Hello Rabbi! In the beginning of amud ב, the Gemara says ויניח וייתי ישראל ויהיב ביה סימנא ושקיל, my question is, how would the yid know about his lost item existing? And furthermore, would this interpretation hold that in every case of Rov Cnaanim (I assume the principle in Bava Kamma that rov doesn’t establish ownership only applies when slight majority, if there is 99 goyim and one yid, would we still have chashash that the item is of the yid) the Rabbanan would say that we just hold on to the object indefinitely. That doesn’t make any sense, the whole time the Gemara implies that when he doesn’t have to announce his find it means he keeps the item, and wasn’t one of the questions on רשבא whether the Jew is meyaesh because of Rov Cnaanim, how can the Gemara bring a raya from something we are mesupek on?

ב"ה Shalom In regard to your first question, even if nobody declared that an item was found, the person who lost the item, since he has a "siman" can declare his item lost with his "simanim" and when the finder hears the "simanim" he will return it. The Gemara at the top of כ"ד , amud ב in Baba Metzia, are at the point of explaining that we have no proof that Rabanan agree with R. Shimon that when there is a majority of Nochrim the lost item belongs to the finder since the Braita did not say the finder can keep it only said that he doesn't have to declare it. The reason he does not have to declareit because, since there is a majority of nochrim, Chachamim did not trouble him to declare it, but he may not use the found object. As far as, what is the din when there is a majority of Nochrim, the Shulchan Aruch Choshen Mishpat 259:3 says that even if an item is found when the majority of the city is Nochrim, if most of the passersby in the place are Jewish, he must return the item. All the best