WOOD, Circuit Judge.

Charles Craig worked for Ontario Corporation and participated in its employee stock option plan. Under the plan, he was entitled to transfer some of the shares of the stock he acquired to his wife Barbara, and he did so. The plan also provided for a bonus distribution of stock shares upon the participant's retirement. When Craig retired in 2001, he offered to sell his shares back to Ontario. Ontario accepted, but it paid with three promissory notes rather than cash.

By their terms, these notes were subject to "Standby and Subordination Agreements," which subordinated the Craigs' rights to those of certain senior creditors (Fifth Third Bank and First Merchants Bank). By December 2003, Ontario was facing difficulties in meeting its financial obligations. Eventually it reached an agreement with the Craigs to suspend principal payments until December 2004. The agreement was not renewed, however, and the Craigs sent Ontario a notice of default and sued in the district court for the Southern District of Indiana, to recover on the notes. They contended that their case fell within the district court's diversity jurisdiction, under 28 U.S.C. § 1332(a) and (c).

The Craigs were not the only creditors trying to get money from Ontario. Fifth Third sent Ontario a notice of default; that claim was settled in June 2006. First Merchants also asserted that Ontario had defaulted on its notes, but as of the time this case reached the district court, its claim was still outstanding.

The district court entered judgment for the Craigs on the notes, stating that even though the terms seem to prevent any payment to them, they do not bar the Craigs from reducing their claim to judgment. The district court denied a motion for relief from judgment by Ontario in November 2006, and the first appeal before us (No. 06-4409) challenges that ruling.

Subsequently, however, Ontario discovered facts that draw the district court's subject-matter jurisdiction into question. It appears that the parties may not be of diverse citizenship. Ontario moved under FED.R.CIV.P. 60(b)(4) for relief from the judgment on this basis (its second motion under Rule 60, but that detail is unimportant for our purposes), but the district court held that it had no jurisdiction to rule on the motion because the case was before this court on appeal. The court further held that it had no jurisdiction even to conduct a hearing or to review new filings while the appeal was pending. That ruling led to a second notice of appeal, No. 08-1013, which we have consolidated for disposition with the first one.

Naturally, the first question we must confront is that of jurisdiction. Here we pause to note an oddity in the jurisdictional statement that the Craigs filed in their brief before this court. Appellant Ontario, which is contesting jurisdiction, asserts in its jurisdictional statement that the Craigs had said at the outset of the litigation that they were "residents" of Arizona, and that Ontario is an Indiana corporation with its principal place of business in Indiana. In fact, Ontario continues, it has uncovered facts leading it to believe that the Craigs are citizens of Indiana. It thus challenges the authority of the federal courts to hear this case at all. When we looked to the Craigs' brief to see what response they had, all we found was that they "state that the Jurisdictional Statement in Appellant's Brief is complete and correct." This seemed like a concession either that the requirements of diversity jurisdiction have not been satisfied, or at a minimum a concession that a hearing is necessary to get to the bottom of this.

Whether or not there was such a concession, Ontario is correct that the facts relating to subject-matter jurisdiction must be explored here. The district court was mistaken that it had lost all authority to do so when the motion under Rule 60(b)(4) was presented to it. We therefore vacate the court's judgment on the merits in No. 06-4409 and reverse the court's order denying the Rule 60(b)(4) motion in No. 08-1013 and remand for an evidentiary hearing on subject matter jurisdiction.

I

After an appeal has been filed, the district court may still consider a motion for relief from judgment under FED.R.Civ.P. 60(b). See Graefenhain v. Pabst Brewing Co., 870 F.2d 1198, 1211 (7th Cir. 1989). In general, if the motion lacks merit, the court should rule promptly and deny it; if the court finds some merit, it should issue a short memorandum so that the court of appeals can be informed of its views and take appropriate action. See 7TH Cm. RULE 57; Boyko v. Anderson, 185 F.3d 672, 675 (7th Cir. 1999).

Here, the district court declined to express any tentative view of the merits. It explicitly disclaimed jurisdiction "to conduct a hearing or to review new filings while this matter pends on appeal." The Craigs somehow find in this statement an indication that the district court thought that it did have jurisdiction over the case and was intimating a negative view of the motion, but we see nothing of the sort. The district court was aware of Boyko, but it thought that Boyko was limited to habeas corpus proceedings. The wording of Boyko does not, however, support any such limitation; in fact, Boyko cites a wide variety of cases for the proposition that a district court has jurisdiction to consider or deny, but not grant, a Rule 60(b) motion. See id. at 675 (collecting cases and discussing the best procedure); see also Bronisz v. Ashcroft, 378 F.3d 632 (7th Cir. 2004) (applying Boyko in immigration context); Williamson v. Indiana University, 345 F.3d 459 (7th Cir. 2003) (mentioning "the procedure we approved in Boyko" in an employment case).

This limited power is all the more important when subject-matter jurisdiction is at stake. "[I]t has been the virtually universally accepted practice of the federal courts to permit any party to challenge or, indeed, to raise sua sponte the subject-matter jurisdiction of the court at any time and at any stage of the proceedings." Sadat v. Mertes, 615 F.2d 1176, 1188 (7th Cir. 1980). The Federal Rules of Civil Procedure are no less insistent: "If the court determines at any time that it lacks subject-matter jurisdiction, the court must dismiss the action." FED.R.CIV.P. 12(h)(3). Subject-matter jurisdiction is so central to the district court's power to issue any orders whatsoever that it may be inquired into at any time, with or without a motion, by any party or by the court itself. The order denying Ontario's second motion for relief was therefore in error, and the district court should have taken up the issue.

