
594 F.3d 1260 (2010)
Robert Wayne LAMBERT, Petitioner-Appellant,
v.
Randall WORKMAN, Warden, Respondent-Appellee.
No. 09-5108.
United States Court of Appeals, Tenth Circuit.
February 10, 2010.
*1261 Submitted on the briefs:[*] Mark Henricksen and Lanita Henricksen, Henricksen & Henricksen, Oklahoma City, OK, for Petitioner-Appellant.
Before GORSUCH and ANDERSON, Circuit Judges, and BRORBY, Senior Circuit Judge.
ANDERSON, Circuit Judge.
Petitioner Robert Wayne Lambert was tried and convicted in Oklahoma twice for the first-degree murders of Laura Lee Sanders and Michael Houghton. The Oklahoma Court of Criminal Appeals (OCCA) rejected numerous objections to affirm his second convictions and associated death sentences. Lambert v. State, 984 P.2d 221 (Okla.Crim.App.1999). He then sought habeas relief on many of the same grounds in the federal district court, which denied his petition in a thorough opinion. Lambert v. Workman, 2009 WL 1941971 (N.D.Okla. July 2, 2009).[1] Lambert filed a notice of appeal and now asks this court to issue a certificate of appealability (COA) limited to the claim that his second trial for, and resultant conviction of, felony murder violated the constitutional prohibition *1262 on double jeopardy. We deem this claim "adequate to deserve encouragement to proceed further," and therefore grant COA to afford it "full consideration" on appeal. Miller-El v. Cockrell, 537 U.S. 322, 336, 338, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003). Upon full review, however, we affirm the district court's decision to deny relief for the reasons explained below.

I
Lambert's initial murder conviction, on a general verdict encompassing both malice-aforethought and felony murder, was reversed on appeal because he had been charged solely with malice-aforethought murder and had conducted his defense accordingly, to his demonstrable prejudice. Lambert v. State, 888 P.2d 494, 503-05 (Okla.Crim.App.1994). The OCCA remanded for a new murder trial, with the express understanding that the State could re-file the charging information to add felony murder. Id. at 505. At the same time, the OCCA affirmed Lambert's associated felony convictions, including the armed robbery that served as the predicate for felony murder in the first trial. Id.
On remand, the State elected to charge both forms of first-degree murder. Lambert was retried and again found guilty under a general verdict. He argued that double jeopardy should have barred his trial on the felony-murder charges, citing the established rule that a final judgment of conviction on a lesser-included offense (here, the predicate felony affirmed on Lambert's first appeal) precludes subsequent prosecution for a greater offense (the felony-murder charges), see Brown v. Ohio, 432 U.S. 161, 168-69, 97 S.Ct. 2221, 53 L.Ed.2d 187 (1977). The OCCA rejected this argument, citing the equally established principle of "continuing jeopardy," see Justices of Boston Mun. Court v. Lydon, 466 U.S. 294, 308, 104 S.Ct. 1805, 80 L.Ed.2d 311 (1984), which sanctions retrial on charges (here, for felony murder) after a prior conviction thereon has been reversed for trial error. Lambert, 984 P.2d at 227-29. The OCCA affirmed the murder convictions and, to obviate concerns about multiple punishment following conjoint conviction of greater and lesser-included offenses, see Rutledge v. United States, 517 U.S. 292, 307, 116 S.Ct. 1241, 134 L.Ed.2d 419 (1996), vacated the predicate felony conviction.[2]Lambert, 984 P.2d at 229, 238.
On habeas review, the district court concluded that Lambert "ha[d] not demonstrated that the OCCA's rejection of his double jeopardy challenge was contrary to [or] an unreasonable application of Supreme Court precedent." Lambert, 2009 WL 1941971, at *12. Thus, under the deferential standard of review in 28 U.S.C. § 2254(d), the state court's adjudication was not subject to federal interference. Lambert, 2009 WL 1941971 at *12. We agree with this assessment.

