
33 P.3d 495 (2001)
STATE of Alaska, Appellant,
v.
John MARTIN, Jr., Appellee.
Nos. A-8040, A-8051.
Court of Appeals of Alaska.
September 21, 2001.
As Modified on Rehearing October 5, 2001.
Kenneth M. Rosenstein, Assistant Attorney General, Office of Special Prosecutions and Appeals, Anchorage, and Bruce M. Botelho, Attorney General, Juneau, for Appellant.
Arthur S. Robinson, Robinson & Beiswenger, Soldotna, for Appellee.
Before COATS, Chief Judge, and MANNHEIMER and STEWART, Judges.

OPINION
MANNHEIMER, Judge.
The State, having filed this appeal, now proposes to dismiss it. Ordinarily, we would grant such a request without comment. However, the State also asks this court to vacate the action of the district court that prompted the State to file the appeal in the first place. This request raises a jurisdictional problem, and it therefore requires separate, detailed attention.

History of this litigation, and the problem presented by the State's motion to dismiss its appeal
This litigation arises from the State's attempt to prosecute Martin for failing to register as a sex offender. In 1982, Martin pleaded no contest to incest and received a suspended imposition of sentence. He later successfully completed his probation, and his conviction was set aside. But in 1998, the Department of Public Safety promulgated a regulation that expressly defined "sex offender" to include people whose convictions had been set aside following a suspended imposition of sentence. Based on this new definition of "sex offender", the State charged Martin with failing to register in two separate years.
The district court dismissed these two charges because the court concluded that the Department of Public Safety had exceeded its authority when it redefined "sex offender". The State appealed the district court's decision. While that appeal was pending, we decided State v. Otness,[1] in which we upheld the Department of Public Safety's authority to redefine "sex offender". Based on our decision in Otness, we reversed the district court's ruling in Martin's case and reinstated the charges against Martin. See State v. Martin, 17 P.3d 72, 73 (Alaska App.2001).
*496 We issued our decision in Martin on January 26, 2001. Because neither party filed a petition for hearing within the ensuing 15 days, jurisdiction over Martin's case returned to the district court on February 12, 2001. See Appellate Rules 507(b) and 512(a)(2).
But two months later, the supreme court allowed Martin to file a late petition for hearing. And two months after that, on July 20, 2001, the supreme court granted hearing. That litigation, File No. S-10139, is currently pending before the supreme court.
In the meantime, the district court had already renewed its consideration of Martin's case. On May 22, 2001that is, after the supreme court decided to let Martin file a late petition for hearing, but before the supreme court granted the petitionthe district court again dismissed the charges against Martin. This time, the district court ruled that the prosecution against Martin was barred by the ex post facto clause of the federal Constitution as interpreted by the Ninth Circuit in Doe v. Otte, 248 F.3d 832 (9th Cir.2001).[2]
The State has appealed the district court's new decision, and that is the appeal that the State now wishes to dismiss. The State asserts that no appeal is necessary because the district court's underlying action is void. The State argues that, because of Martin's pending petition for hearing in the supreme court, the district court has no jurisdiction over Martin's caseand thus no authority to dismiss the charges against Martin. For this reason, the State asks us to vacate the district court's order of dismissal and then dismiss the State's appeal (because the appeal would be moot).

