Patek Philippe

I spotted two certs belong to 3710, one indicate 29 jewels and the other is 30. Which is correct? ...  

I believe the 330 and 315 movements were first introduced with 29 jewels. Then it was changed to 30, and then later back to 29 again. I guess they went back and forth what is the best material to use at the position where the 30th jewel may be.