Yisrael is Shabbos's Torah partner

איתא בגמ' דכ"ע בשבת ניתנה תורה זכור בעצומו של יום.

It is taught in the Gemara that all agree the Torah was given on Shabbos — "Remember" was said on the very essence of the day.

The Gemara concludes that everyone holds Matan Torah took place on Shabbos, connecting it to the commandment "Zachor" (Remember the Shabbos), which was spoken on that very day.

דאיתא אמרה שבת לכל יש בן זוג ולי אין בן זוג השיב לה כנס"י יהי' בן זוגך הה"ד זכור אשר אמרתי כנס"י יהי' בן זוגך ע"ש בפסיקתא.

For it is taught: Shabbos said, "Every day has a partner, but I have no partner." He answered her, "Knesses Yisrael shall be your partner" — this is the meaning of "Remember" — that I said Knesses Yisrael shall be your partner — see there in the Pesikta.

The Midrash relates that the six weekdays were paired off (day one with two, three with four, and so on), leaving Shabbos without a mate. Hashem assigned Knesses Yisrael as Shabbos's partner — and this pairing is what "Zachor" recalls.

והענין הוא דאיתא שבת יעשה כולו תורה הגם כי כל מעשה בראשית בכח התורה כדאיתא בשביל התורה שנקראת ראשית.

The matter is, as it is taught, that Shabbos should be made entirely Torah; for although all of creation came about through the power of the Torah, as it is taught, "for the sake of the Torah, which is called 'reishis.'"

Shabbos is meant to be wholly devoted to Torah. True, the entire creation was brought into being through Torah — Chazal read "In the beginning (reishis)" as "for the sake of Torah, called reishis" — yet on the weekdays that power is clothed within action.

אבל כל הששה ימים הי' כח התורה בהשתתפות המעשה כדכתיב ששת ימים עשה.

But all six days, the power of the Torah was in partnership with action, as it is written, "six days He labored."

During the six workdays the Torah's power was bound up with physical creation; the divine light was active through deed, "six days He made."

ולכן יש בתחתונים דרך לקבל זו ההארה המתלבשת בכל מעשה בראשית.

Therefore there is a way for those below to receive this illumination that is clothed within all the work of creation.

Because the weekday light is enclothed in physical action, beings of the lower world have a means to grasp and receive it through their own deeds.

אבל בשבת כתיב וינפש ולא הי' בו מעשה והיא כולה תורה לכן אין בתחתונים מי שיוכל לקבל זו ההארה של השבת רק כנס"י יהי' בן זוגך שהם עתידין להיות למעלה מן העשיה ושיהי' כולו תורה ונתקיים במעמד הר סיני ונשאר מזה זכר בכל ש"ק שמבטלין בנ"י כל המעשים והוא יום שביתה והוא עדות על ישראל שהם מיוחדים לתורה למעלה מעשי':

But on Shabbos it is written "and He rested" — there was no action in it, and it is entirely Torah; therefore there is no one among those below who can receive this illumination of Shabbos, except "Knesses Yisrael shall be your partner" — for they are destined to be above action, and that it be entirely Torah; this was fulfilled at the standing of Har Sinai, and a remembrance of it remains on every Shabbos Kodesh, when Bnei Yisrael nullify all deeds — it is a day of rest, and a testimony upon Yisrael that they are designated for Torah, above action.

Shabbos, marked by "vayinafash" (rest) with no action, is pure Torah — and no lower being clothed in deed can receive its illumination. Only Knesses Yisrael can be its partner, because Yisrael is destined to rise above mere action into a state that is wholly Torah. This was realized at Har Sinai (which fell on Shabbos), and an echo remains every Shabbos, when Yisrael cease all melachah; their rest itself testifies that they belong to Torah, above the realm of action.

Summary: All agree the Torah was given on Shabbos, the day that had no "partner" until Hashem paired it with Knesses Yisrael. On the six weekdays the Torah's light is clothed in action, so the lower world can receive it through deed; but Shabbos is "rest" with no action — pure Torah — which no action-bound being can grasp. Only Yisrael, destined to rise above action into a state wholly of Torah, can be Shabbos's partner. This was fulfilled at Sinai, and every Shabbos, when Yisrael cease all melachah, testifies that they are designated for Torah, above the realm of deed.