No. The Judge will produce a trial summary report in the next 90 days. The defense will then have 45 days to appeal. The prosecution may respond to those appeals. That will be presented to the Supreme Court.
The Supreme Court will make a decision to:
- accept the appeal and return the case to the Appeals level, or
- that the appeals are unfounded, and confirm the verdict, or
- that the sentence should be reduced/increased.
If there are no errors in logic and reasoning, the appeal will most likely be denied and the verdict will be confirmed. Then it's written in stone. That is most likely when the extradition process will begin.
Double jeopardy is not an issue as Knox is not being tried in Italy after being tried in the US. Italy has to produce a brief statement of facts of the case, relevant laws, a description of the punishment and the statute of liminations. On that basis, a decision will be made. I see no reason why the US would not recognize a murder conviction in a country where there are extradition treaties.