Rumi and Sir Carter Birth Certificates, Delivered by Kardashians' OB/GYN

Now we know ... Rumi Carter is the big sis and Sir is the little bro -- their birth certificates reveal when and how they came into the world.

TMZ obtained the docs for Beyonce and Jay-Z's twins, and it nails down their delivery date and time -- June 13 at 5:13 AM. Rumi came out first, and Sir followed shortly thereafter.

What's really interesting is the doctor who pulled off the delivery -- none other than Dr. Paul Crane. The same guy who delivered Kim and Kourtney Kardashian's 5 kids ... and Rob and Blac Chyna's little girl, Dream.