@JonEricson Very little. "Authentic" means it is not a later forgery, that it really was written in the 4th century, not that it speaks the truth. It is one piece, and a very small piece, separated by several centuries from any eye witnesses or even second hand accounts. The writing represents a sect that believed Jesus was married. Even in the article, the professor repeatedly cautions that this should not be taken as proof that Jesus was married.
On the other hand, Dan Brownand other conspiracy theorists will take this as solid proof that Jesus was married and the church covered it up to hold women down.
I'm not ready to bring the mod hammer down, but this doesn't seem like the most productive question in the world. It doesn't seem ontopic (it's explicitly not about Biblical texts), but I can see the possible application of any answer it might get. What do y'all think?