Fixing the day and date of the Revelation at Sinai. There is some disagreement about whether it took place on the sixth or seventh of the Hebrew month Sivan. However, the day of the week is known:
all agree that the Torah was given to Israel on the Sabbath.
Now this is not just wishful thinking – it is determined by a textual analysis:
[For] here it is written [in the Ten Commandments given at Sinai], Remember the Sabbath day, to keep it holy (Ex. 20:8) and elsewhere it is written, And Moses said unto the people, Remember this day (Ex. 13:3).
Comparing the similarity of the phrase: zachor et yom haShabbat and zachor et hayom haze
Just as there (the second phrase relating to Exodus), [G-d spoke] on that very day, so here too (the first phrase relating to Shabbat) was on that very day.
Therefore – the law of Shabbat (along with all the others) was given on Shabbat!