Gemara

68b (Mishnah): A boy can become a Ben Sorer u'Moreh from the time he brings two hairs (after 13 years) until his beard fills out. This refers to the lower (i.e. pubic) beard, and not the upper one. Chachamim use a clean expression. A minor is exempt, for he is not yet obligated to guard Mitzvos.

69a (R. Kruspedai): A boy can become a Ben Sorer u'Moreh during only three months.

Question (Mishnah): A boy can become a Ben Sorer u'Moreh from the time he brings two hairs until his beard fills out.

Answer: He cannot become a Ben Sorer u'Moreh once his beard fills out, or after three months into his adulthood.

Yevamos 33b (Mishnah): If two brothers were Mekadesh two sisters, and at the time of Chupah they switched wives, they are liable for Eshes Ish, Eshes Ach, Achos Ishto, and if they were Nidos, for Nidah.

The Tana obligates for all Isurim that come at the same moment.

(Rav Amram): If the girls were spurting Dam Nidah when the boys finished 13 years, all the boys' Isurim, including Nidah, come together. If the girls finished 12 years when they were spurting, all their Isurim come together.

80b (Beraisa): If a male did not bring two hairs within 20 years is a Seris, even if he brings hairs later. The Simanim are that he has no beard...

Nidah 46a (Rava): A girl may not do Mi'un (retroactively annul a marriage mid'Rabanan) or Chalitzah after 12 full years.

Rava is not in Safek whether she is an adult, for he taught that we need not check a girl above 12. She is Muchzhekes to be an adult.

Normally, we assume that she is an adult. She may not do Chalitzah in a case when we see that she does not have hairs now. She may not do Mi'un, lest she brought hairs after 12 years, and they fell out.

According to the opinion that is not concerned lest hairs fell out, we can say that we did not check her. Rava's Chazakah is for Mi'un (to forbid it). She may not do Chalitzah until we see hairs.

(Rav Dimi of Neharde'a): The Halachah is, we are concerned lest hairs fell out (regarding Mi'un) only if she had Bi'ah after 12 years, for then it is a Safek mid'Oraisa). If not, she may do Mi'un (she is married only mid'Rabanan).

48b: Just like a man is established to be an adult only through the lower Siman, also a woman.

Berachos 20a (Mishnah): Women, slaves and minors are exempt from Shema and Tefilin, and obligated in Tefilah, Mezuzah and Birkas ha'Mazon.

Sukah 42a (Beraisa): If a minor knows how to guard his body, his father buys Tefilin for him.

Rishonim

Rambam (Hilchos Ishus 2:15): If a boy above 13 did not bring a Siman below, and he brought all the Simanim above, he is a Safek adult. If he was not checked below, since he has Simanei Bagrus above, he is assumed to be an adult.

Rebuttal (Ra'avad): There are no Simanei Bagrus in a boy. There are Simanei Seris, but they do not make him an adult until 20 years.

Magid Mishneh: I do not know the Rambam's source. Nidah 48b says that there is only one Siman in a man.

Lechem Mishneh: Nidah 48b equates men and women. For both, the upper Siman helps only if we do not know about the lower Siman.

Gra (CM 35:5): For a man, surely only the lower Siman helps, like it says in Sanhedrin (the lower beard, and not the upper one; a minor is exempt). It cannot refer to until the lower beard fills out, for we say that this is only three months; the upper beard takes much longer to come. Yevamos 80b connotes that the upper beard can come before lower hairs, but usually the lower comes first. This is why the Rambam says 'if he was not checked below.'

Rosh (Berachos 3:13): Rashi explains that the Mishnah discusses a minor who reached the age of Chinuch. He is exempt from Tefilin for he does not know how to guard his body. R. Tam disagrees, for if a minor knows how to guard his body, his father buys Tefilin for him (Sukah 42a). This is the Shi'ur of Chinuch! Rather, the Mishnah exempts a minor who did not reach the age of Chinuch.

Tosfos (20a DH DH u'Ketanim): The Seifa obligates in Tefilah, Mezuzah and Birkas ha'Mazon. This discusses a minor who reached the age of Chinuch, unlike the Reisha. Alternatively, it applies only to women and slaves.

