Shemini Atzeres as the unity of the festival

שמיני עצרת הוא כולל כל ז' ימי החג כמ"ש תשלומין דראשון הוא.

Shemini Atzeres encompasses all seven days of the chag, as it is said that it is the "completion" of the first day.

Shemini Atzeres is not merely an eighth, separate day; it gathers and completes the entire festival of Sukkos.

דכתיב תחגו את חג ה' שבעת ימים ביום הראשון שבתון וביום השמיני שבתון.

For it is written: "You shall celebrate the festival of Hashem for seven days; on the first day a rest, and on the eighth day a rest" (Vayikra 23:39).

The Torah pairs the first day and the eighth day, both called "a rest," linking the close of the festival back to its opening.

שמיני מאן דכר שמי' שבעת ימים כתיב.

"The eighth" — who mentioned it? The verse speaks of seven days!

The Sefas Emes raises the textual difficulty: the verse states "seven days," so how does it suddenly refer to an "eighth day"?

רק כי השמיני הוא כלל הז' ימים והם בפרט ואח"כ בכלל.

Rather, the eighth day is the all-encompassing whole (klal) of the seven days — they exist first as separate details (perat), and afterward as a unified whole.

The seven days unfold as distinct particulars, and Shemini Atzeres draws them all back together into a single, unified totality.

ולכן בפרטות מתפשטין הז' ימים גם לשבעים וזהו ע' פרי החג.

Therefore, in their particular state, the seven days spread out even into seventy — and this is the seventy bulls of the chag.

In their "detail" mode, the seven days expand outward to embrace the seventy nations, represented by the seventy bulls offered over Sukkos.

אבל שמיני עצרת תהי' לכם שהוא האחדות.

But "Shemini Atzeres shall be for you" (cf. Bamidbar 29:35) — for it is the oneness.

The eighth day is "for you" alone, expressing the unity that gathers all the scattered particulars into one.

ובזה אין חלק רק לבנ"י.

In this there is a portion for none but Bnei Yisrael.

The unity of Shemini Atzeres belongs exclusively to the Jewish people; the nations have no share in it.

דסט"א שארי בחבורא ומסיים בפרודא.

For the sitra achra (the side of impurity) begins in unity but ends in separation.

The way of impurity may appear unified at first, but it inevitably leads to fragmentation and division.

אבל סטרא דקדושה להיפוך מן הפרטים נעשה אח"כ כלל אחד:

But the side of holiness is the reverse: out of the separate particulars there comes afterward a single unified whole.

Holiness works in the opposite direction — it begins with multiplicity and diversity and culminates in true oneness, just as the seven days of Sukkos culminate in the unity of Shemini Atzeres.

Summary: The Sefas Emes explains that Shemini Atzeres is the klal — the unifying whole — that completes the seven days of Sukkos. During the chag, the days spread out into seventy, corresponding to the seventy bulls offered for the seventy nations; but Shemini Atzeres, "for you" alone, draws all these particulars back into a single oneness that belongs exclusively to Bnei Yisrael. This reflects a deep principle: the sitra achra begins in unity and ends in fragmentation, whereas the side of holiness begins with diverse particulars and culminates in true, lasting unity.