The birth certificate -- obtained by TMZ -- mostly confirms what we already knew thanks to Khloe ... True weighed in at 6 lbs 13 oz and was 21 inches long. It also confirms True was born without a middle name, much like her cousins North, Saint, Stormi and Chicago.

We broke the story ... Tristan was there for True's birth despite the tumultuous time for the couple, and Kourtney, Kim, Kris and Khloe's BFF Malika were also by her side. This is Khloe and the Cavs star's first child together.

As we reported ... True is a family name -- it was the name of Kris' grandfather -- but it's interesting Khloe chose to use Thompson as the baby's last name in wake of his cheating scandal when she didn't have to ... and their relationship is in ruins.