What is the oldest manuscript of Torah Shebaal Peh?

Question

We don't have (and more's the pity!) R' Yehudah Hanassi's autograph copy of the Mishnah (well, okay, it's a controversial issue whether he actually wrote it or only arranged it orally), or Ravina and Rav Ashi's of the Gemara, etc.

But what is the oldest known manuscript of the Mishnah, Gemara, Mechilta, or any other part of Torah Shebaal Peh? (Or perhaps there are manuscripts of Geonic writings - responsa, Halachos Gedolos, or whatever - that predate any known copies of the foundational texts?)

Answer 1

The oldest written Torah Sheb'al Peh (though not exactly a manuscript) would seem to be the recently-discovered mosaic of the ancient shul in Beit Shaan. The Hebrew Wikipedia article about that shul (which was destroyed 1300 years ago, and existed a few hundred before that) can be found at this link. Here is their image of the mosaic (I hope I'm allowed to use their image link):

The text is similar to passages in Yerushalmi Sheviis. An analysis of this text can be found in Teshuvos Mishnas Yosef 1:51, and at the end of Kaftor Vaferach vol. 1 (in the 3-volume edition).