II
As our summary of Lambert's appeal before the OCCA reflects, this case involves the intersection of two distinct and potentially opposing principles. On the one hand, a defendant cannot be prosecuted for a greater offense following his conviction for a lesser-included offense. *1263 Thus, leaving aside the unified character of the prosecution here, Lambert's conviction on the predicate felony charge, affirmed by the OCCA on his first direct appeal, would have precluded his subsequent prosecution for felony murder. On the other hand, the State may retry a defendant who remains in "continuing jeopardy" after his conviction has been reversed on appeal for trial error. Thus, leaving aside Lambert's affirmed conviction on the lesser-included felony charge, the State could have retried him following the reversal of his initial murder convictions. This case essentially requires a choice between the two principles: did Lambert's lesser-included felony conviction preclude the felony-murder retrial otherwise permitted by the continuing-jeopardy principle, or did Lambert's continuing jeopardy on the felony-murder charge override the prohibition on successive prosecution of greater and lesser-included offenses?
This habeas proceeding is governed by the deferential review standards set out in § 2254(d), which, when factual determinations are not at issue or in dispute, turn conclusively on the presence or absence of Supreme Court precedent clearly establishing the legal right on which the petitioner's claim is premised. As we recently summarized:
Our review of a petition for writ of habeas corpus is governed by the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"). If the state court adjudicated the claim on the merits, a petitioner is entitled to habeas relief only if he can establish that the decision was "contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," 28 U.S.C. § 2254(d)(1)....
In ascertaining whether the law is clearly established, we review Supreme Court holdings extant when the state court conviction became final.... Federal courts may no longer extract clearly established law from the general legal principles developed in factually distinct contexts. Finally, whether the law is clearly established is dispositive of the § 2254(d)(1) analysis. Specifically, only if we determine that the law is clearly established do we inquire whether the state court decision is either contrary to or an unreasonable application of that law.

Fairchild v. Workman, 579 F.3d 1134, 1139 (10th Cir.2009) (emphasis added) (case citations and quotations omitted).
Lambert has not cited, nor have we found, any Supreme Court authority clearly establishing the proper reconciliation of the competing double-jeopardy principles at issue here. Under the AEDPA standards set out above, that is fatal to his claim. Unless and until the Supreme Court decides that retrial following the reversal of a conviction is barred when a lesser-included offense conviction is simultaneously affirmed, habeas relief on this basis is unavailable, and it is not the province of this court to resolve the issue here. But, just to buttress our dispositive holding that Lambert's claim was not clearly established, we note that the Ninth Circuit rejected precisely the same claim in a recent direct criminal appeal. After an extensive analysis that acknowledged the lack of controlling Supreme Court precedent and looked to relevant circuit authority, the court held that the continuing-jeopardy principle permitted retrial on felony-murder charges despite the concomitant affirmance of the underlying felony convictions. See United States v. Jose, 425 F.3d 1237, 1239-48 (9th Cir.2005).

III
Lambert advances another, related argument in support of his double-jeopardy *1264 claim. He contends that, after affirming his murder convictions on his second direct appeal, the OCCA acted improperly by curing the resultant multiple-punishment problem (joint conviction of greater and lesser-included offenses) by sua sponte directing the dismissal of the predicate felony conviction affirmed on his first appeal. He insists that the only curative action left to the OCCA at that point was to reverse his felony-murder convictions instead. This argument fails as well.
After reversing Lambert's murder conviction on his first appeal, the OCCA indicated that, should the State successfully retry him for felony murder, the trial court was to abrogate any lesser-included felony conviction. Lambert, 888 P.2d at 505. The trial court failed to do this, and the OCCA simply corrected the error on Lambert's ensuing appeal. Lambert, 984 P.2d at 229. We fail to see how this constitutes a "violation of the Constitution or laws or treaties of the United States" subject to redress under § 2254(a). The basic curative procedure followed by the OCCA, vacating the lesser of two multiplicious convictions left standing by the trial court, is standard practice in double-jeopardy jurisprudence. See, e.g., United States v. Hernandez, 94 F.3d 606, 612 (10th Cir.1996); United States v. Morehead, 959 F.2d 1489, 1507 (10th Cir.1992). The OCCA did the same thing when it affirmed the murder conviction of Lambert's co-defendant. See Hain v. State, 852 P.2d 744, 752 (Okla.Crim.App.1993).
