Challenging a biased judge

1. Whether the Due Process Clause of the Fourteenth Amendment requires a State to afford some procedural mechanism, subject to appellate review, through which a litigant may raise a substantial claim that the judge who decided his case was constitutionally disqualified by criminal conduct the judge concealed, where the facts supporting the claim could not have been discovered until after the ordinary time to appeal had run, and where the State’s appellate courts have dismissed the claim as untimely without reaching it, pointing only to a trial-court motion whose availability for such a claim is unsettled under state law. 2. Whether Rippo v. Baker, 580 U.S. 285 (2017) — which holds that the Due Process Clause guarantees an objectively impartial tribunal — together with the principle this Court applied in Bracy v. Gramley, 520 U.S. 899 (1997), in permitting a habeas petitioner to develop a comparable bias claim through discovery before being held to his ultimate burden of proof, is satisfied by a State’s direction to file a fresh motion in the trial court under a provision whose availability for a claim of this kind is unsettled under state law, with appellate review available only from a denial and no tolling of the clock that has run in the interim. 3. Whether Bowles v. Russell, 551 U.S. 205 (2007), which holds that courts lack authority to create equitable exceptions to a jurisdictional filing deadline, applies with the same force where the litigant’s claim could not have been formulated at all before the deadline expired, because the fact giving rise to it was concealed by the very judicial officer whose conduct is at issue — or whether that circumstance instead bears on when such a claim accrues, a question Bowles did not present or decide.