A good question. Some people think that they were written by the Rosh but Rabbi Chaim Kanievsky said that they are not from the Rosh but were written by one of the other Rishonim- we do not know who.

Some have suggested that since the end of fourth and ninth perek mark the end of Pesach Rishon and Pesach Sheni (a division made by the Meiri) which discuss different aspects of the masechta, the printer wanted to fill in the page with Halachos so that the next part would appear on a different page.

Others say that these halachos are based on the Rambam and include a number of his halachos verbatim. In some old editions it says explicitly that the Halachos are based on Rambam. This compilation has also been ascribed to Rabbi Yehoshua Boaz, who authored the Masores Hashas which references to Rambam and other gemaros.

However another tradition ascribes them to the Amsterdam edition of the Talmud which was printed in 1714-1717 by the Dayan Rabbi Yehuda Aryeh Leib of Krakow who resided in Frankfurt on Main. (This is brought in a book about the various different editions of the printed Shas- "From Soncino to Vilna" (Heb.)-Yaakov Laufer.) This would fit with the earlier theory we brought of the printer- in this case a Talmid Chacham -filling in the page.

Yoel Domb

This addition is in brackets and refers to the content of the last Perek which indeed is discussed in the Shulchan Aruch. However the previous Halachos are not part of Shulchan Aruch as they do not refer to our time and it is possible that they were written by a Rishon.

Yoel Domb