Nanchang CJ-6 Spotted

A Nanchange CJ-6 flew over my house in Austin a couple of times today. I did not see a tail number. Is the number in the front unique for these? If so, I found another one online with the same number. Here are images of the plane that flew over my house.

Here is a website showing the one with the same 69 in front.
http://warbirds-eaa.net/charlie-nelsons-nanchang-cj-6a/

N6313N

I read somewhere this can be distinguished from the Soviet Yak by the square tail. True?

CJ-5 was built based on the Yak-18:

CJ-6 was different:
Nanchang CJ-6 - Wikipedia

It sounds like you’re trying to contradict me, but the website you posted seems to back up what I said, namely that my picture is of a Nanchang CJ-6, not a Yak. Do you disagree with this? More relevant to what I was originally after, is there any way to determine the registration from my photos?

Not contradicting, I was just pointing that CJ-6 is not based on YAK, not directly. Only CJ-5 was.

Also the wiki CJ-6 page shows the plane in your case was indeed CJ-6 (not that you needed a confirmation) :
The dihedral and an angular vertical tail distinguish it externally from the otherwise rather similar Yak-18A.