Obama gave up his opportunity to prove he is eligible, so he no longer has a right to submit evidence to either this judge or any appeals court. He is stuck with the facts of this case.
He is not stuck with the facts. The judge declared he was issuing a default judgement before any evidence was submitted because Zippo and or his attorney decided not to show. So the facts of the judgement are "Defendant failed to appear before, and show this court that he is eligible for the office he seeks and to appear on the Georgia primary ballot." That's it. All the Orly stuff and the MvH stuff is fine but it is not "fact" of the decision.
Only in Georgia, and barring some legal maneuver of which I am unfamiliar. I've seen people suggest that a Federal court could enact an injunction and tie the issue up till after the election. Maybe, I don't know.
I would like to see more states file suit to keep him off the ballot. If he keeps not showing up and not presenting evidence, the snowball just gets bigger and bigger.