Who authored the three hagahos in Rosh HaShanah?

Question

In Rosh HaShanah 11b, at the top of the page in the standard Vilna style printings, is a marginal gloss introduced with the word הג״ה. There is another, introduced with the same word, on the right-hand margin of 17b, and one starting with הכי גרסינן at the bottom of 35a. Who is the author of these notes?

From the fact that the Bach comments on the girsa of both the first and the last of these three notes, we can assume that their author lived prior to the 16th century. The first of them makes reference to Rashi, and the second concludes with a reference to "the Rav", but I don't know who that is referring to.

Answer 1

It seems that these hagahot were written mostly by a number of Tosafists, though I don't know who added them to the Shas/connected them to the Tosfot in R"H¹. From what I can tell, they don't appear in this 15th-16th century manuscript of the Tosfot of R"H (and other masechtot), though I may be wrong, as it's hard to read².

The one at 11b appears to be divided into sections: The first is based on the Riva on Beresheet 18:10 and 18:12 (with a number of (minor) differences in wording, perhaps due to scribal error). I haven't managed to discover where the other section comes from, although as the Riva is quoting the Ra"Sh of Senz, it may be from him, but I haven't managed to find where the Ra"Sh wrote this.

The one at 17b appears to be from the Riva on Shemot 34:6 (although there's at least a one word difference between the הגה"ה and Sefaria's version, from what I can tell, perhaps also due to scribal error).

According to this book, the one in 35a was written by Rabbi Meir ben Shmuel, the son-in-law of Rashi.

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¹ It was suggested to me on the Daf-Yomi forum that the hagahot were most likely written by whoever wrote the manuscript of the Tosfot on R"H that was used by the Bomberg press (in whose edition these hagahot also appear). Likely they were personal marginal notes by that scribe that were then copied over to the printed edition. It seems the reason that no hagahot appear in other masechtot (to my knowledge) is because the Tosfot MSS used for those lacked hagahot.

² If there's anyone who's willing to go over the manuscript and check if I'm correct about it not including the hagahot, that would be great.