After a day at the beach I am tired. But I would like to mention a important point. The Gemara in Nida pg 2b says if one goes into a natural body of water [like a mikve] and it was found lacking the proper volume is not clean. [R Shimon said the pure things made after that are in doubt if in a private domain and pure in a public domain.] The Gemara asks from the teaching about a barrel.  One puts aside a barrel of wine to use for truma and later was found to have soured. For the first three days the truma is truma. After that is a doubt. Rav Hanina from Sura said the teaching on the barrel is R. .Shimon.

The Gemara then explains why. While at the sea it occurred to me that even before the explanation of the gemara the teaching of R Shimon in the Mishna and the braita do not seem to correspond. Another point that Rav Shach brings is the explanation of the Gemara is a bit disjointed

The gemara says both the sages and R Shimon learn from sota, and in the middle of this explanation they insert that the sages are learning from two status's opposed to one, The man was not clean and the mikve is now not okay, while one status is that originally the mikve was ok,

This explanation has no need to learn from sota. 

Rav Shach thus say that these are two separate explanations and it was  Rav Hanina that said one [תרתי לרעיותא] while and according to that one, the barrel teaching is R Shimon. But to the explanation from sota the barrel can be also the sages, This answers why the Rambam decides the law like the sages and also barrel.