Lambert argues that the OCCA lacked jurisdiction to abrogate the felony conviction because it had been affirmed on his first appeal. The OCCA rejected this argument, explaining that it had "specifically retained jurisdiction over the underlying felony" in connection with its earlier remand. Lambert, 984 P.2d at 229. The OCCA's understanding of its own authority in the state appellate process is a matter of state law and, as such, generally beyond the purview of federal habeas review.[3]See Wright v. Angelone, 151 F.3d 151, 157-58 (4th Cir.1998) (holding state court determination of jurisdiction under state law is binding on federal habeas court); Poe v. Caspari, 39 F.3d 204, 207 (8th Cir.1994) (same). See generally Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) (discussing general limitation on federal habeas review of state law determinations). While the "Supreme Court has suggested that, in rare circumstances, a determination of state law can be `so arbitrary or capricious as to constitute an independent due process ... violation,'" Cummings v. Sirmons, 506 F.3d 1211, 1237 (10th Cir. 2007) (quoting Lewis v. Jeffers, 497 U.S. 764, 780, 110 S.Ct. 3092, 111 L.Ed.2d 606 (1990)), cert. denied, ___ U.S. ___, 128 S.Ct. 2943, 171 L.Ed.2d 872 (2008), that is not the case here. Having expressly preserved the trial court's authority to vacate the affirmed felony conviction if constitutionally required on remand, it was neither arbitrary nor capricious for the OCCA to retain and exercise its customary appellate authority to correct the trial court's error *1265 in the event the trial court failed to take the required action.
Appellant's limited request for a certificate of appealability is GRANTED and the judgment of the district court is AFFIRMED.
NOTES
[*]  After examining appellant's brief and the appellate record, this panel has determined unanimously that oral argument would not materially assist the determination of this appeal. See Fed. R.App. P. 34(a)(2); 10th Cir. R. 34.1(G). The case is therefore ordered submitted without oral argument.
[1]  The habeas proceeding was stayed for a lengthy period of time, during which Lambert secured a reduction of his death sentences to life without parole by demonstrating mental retardation under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). See Lambert v. State, 126 P.3d 646, 650, 659 (Okla.Crim.App.2005).
[2]  Because the general murder verdict made it impossible to tell whether Lambert's convictions were for felony murder or malice-aforethought murder, the OCCA treated them as based on the former for purposes of assessing and remedying any double-jeopardy claims, Lambert, 984 P.2d at 227. See generally Griffin v. United States, 502 U.S. 46, 53, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991) ("[W]here a provision of the Constitution forbids conviction on a particular ground, the constitutional guarantee is violated by a general verdict that may have rested on that ground.").
[3]  We have recognized this point, explicitly or implicitly, in a number of unpublished decisions. See, e.g., Elston v. Roberts, 232 Fed. Appx. 824, 826-27 (10th Cir.2007); Shaffer v. Boone, 3 Fed.Appx. 675, 688 (10th Cir.2001); Anderson v. Champion, No. 96-7110, 1997 WL 383187 at *2 (10th Cir. July 11, 1997). For a contrasting example of a state jurisdictional question turning on federal rather than state law, and therefore properly addressed on habeas, see Negonsott v. Samuels, 933 F.2d 818, 819 (10th Cir.1991) (addressing challenge to state jurisdiction pursuant to federal grant of criminal authority over Indian lands in the Kansas Act, 18 U.S.C. § 3243), aff'd, 507 U.S. 99, 113 S.Ct. 1119, 122 L.Ed.2d 457 (1993).
