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You’re welcome to share the info and any other pics you have of the watch. As I said before, got it from private seller on Chrono24 for 1100 euros.
This makes your .004 quite interesting as there are only a relatively small number of .004s with a cal564 movt.
(There is a dedicated thread I started about this)
It also means it is a very late .004 not a very early one as you first thought.
Around 1967.
Do you have the movt serial number yet?
Original crystals are not uncommon on these watches.
You will get a replacement crown which is slightly expressed, unlike the original hidden crown - not original but much easier to use.