Miscellaneous, the important thing is the certificate, and other envelopes and cards are useless.
The numbers and letters on the inner wall you mentioned are relevant proof of authenticity. Finger code number, independent label, 18K gold mark, and origin mark.
This little brother depends on the authenticity of the ring. You can't see clearly when you take the ring out. There are several boxes, just one with a ring.
There are many styles in the 31 series. Yours seems to be the basic model. Is it narrow? Wide?