seudas mitzvah for a siyum by a woman or katan

Is a siyum made by a katan enough of a reason to allow eating meat during the 9 days? What about a siyum by a woman? Why am I bringing this up when the 9 days ended last week and we are now approaching T"u b'Av?

I think the answer to this question may hinge on what the source is for the idea of making a siyum. One of the sources is the celebration of T"u b'Av. The gemara (B"B 121b) tells us that 15 Av was the day when the season of cutting of wood for use on the maaracha came to a close because after that day the wood was not dry enough to be usable. Rashbam comments:

ואותו יום שפסקו היו שמחים לפי שבאותו יום היו משלימין מצוה גדולה כזאת:

The completion of a mitzvah, says Rashbam, is a cause for celebration.  This is exactly what a siyum is.

Rabeinu Gershom reads the gemara differently. He comments:

ולפי שעה שהיו עסוקים לכרות עצי המערכה היו מתבטלין בתלמוד תורה אבל אותו יום פסקו ועשאוהו יום טוב שמיכן ואילך היו עוסקין בתורה:

The celebration was not because of the siyum of a mitzvah, but rather because not having to chop wood allowed more time for learning. The motivation behind R' Gershom's reading becomes clear from the next line in the gemara:

מִכָּאן וְאֵילָךְ, דְּמוֹסִיף – יוֹסִיף, שֶׁאֵינוֹ מוֹסִיף – יְסִיף. מַאי ״יְסִיף״? תָּנֵי רַב יוֹסֵף: תִּקְבְּרֵיהּ אִמֵּיהּ.

Since the nights grow longer after 15 Av, a person is required to spend more time at night learning.

According to Rashbam, this is a stand alone statement.  It has nothing to do with wood chopping except in the sense that it's the change in season that is the root cause of both events, i.e. a shortened day means both less sun to dry the wood and a longer night to learn. According to R' Gershom, there is a direct connection between the two statements.  The whole celebration of the cessation of wood chopping was because it allowed for more time to learn.

A second source for the idea of making a siyum quoted in Rishonim has to do with a feast made by Shlomo haMelech. In Sefer Melachim ch 3, Shlomo haMelech is told by Hashem to ask for what he pleases, and he responds by requesting chochma. Hashem was so pleased by that choice that in addition to chochma, Hashem gave Shlomo riches and all the other good things he could have asked for instead. Shlomo responded by celebrating.

וַיִּקַץ שְׁלֹמֹה וְהִנֵּה חֲלוֹם, וַיָּבוֹא יְרוּשָׁלִַם וַיַּעֲמֹד לִפְנֵי אֲרוֹן בְּרִית ה', וַיַּעַל עֹלוֹת וַיַּעַשׂ שְׁלָמִים וַיַּעַשׂ מִשְׁתֶּה לְכָל עֲבָדָיו.

The Midrash (Koheles Rabbah) learns from here אמר רבי יצחק: מכאן שעושין סעודה לגומרה של תורה.

The Ohr Zarua (vol 2 hil sukkah) writes that this is the source for our celebration of Simchas Torah:

בתשיעי ספק שמיני אנו עושין שמחת תורה, ומסיימין התורה ומתחילין בראשית, וחתני תורה עושין סעודה לכבוד גמר תורה. ובמלכותנו בשושני"א עושים חתני תורה סעודה גמורה, ומזמנין מבני הקהל ונותנים להם מאכלים טובים אווזות ותרנגולין. ומצאתי עיקרו של מנהג אני המחבר יצחק ב"ר משה נב"ה בתחילת מדרש שה"ש, ויבוא ירושלים ויעמוד לפני ארון ברית ה', אמר רבי יצחק מיכן שעושין סעודה לגומרה של תורה... הנה כשנתן לו הקדוש ברוך הוא חכמה, לכבוד החכמה עשה משתה, ומיכן למד רבי יצחק שהגומר תורה שכולה חכמה שצריך לעשות סעודה ומשתה

You cannot characterize Shlomo haMelech's celebration as one of משלימין מצוה גדולה, like the Rashbam's sevara. Aderaba, he hadn't done anything yet; there was no mitzvah which he had completed or fulfilled. Shlomo was simply the beneficiary of a gift from Hashem. The reason for his celebration was because he now had achieved a higher level of ruchniyus and could potentially accomplish more. The idea of a siyum, of Simchas Torah, is that the completion of a masechta, or of a cycle of Torah reading, means a person has grown and is a better, more elevated person than they were beforehand. Maybe this is why at a siyum we say "hadran alach," that we will return to our learning. The siyum is not celebrating the past, but rather is celebrating the potential for the future.  The next time around is not just a repeat, but is a deeper, richer experience than before, as we are a different person now encountering the text.

I would be remiss if I did not mention in the list of sources the gemara (Shabbos 118b) that says Abayei would make a siyum when a student finished a masechta.  I think this is the source people are most familiar with:

וְאָמַר אַבָּיֵי: תֵּיתֵי לִי, דְּכִי חָזֵינָא צוּרְבָּא מֵרַבָּנַן דִּשְׁלִים מַסֶּכְתֵּיהּ עָבֵידְנָא יוֹמָא טָבָא לְרַבָּנַן

The problem with using this gemara as a source for a siyum is that the sugya there is discussing various hidurim of amoraim for which they were rewarded. The implication is that Abayei's practice was not the norm, but was something exceptional done on his part. Secondly, Rashi comments: עבידנא יומא טבא לרבנן - לתלמידים ראש ישיבה היה. The point of telling us Abayei's job - rosh yeshiva - is that it seems that making the siyum was part and parcel of his job function. How do you encourage the students? By celebrating their achievements. It is hard to generalize from there to someone making a seudah to celebrate their own completion of a masechta.

Since a woman or a katan have no mitzvah to learn, I would think that we can't really call their accomplishment being משלימין מצוה גדולה. How can you be mashlim a mitzvah when there is no mitzvah incumbent upon you to do? I do hear the counterargument that even an "aino metzuveh" deserves credit for accomplishment, but I am not entirely convinced.  The source from Shlomo haMelech, however, would include even a woman and even a katan, as it has nothing to do with the mitzvah per se so much as the effect it has on the individual.