You are completely misinformed. Reasonable doubt applies at trial, not on appeals. Also, the ad hominem adds nothing to your point.
Edit: look at Herrera v. Collins (SCOTUS): "Petitioner's claim of actual innocence based on newly discovered evidence is not ground for federal habeas relief. United States Court of Appeals for the Fifth Circuit affirmed."
Two questions were presented for the Supreme Court's review:
Do the Eighth and Fourteenth Amendments permit a state to execute an individual who is innocent of the crime for which he or she was convicted and sentenced to death?
What post-conviction procedures are necessary to protect against the execution of an innocent person?
Is the critical distinction in "federal habeas relief"? Does that mean that state appellate courts can/do consider evidence of innocence in order to vacate a conviction?
No it doesn't. It just means that this particular case doesn't speak to states doing that or not. It has no applicability outside of federal habeas relief.
Edit: look at Herrera v. Collins (SCOTUS): "Petitioner's claim of actual innocence based on newly discovered evidence is not ground for federal habeas relief. United States Court of Appeals for the Fifth Circuit affirmed."
Two questions were presented for the Supreme Court's review:
Do the Eighth and Fourteenth Amendments permit a state to execute an individual who is innocent of the crime for which he or she was convicted and sentenced to death? What post-conviction procedures are necessary to protect against the execution of an innocent person?
https://en.wikipedia.org/wiki/Herrera_v._Collins