Question: Why are the Isurim Chal the moment the day begins? They are not adults until they bring hairs after 13. Hairs from before do not help!

Answer #1 (Rashba 34a DH Hachi): We hold like Rav, who says that if a girl brings Simanei Bagrus on the day of Bagrus, we say that she brought them at the beginning of the day (Kidushin 79a). The same applies here.

Answer #2 (Tosfos): Some texts say that the boys' Isurim come at once if the girls were spurting when they turned three years old, and the girls' Isurim come at once if they were spurting when they turned 12. We need not say that they were born the same day, or that they were spurting the entire time. It suffices that they did not immerse in between.

Answer #3 (Mishneh l'Melech Ishus 4:7 DH Shuv): Rashi holds like R. Tam and the Rosh (Nidah 6:2), that R. Yehudah says that during the Perek (the last day of her 12th year) is like after the Perek. (If hairs were found that day, the child becomes an adult immediately at night. The Mishneh l'Melech's text of the Rosh omitted 'and a day'. In our texts of the Rosh, 'and a day' is in brackets.)

Poskim

Shulchan Aruch (OC 37:3): If a minor knows to guard Tefilin in Taharah, his father must buy Tefilin for him to train him in the Mitzvah.

Rema: Some say that this is only for a boy above 13 years. This is our custom. One should not deviate.

Eshel Avraham (4): If the boy is an adult, he himself is obligated! If he is poor, all of Yisrael (not only his father) are obligated to support him (and buy Tefilin for him)! We must say that he is 13, but did not bring two hairs. Until (he brings hairs or) he passes 35 years, his father is obligated to train him. Bach (DH Katan, based on Tosfos Berachos 20b) obligates also a minor; he must be at least 12, and learns and understands.

Beis Yosef (DH Kosav ha'Itur): Ba'al ha'Itur says that we discuss a boy past 13 years. He brought a proof. It does not suffice to override the simple reading of the Beraisa, which obligates a minor. All the Poskim discuss a minor Stam (without specifying 13 years).

Birkei Yosef (6): Tosfos, R. Yonah, the Rashba and the Rosh explicitly say that we discuss a minor past the age of Chinuch! Perhaps the Ba'al ha'Itur learns from Berachos 20a. It totally exempts minors from Tefilin, for the Seifa obligates in Tefilah, i.e. mid'Rabanan due to Chinuch. Tosfos answered this, but Ba'al ha'Itur explains simply. Therefore, Sukah 42a must discuss a boy above 13. Similarly, Rashi needed to say that 'a boy who knows how to spread his hands can Duchan' discusses a boy who brought two hairs, for a Mishnah says that minors do not Duchan.

Ha'arah 9: Hagahos Ish Matzli'ah says that Ba'al ha'Itur holds that Chinuch applies to an adult son in matters that he cannot do himself.

Bi'ur Halachah (DH v'Yesh): Even though after 13 he is obligated letter of the law due to Chazakah d'Rava, his father's obligation of Chinuch is until we know that he brought two hairs. This is very difficult. When he reaches 13 years, his father blesses 'blessed is He Who exempted me (from punishment due to my son).' Some explain that now the father is exempt from Chinuch (Magen Avraham 225:5)! No one says that this is only if he brought hairs. Rather, for Chinuch mid'Rabanan, we rely on Chazakah d'Rava. The Eshel Avraham did not see part 2 of Ba'al ha'Itur (it was printed only later), in which he says that there was no enactment mid'Rabanan. Rather, mid'Oraisa a 13 year-old is obligated to wear Tefilin only if he can guard their Kedushah, even if he brought hairs. This is like Ba'al ha'Itur, but we hold like the other Poskim that this law applies only to a minor. However, the custom is to be stringent for minors not to wear Tefilin, like Ba'al ha'Itur.

R. Akiva Eiger (186:2): If one ate to satiation on the last day he was a minor, and blessed Birkas ha'Mazon before dark, and at night the food was still not digested, does he bless Birkas ha'Mazon. Or, does the Torah obligate only one who ate when he was an adult? This requires investigation.

Ohr l'Tziyon (1:36 DH v'Nir'eh): He asked about one who blessed before dark, for if not, surely he must bless now. If he is not liable mid'Oraisa, he is liable due to Chinuch, even though he is now an adult!