howdy,

If I had to guess, I would say those posts are 8X8 and the and that carrying beam an 8X10, but it does look beefy. but then again it is hard to tell without a human

I like your timber sizes better, maybe 3X5 for braces.

p.s. that pergola could probably survive a direct hit from a meteorite.

p.p.s in my opinion it would look better to have the upper members of the pergola run all the way to the end of the carrying beam to emphasize the top. the one above looks light up there from an aesthetic point of view. my two cents.