II

The only thing that might have justified the court's decision to pass on the jurisdictional challenge is if Ontario's showing were so inconsequential as to be frivolous. But it was not. Indeed, as we understand the proffered facts, there is a serious jurisdictional problem here. On Ontario's side, the facts that originally were alleged are not contested: it is an Indiana corporation with its principal place of business in Indiana. Matters are far less clear on the Craigs' side. They claim to be "residents" of Arizona — an inadequate jurisdictional claim to begin with, as we repeatedly have reminded litigants and district judges, see, e.g., Camico Mut. Ins. Co. v. Citizens Bank, 474 F.3d 989, 992 (7th Cir. 2007); Meyerson v. Harrah's East Chicago Casino, 299 F.3d 616, 617 (7th Cir. 2002); McMahon v. Bunn-O-Matic Corp., 150 F.3d 651, 653 (7th Cir. 1998). But even if they had properly alleged that they were citizens of Arizona, they are in trouble. Ontario presented evidence that they may in fact be citizens of Indiana.

It was not until the Craigs began efforts to collect on their judgment that Ontario discovered some disturbing pieces of evidence. It correctly presented this information to the district court in its second motion for relief:

The 2005 and 2006 property tax records for the Craigs' property in Arizona — which was used to allege their residence there — listed an Indiana address in the "taxpayer information" section.

The Craigs purchased a second Indiana property (the "Wentworth Property") right before filing their complaint (February 2005), and sold another one (the "Hickory Hills Property") right after filing the complaint (July 2005).

Barbara Craig has remained registered to vote in Indiana, and did so in person in 2006. Under Indiana law, a person must be resident in a precinct for 30 days prior to the election in order to vote there, IND. CODE § 3-7-13-1, and if a voter moves to another state with the intention to establish residency there, then he or she is no longer considered an Indiana resident for voting purposes, IND. CODE § 3-5-5-8.

In April 2005, the Craigs received the Indiana homestead tax credit for the Wentworth Property, which they continued to receive in 2006 and 2007. For the purposes of the credit, a homestead is "an individual's principal place of residence which . . . is located in Indiana. . . ." IND. CODE § 6-1.1-20.9-1(2). Before 2005, the Craigs had received the homestead credit on the Hickory Hills Property. Principal place of residence, or domicile, is central to determining citizenship. See Galva Foundry Co. v. Heiden, 924 F.2d 729, 730-31 (7th Cir. 1991).

All of these facts call into question the Craigs' citizenship, which is their burden to prove as the litigants claiming the right to the federal forum. They complain that the jurisdictional criticisms were not supported by admissible evidence, but this puts the shoe on the wrong foot: the Craigs, as the plaintiffs, have always had the burden of proving federal jurisdiction. They cite many cases requiring a heightened showing for a Rule 60(b) motion, but in all of those the Rule 60(b) movant also had the burden of proof on the issue raised. Where jurisdiction is in question, the party asserting a right to a federal forum has the burden of proof, regardless of who raises the jurisdictional challenge and who presents the motion under Rule 60(b). See Grafon Corp. v. Hausermann, 602 F.2d 781, 783 (7th Cir. 1979). Ontario has raised a serious question about the Craigs' true citizenship at the time this case was filed (June 8, 2005), and the Craigs now have the obligation to respond.

The Craigs' last argument is a curious one. Perhaps not understanding the fundamental importance of subject-matter jurisdiction or the ban on advisory opinions, they contend that this court should reach the merits even if it decides to remand the case to the district court for a hearing on jurisdiction. They think that Brown v. United States, 976 F.2d 1104 (7th Cir. 1992), supports this method of proceeding. But it does not; Brown was a case in which a taxpayer, faced with the prospect of being whipsawed by different creditors after losing to one on summary judgment, moved for relief under Rule 60(b). All the court did was to rule on Brown's appeal from the underlying judgment and remand the Rule 60(b) matter — which had nothing to do with subject-matter jurisdiction — to the district court. Nothing in Brown, indicated that subject-matter jurisdiction could or should be treated the same way. The challenge presented here goes directly to the district court's fundamental power to hear the case at all: if the parties are not diverse, then an entirely different sovereign will be adjudicating the case.

Enough of a challenge to the district court's power to adjudicate was presented that it should have assured itself that its jurisdiction was proper. We therefore remand the case for an evidentiary hearing on the question whether the parties are properly diverse. At this hearing, the Craigs bear the burden of proving that they were citizens of Arizona at the time the suit was filed.

III

As a final note, we observe that several thorny issues may arise once the question of citizenship is opened up. What happens if Charles Craig is properly diverse, but Barbara Craig is not? She is named on some of the notes, but it is not clear whether she is a party who must be joined. Another complication arises from the fact that Arizona is a community property state, but Indiana is not. It is possible, even if Charles Craig turns out to be a citizen of Arizona and Barbara Craig has remained a citizen of Indiana, that a non-diverse party may have a one-half interest in the notes.

These are questions that the district court must answer first. Ontario properly called the problem to the district court's attention, and the court had the power to consider the motion under Rule 60(b), even though an appeal had already been filed. Indeed, it is under a continuing obligation to assure itself of subject-matter jurisdiction, no matter how the issue is raised. We VACATE the judgment on the merits in No. 06-4409, REVERSE the denial of Ontario's second Rule 60(b) motion in No. 08-1013 and REMAND for further proceedings in accordance with this opinion.