Where no clearly established United States Supreme Court precedent establishes a defendant’s due process right to a speedy appeal, AEDPA requires dismissal of writ petition. Sentenced to death, petitioner sought a writ of habeas corpus because the California Supreme Court’s delay in resolving his direct appeal denied him due process under the Fourteenth Amendment. To the extent petitioner claims a present harm from the delay, his petition is moot because the California Supreme Court denied his appeal. Further, under current United States Supreme Court law, the federal court lacks jurisdiction to order the state court to process his appeal. There is a distinction between claims that challenge the validity of the conviction and requests to compel speedier processing of an appeal to which state law entitles the petitioner – the later raises an issue of process and does not “necessarily imply the invalidity of [a] conviction” or “spell speedier release” and therefore does “not lie at the core of habeas corpus.” As to future harm from the delay, such as fair trial on remand, the Anti Terrorism and Effective Death Penalty Act of 1996 (“AEDPA”) prohibits the federal court from granting habeas relief unless the state court decision was contrary to clearly established United States Supreme Court authority. No clearly established Supreme Court authority “recognizes a due process right to a speedy appeal.” Dismissed.