Did the district court have jurisdiction to dismiss Martin's case in May?
The filing of an appeal vests the appellate court with jurisdiction over the case"supervision and control of the proceedings"for most purposes. See Appellate Rule 203. And when a timely petition for hearing is filed, jurisdiction does not return to the trial court until the petition is decided. See Appellate Rule 512(a)(2)-(3).
Because Appellate Rule 512(a) specifies that the filing of a timely petition for hearing delays the return of jurisdiction to the trial court, this suggests that the filing of an untimely petition has no effect on jurisdictioni.e., jurisdiction over the case returns to the trial court on the scheduled day, and the trial court's jurisdiction is not affected by the filing of an untimely petition. But the Appellate Rules do not explain what happens when, as in Martin's case, the supreme court elects to accept and later grant an untimely petition for hearing.
Potentially, one could argue that the supreme court's decision to accept a late petition for hearing deprives the trial court of jurisdiction and vests jurisdiction in the supreme court. Conversely, one could argue that the supreme court's acceptance of a late-filed petition creates concurrent jurisdiction in both the supreme court and the trial courtsimilar to what happens when a petition for review or an original application for relief is filed. See Appellate Rule 405(b), which specifies that proceedings in the trial court are not stayed by the filing of a petition for review or an original application for relief unless the appellate court orders otherwise.
But the State does not address this issue. Instead, the State focuses on the supreme court's subsequent decision to grant Martin's petition for hearing. The State argues that this action divested the district court of jurisdiction over Martin's case (and vested jurisdiction in the supreme court).
Even if we accepted the State's premise, this would not necessarily mean that the district court lacked authority to dismiss the charges against Martinfor, as explained above, the district court issued its order of dismissal on May 22nd, two months before the supreme court granted Martin's petition for hearing. The State's argument hinges on one additional assertion: that the supreme court's decision to grant Martin's petition *497 had the effect of retroactively divesting the district court of jurisdictionthus invalidating the district court's order of dismissal (and any other orders that the district court might have issued between February 12th and July 20th, with the possible exception of orders related to bail release or enforcement of probation).[3]
There is surprisingly little authority on this issue. In part, this may be due to the fact that many states view the time limits for seeking discretionary appellate review as "jurisdictional". That is, if the petitioner fails to meet the deadline, the court has no authority to take the case. We assume that our supreme court would follow the lead of the United States Supreme Court in Schacht v. United States, 398 U.S. 58, 90 S.Ct. 1555, 26 L.Ed.2d 44 (1970), and hold that the time limit for filing a petition for hearing is not jurisdictionalthat the court retains the authority to relax the deadline and accept the petition.[4]
We were able to find only one case arguably relevant to the question of whether the filing of an untimely petition for discretionary review affects a trial court's jurisdiction. That case is United States v. Gonzalez-Perez, 629 F.2d 1081 (5th Cir.1980). The defendant, Gonzalez Perez, had been a fugitive from justice for eight years; he was then captured and returned to the United States. Federal Criminal Rule 35 declares that a defendant can petition the sentencing court to modify a sentence within 120 days of the Supreme Court's denial of certiorari. In order to trigger this provision, Gonzalez-Perez filed a very untimely petition for writ of certiorari, which the Supreme Court denied without comment. Then, relying on Criminal Rule 35, Gonzalez-Perez petitioned the federal district court to modify his sentence. The Fifth Circuit concluded that Criminal Rule 35 presupposes a timely petition for certiorari. The court noted that if an untimely petition were sufficient to trigger the 120-day window, defendants could manipulate the rule in a way that would effectively negate the intended time limit.[5]
There are clearly good reasons to have sole jurisdiction vest in the supreme court when that court grants an untimely petition for hearing. Normally, the issue(s) on which hearing has been granted will be dispositive of the litigation or, at least, crucial to the course of any continued litigation. But as explained above, the State is not just arguing that the supreme court currently has sole jurisdiction over Martin's case. Rather, the State is arguing that the supreme court's decision to grant Martin's petition retroactively deprived the district court of the jurisdiction that, earlier, it had lawfully exercisedthus invalidating any orders issued by the district court in the interim.
This is a harder issue. As suggested by the Fifth Circuit in Gonzalez-Perez, such an interpretation of the law might allow a party to unfairly manipulate the trial court proceedings by using a late-filed petition for hearing as a tool for erasing unfavorable trial court rulings after the fact.
(That is, even if the trial court's rulings had nothing to do with the issue raised in the petition for hearing, the granting of the petition would retroactively deprive the trial court of the authority to issue those rulings. Thus, even if the supreme court ultimately ruled against the petitioner and affirmed the decision of the intermediate appellate court, the trial court would arguably have to re-decide all of the issues it had ruled on during the interim period before the supreme court granted hearing.)

Assuming that the district court lacked jurisdiction to dismiss Martin's case, does this court have the authority to vacate the district court's order? Or must the State seek relief from the supreme court?
The questions we have discussed are difficult to answer. Moreover, it appears that this court should not answer them.
*498 As explained above, the State contends that the supreme court's decision to grant Martin's petition for hearing means that, in the eyes of the law, the district court never regained jurisdiction over Martin's case. Thus, the district court had no authority to dismiss the charges (for the second time) on May 22ndbecause the supreme court granted Martin's petition for hearing two months later, on July 20th.
Assuming that the State's position is correct (i.e., assuming that the supreme court's decision to grant Martin's petition for hearing had the effect of retroactively divesting the district court of jurisdiction over Martin's case), jurisdiction may have returned to the appellate courts, but it certainly did not return to this court. Rather, sole jurisdiction over Martin's case would now be vested in the supreme court. So even if the State is correct that the district court had no authority to dismiss Martin's case on May 22nd, this court would have no authority to grant the State's request to vacate the district court's order. Instead, the State would have to seek relief from the supreme court.
This court arguably has the authority to grant the other part of the State's request the State's motion to dismiss its pending appeal. But it is obvious that the State's willingness to abandon its appeal hinges on its assumption that the orders it is appealing (the district court's dismissal of the charges against Martin) are void. Since it is not clear that this assumption is true, we decline to dismiss the State's appeal at this time.

We refer the State's motion to the supreme court
Under AS 22.05.015(b), this court is authorized to certify a question to the supreme court if the issue is "of substantial public interest" and should be determined by the supreme court. We believe that the issue raised in the State's motion meets this test. The question is important: What is the relationship between the supreme court's jurisdiction and the trial court's jurisdiction when an untimely petition for hearing is accepted for filing, or when such a petition is later granted? And, because the supreme court has granted hearing in Martin's case, it is quite probable that this court has no jurisdiction to decide the question. For these reasons, we certify this question to the supreme court.
We will stay our consideration of the State's motion to dismiss its appeal until the supreme court rules on this certified question (either by declining the certification or by deciding the question).
NOTES
[1]  986 P.2d 890 (Alaska App.1999).
[2]  The Ninth Circuit's original opinion in Doe v. Otte, 248 F.3d 832, has since been superseded by a revised opinion, 259 F.3d 979 (9th Cir. 2001). However, the Ninth Circuit's conclusion remains unaltered: Alaska's sex offender registration statute is "punitive" for purposes of the ex post facto clause, and thus the statute can not be enforced against persons whose offense predates the enactment of the statute.
[3]  See Jackson v. State, 926 P.2d 1180, 1184-85 (Alaska App.1996) (recognizing that, despite a pending appeal, the trial court retains jurisdiction to decide matters pertaining to the defendant's bail release; and holding that, despite a pending appeal, the trial court retains jurisdiction "to entertain and adjudicate a petition to revoke [a defendant's] probation").
[4]  See Schacht, 398 U.S. at 63-64, 90 S.Ct. at 1559 (holding that the time limit for filing a petition for certiorari is not jurisdictional).
[5]  See id. at 1183.
