What sources are there for the meaning of Yom HaMeyuchos (2nd Sivan)?

Question

Ohr Sameach gives the chronology according to Rashi of the giving of the Torah.

Early the following morning, the 2nd of Sivan, Moshe goes up Mt. Sinai for the first time. He is instructed to offer the Jews the opportunity of accepting the Torah, and of becoming a holy people. (19:3-6). That same day Moshe descends and assembles the elders and passes on the message. The entire people respond in unison that whatever HaShem says, they will do. (19:7-8).

Beis Tefillah Yonah Avraham points out that this day

is traditionally known as Yom HaMeyuchos (loosely–the special day). Aruch haShulchan explains why: This is the day that Moshe Rabbeinu told B’nei Yisrael that they must sanctify themselves in preparation for mattan Torah.

I always thought that it had this name because we became a ממלכת כהנים וגוי קדש and that is the yichus, distinguished lineage that we have.

What sources are there for the meaning of Yom HaMeyuchos?

Answer 1

• Because it stands between the two holy days of Rosh Chodesh Sivan and the Shloshes Yemei Hagbala (similar to Taanis 18a: "Since it was between two festivals, they made it a festival itself. See also Sanhedrin 104a. - Ta'amey Haminhagim (610). Nitey Gavriel brings it in the name of Shu"t Haelef Lecha Shlomo (331)
• Since on that day Hashem said to us "ואתם תהיה לי ממלכת כהנים וגוי קדוש" and we thus became מיוחסין. - Likutey Maharich. Ta'amey Haminhagim (611) in the name of Sha'ar Bas Rabim

• Because Moshe told the Jewish people on that day to sanctify themselves in preperation of Matan Torah. (Aruch Hashulchan 494:7)

• Because Yom Kippur will always fall on the same day of the week as Beis Sivan (Aruch Hashulchan there)

• The reason the Jewish people recieved the Torah was because of our יחוס, as the Yalkut says: When the Jews recieved the Torah, the nations of the world were jealous and protested, "How are these people more fit than the other nations?" Hashem replied to them: "Bring me your books of lineage.." - Ta'amey Haminhagim (612) in name of Ezor Eliyahu Parshas Bamidar