Did the appellate court violate Greene's due process rights by creating an impermissible risk of actual bias by allowing Justice Montgomery to decide Greene's case?

QUESTION PRESENTED Beau Greene is an Arizona death-row prisoner. Due to recent amendments to Arizona’s death-penalty statute by the Arizona legislature, the sole aggravating factor in his case was repealed and subsequently his death sentence was vacated by the Pima County Superior Court. The state appealed, and the Arizona Supreme Court vacated the lower-court ruling and reinstated Greene’s death sentence. Before the court ruled, Greene alerted the court that one of the justices had a conflict of interest in this case. Before his appointment to the Arizona Supreme Court, William Montgomery was the elected Maricopa County Attorney. While he was the County Attorney, his office proposed the amendments in question here and supported passage of the legislation. The legislation went into effect while Montgomery was still in office as the county attorney. Despite Greene’s notice to the court that this legislation played a key role in the litigation, Montgomery declined to recuse himself and went on to write the opinion reinstating Greene’s death sentence. In Williams v. Pennsylvania, 579 U.S. 1 (2016), this Court held that “under the Due Process Clause there is an impermissible risk of actual bias when a judge earlier had significant, personal involvement as a prosecutor in a critical decision regarding the defendant’s case.” Id. at 8. This case is factually analogous to Williams. Did the appellate court violate Greene’s due process rights by creating an impermissible risk of actual bias by allowing Justice Montgomery to decide Greene’s case? i