Mishneh Torah, Fasts 5:6-7
משנה תורה, הלכות תעניות ה׳:ו׳-ז׳
Mishneh Torah, Fasts 5:6-7
The Rambam discusses communal mourning practices for national calamities and the customs of abstention associated with mourning for the destruction. While not about siyumim specifically, it provides the conceptual basis for later mourning restrictions.
מִשֶּׁיִּכָּנֵס אָב מְמַעֲטִין בְּשִׂמְחָה. וְשַׁבָּת שֶׁחָל תִּשְׁעָה בְּאָב לִהְיוֹת בְּתוֹכָהּ אָסוּר לְסַפֵּר וּלְכַבֵּס וְלִלְבּשׁ כְּלִי מְגֹהָץ אֲפִלּוּ כְּלִי פִּשְׁתָּן עַד שֶׁיַּעֲבֹר הַתַּעֲנִית. וַאֲפִלּוּ לְכַבֵּס וּלְהַנִּיחַ לְאַחַר הַתַּעֲנִית אָסוּר. וּכְבָר נָהֲגוּ יִשְׂרָאֵל שֶׁלֹּא לֶאֱכל בָּשָׂר בְּשַׁבָּת זוֹ וְלֹא יִכָּנְסוּ לַמֶּרְחָץ עַד שֶׁיַּעֲבֹר הַתַּעֲנִית. וְיֵשׁ מְקוֹמוֹת שֶׁנָּהֲגוּ לְבַטֵּל הַשְּׁחִיטָה מֵרֹאשׁ הַחֹדֶשׁ עַד הַתַּעֲנִית:
When the month of Av enters, we reduce our joy. During the week of Tish'ah B'Av, it is forbidden to cut one's hair, to do laundry, or to wear a pressed garment - even one of linen - until after the fast. It has already been accepted as a Jewish custom not to eat meat or enter a bathhouse during this week until after the fast. There are places that follow the custom of refraining from slaughtering from Rosh Chodesh Av until after the fast.