Beit Hillel and Beit Shammai.

Another day of mishnayot: 1 - One who takes wages to be a judge or give testimony or a kohen who does so to facilitate a red heifer -- all of those efforts would be void. Note that the kohen who facilitates the red heifer becomes impure and cannot partake of terumah, which is his own monetary loss. 2 - If one is suspect with regard to bekhorot, for example, a kohen who is accused of making a blemish on the first-borns, then one may not purchase regular meat from him either, including the kind for which the first-born law was irrelevant (like venison). 3 - One who is suspected of not being careful with the laws of the shemitah year -- you can't buy any plant-based items from him, but you can buy non-plant based items. 4 - One who is not trustworthy with regard to terumot and ma'aserot may be untrustworthy when it comes to water and salt, no less.

4 mishnayot! 1 - On determining that an animal has a blemish - after slaughtering, and the tension of having non-experts involved in determining whether the animal has a blemish. 2 - What if the kohen makes an error in judgement? What is done is done. But the judge may well be liable. With mention of dina de-garmi. 3 - A story (in the mishnah!) about the error of the previous mishnah. 4 - Making sure that one's salary was not contingent on the assessment of blemishes - unless the person checking was an expert.

If the kohen demands the first-born before the prescribed time, the owner does not need to provide it, because it seems that such a kohen would look too close to an employee of the owner -- for taking care of the animal. Also, more on the question of giving terumah to the kohen when it does appear that he assists "on the threshing floor." Note the fact of a rabbinic level of terumah as well as a Torah level. Also, delving into the meaning of "shanah be-shanah" - year by year, with regard to the first-born's year, the calendar year, or perhaps the time of eating the sacrifice of the first-born.

To close the 3rd chapter: What if wool were plucked from an unblemished burnt-offering? What would the halakhah be regarding benefiting from that detached wool? The sacrifice might be postponed because of this question, and that can really complicate matters. And the new chapter begins -- with a new mishnah, and some basic questions about when the first-born is given the the kohen. "Small" animals should be given with a 30-day limit (or 3 months, depending on whom you ask) - sheep and goats. "Large" animals - that's cattle - have a 50-day limit.

If you're slaughtering the first-born, you can part the hair and even pluck a hair for the sake of smoother slaughtering. That is, plucking is not considered to be shearing. This might complicate matters for a red heifer -- if one trimmed red hair that had some black, which is allowed, in this case, without actually shearing. So that task is also unintended beyond its actually purpose. Note that cows are not considered "shorn," because their hairs are not wool. Plus, a historical account of 9 red heifers. Also, a new mishnah! A blemished first-born, who has shed hair, and then the animal is slaughtered (or it dies), can that hair be used in the way the body would be allowed for use after the slaughtering? It's a machloket.

One who purchases a nursing female animal from a non-Jew - and the question is whether that animal can conclusively be said to have born progeny before, or perhaps the animal was nursing another animal's offspring, without having borne any herself. Also, what if the first-born has a blemish? What about the slaughtering of the first-born? How one finds the best place for the slaughtering - moving/parting/plucking hair without shearing it. Maybe plucking IS the same as shearing... but it's allowed because the goal is dramatically different (moving the hair or fur aside vs. shearing it).

Coming in the middle of a long discussion with a focus on a mix of sacred and regular ashes -- where impurity would be nullified via the mixture. Also, a new mishnah! If one purchases an animal from a non-Jew, and it is nursing, we don't worry that the nursing animal had a different mother. Which leads into a discussion about the opinions represented in the mishnah here, in terms of anonymity.

NOTE: This daf talks about animal miscarriage and extends the conversation to human miscarriage. Please be forewarned. A new mishnah! With various status questions regarding the first-born. Even when the mother has conceived and had a miscarriage before carrying the animal that becomes her first-born to term. Also, if you buy fish brine from someone who is not reliable with issues of purity and impurity, then you have to purify the fish brine. Which is a different process of purification than that of a vessel, for example, because it's liquid to begin with.

More on the female triplet goats who each have triplets to lead into a discussion of Rabbi Shimon's position, as compared to the tanna kama. Specifically about whether a goat that has miscarried will delay for a spate of time before mating again. Which in turn gets into how to count that time, even to the final day. Also, a dispute between Rav and Shmuel (and Rabbi Yochanan) as to whether one can take it as a given that an animal purchased from a non-Jew has had progeny before. How much should one expect the seller to share about the animal he's selling? How much should the buyer be expected to ask?

More on buying an animal from a non-Jew, with the question of whether the animal has given birth before. A goat that has offspring during its first year - those must be the first offspring, and the first-born goes to the kohen. But what if there was evidence of a miscarriage -- does that count as the first-born, as it were? Note the discussion lands on concern for a minority, when there's a stringency (as compared to a leniency). Also, the case of a goat who has female triplets who each has triplets, which leads to sufficient goats for tithing -- with a substantive discussion as to why triplets are needed, when twins might do just as well.

2 mishnayot to close out chapter 2! Two ewes bear 2 male lambs -- both are first-born. One male, one female - the kohen gets the male. But with twins, what goes to the kohen? What about a C-section? Chapter 3 - and a new mishnah: When a Jew purchases an animal from a non-Jew... has that animal given birth already? Or no? And the certainty for not having given birth depends on the youth of the animal. A goat is considered certainly off-spring-free until 1 year old; a sheep, until 2 years old; and an ox or donkey until 3 years old. What if the animal conceived and miscarried, instead of bearing offspring?

More on the case of the male twins whose heads emerged simultaneously -- where Rabbi Tarfon and Rabbi Akiva disagree. Also, delving in deeper, in terms of assessing the lambs, the stronger would go to the kohen, the weaker to the owner. In contrast to Rabbi Tarfon's claim that the first head out is the healthier stronger lamb - and he retracts that approach, eventually. Plus, narrowing the case of the mishnah and understanding the psychology of Rabbi Akiva and Rabbi Tarfon.

If a ewe gives birth to animal that looks like a goat, or vice versa, but also looks a little like its mother... Rabbi Meir says it is subject to the laws of first-born, but the majority view of the sages say no, the owner is exempt. Plus, when lambs are exempt from the first fleece. Also, a new mishnah! When a female sheep gives birth to twin male lambs - and their heads emerge at exactly the same time. Who gets which of the lambs? Does the first-born status kick in, and for which animal? Plus, can such things happen truly simultaneously?