DUNCAN, Circuit Judge.

After Plaintiff-Appellee James Dillon obtained loans from online lenders and then sued Defendants-Appellants BMO Harris Bank, N.A., Generations Federal Credit Union, and Bay Cities Bank (the "Banks") for facilitating collection of those loans, the Banks sought to enforce arbitration clauses in the loan agreements between Dillon and the lenders. The district court denied these motions, and the Banks filed renewed motions seeking to cure the deficiencies the court relied on in dismissing their claims. The district court then denied the renewed motions without considering their merits; it construed them as motions for reconsideration, and denied them on that basis. The Banks appealed. For the reasons that follow, we vacate the district court's order denying the renewed motions and remand for further proceedings.

I.

A.

In October 2013, Dillon, a North Carolina resident, filed this putative class action against the Banks.1 He alleges that he applied in late 2012 and mid 2013 for four online payday loans from tribal and out-of-state lenders.2 As a part of the application process, Dillon authorized the lenders to collect the amount due under the loan agreements by debiting his checking account. The lenders approved Dillon's applications and deposited a total of $3,575 into his checking account. Soon after, the lenders began collecting loan payments by initiating electronic fund transfers from that account. The Banks, although not parties to the loan agreements, processed these transfers on behalf of the lenders, thereby acting as intermediaries between the lenders and Dillon.

Dillon maintains that North Carolina law prohibits the loans he took out because, among other reasons, they carried interest rates that substantially exceed the maximum allowable rate under State law. In this action, however, Dillon does not sue the lenders or any other party to his loan agreements. Rather, he sues the Banks, alleging that they were complicit in, and necessary parties to, the lenders' unlawful practices. Specifically, Dillon claims that the Banks made it possible for the lenders to make and collect payday loans in North Carolina by providing the lenders with access to the Automated Clearing House ("ACH") Network, an electronic payment system. When payments were due under the loan agreements, the lenders initiated direct payment transactions through the ACH network. The Banks, known as Originating Depository Financial Institutions, then entered the transactions into the ACH Network. Soon after, a central clearing facility transmitted funds from Dillon's account to the lenders' accounts. According to Dillon, this process enabled the lenders to "debit payday loan payments from customers' bank accounts in states where the loans are illegal and unenforceable." J.A. 28 ¶ 7.

B.

In November and December 2013, the Banks filed motions to compel arbitration and stay further court proceedings (the "Initial Motions").3 They argued that Dillon agreed to submit any claims arising from those loans to arbitration as a part of the application process for the loans themselves.4 The Banks substantiated their position by attaching copies of electronic loan agreements containing arbitration clauses and bearing Dillon's name.

Dillon opposed the Initial Motions. Relevant to this appeal, Dillon argued that the Banks failed to carry their burden of showing an agreement to arbitrate. He claimed that the loan agreements were inadmissible hearsay because they did not bear his physical signature and because the Banks did not offer proof that they had been authenticated.

The Banks replied that the loan agreements were properly before the court for three reasons. First, they argued that the agreements were integral to Dillon's complaint because "the loans form the entire basis for his claims." J.A. 170 n.2; see also J.A. 162-63, 172. Second, they argued that Dillon's position was disingenuous because Dillon, and not the Banks, was a signatory to the loan agreements. Third, they pointed out that Dillon had not actually questioned the agreements' authenticity. Rather, his argument concerned the Banks' burden of proof.

In March 2014, the district court denied the Initial Motions, holding that the Banks "ha[d] not met their burden to establish the existence of an agreement to arbitrate," J.A. 173, because they failed to provide authenticating evidence, J.A. 175-76, which, the court held, was necessary to discharge the Banks' burden, J.A. 176-78. The Banks did not appeal this ruling; instead, they attempted to cure the deficiency identified by the district court.5

C.

After the district court denied the Initial Motions, the Banks obtained from the lenders declarations purporting to authenticate the loan agreements. The Banks then filed renewed motions to compel arbitration and stay further court proceedings (the "Renewed Motions").

Dillon opposed the Renewed Motions. He urged the district court to construe the Renewed Motions as motions for reconsideration because, in Dillon's view, the court had "fully and finally decided" the "issues raised in [the Banks'] `renewed' motion[s]." J.A. 331. He submitted that the court should deny the Renewed Motions without considering their merits because "the law of the case doctrine and public policy weigh strongly against reconsideration." J.A. 337.

The Banks argued in reply that the reconsideration standard was inapplicable because "the Court ha[d] not previously decided the merits of [the Initial Motions]." J.A. 364. The Banks pointed out that they were "not asking the Court to revisit" its prior ruling, but were instead seeking a determination of whether "the authenticating declaration[s] [were] sufficient to address the Court's concerns." J.A. 364.

The district court adopted Dillon's proposed construction of the Renewed Motions. The court noted that it had "previously denied motions to compel arbitration," and observed that the Banks had "offered no legal basis to revisit this previously decided issue." J.A. 430. In other words, the district court ruled that, regardless of whether Dillon actually agreed to submit his claims to arbitration, Dillon's right to litigate those claims had become law of the case. It therefore held that it would grant the Renewed Motions "only if `(1) there ha[d] been an intervening change in controlling law; (2) there [wa]s additional evidence that was not previously available; or (3)[its] prior decision was based on clear error or would work manifest injustice.'" J.A. 433 (quoting Akeva L.L.C. v. Adidas Am., Inc., 385 F.Supp.2d 559, 566 (M.D.N.C.2005)). The court then found that the Banks had satisfied none of these factors, and it denied the Renewed Motions for failure to justify reconsideration. The Banks timely appealed.

II.

Our analysis proceeds in three parts. We begin with a brief discussion of the Federal Arbitration Act ("FAA"), 9 U.S.C. § 1 et seq., as necessary context for our analysis. We then explain why the FAA provides us with jurisdiction over this interlocutory appeal.6 Finally, we conclude that the district court erred by treating as motions for reconsideration what were, in both form and substance, renewed motions to compel arbitration and stay further court proceedings.

A.

Congress enacted the FAA in 1925 "to reverse the longstanding judicial hostility to arbitration agreements that had existed at English common law and had been adopted by American courts, and to place arbitration agreements upon the same footing as other contracts." Gilmer v. Interstate/Johnson Lane Corp., 500 U.S. 20, 24, 111 S.Ct. 1647, 114 L.Ed.2d 26 (1991). The FAA manifests an "emphatic federal policy in favor of arbitral dispute resolution," Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 631, 105 S.Ct. 3346, 87 L.Ed.2d 444 (1985), and requires that courts "rigorously enforce agreements to arbitrate," Dean Witter Reynolds, Inc. v. Byrd, 470 U.S. 213, 221, 105 S.Ct. 1238, 84 L.Ed.2d 158 (1985).

Section 2 of the FAA is its "primary substantive provision." Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct.927, 74 L.Ed.2d 765 (1983). This section "provides that written agreements to arbitrate controversies arising out of an existing contract `shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract.'" Dean Witter Reynolds, 470 U.S. at 218, 105 S.Ct. 1238 (quoting 9 U.S.C. § 2).

Sections 3 and 4 "provide[] two parallel devices for enforcing an arbitration agreement: a stay of litigation in any case raising a dispute referable to arbitration, 9 U.S.C. § 3, and an affirmative order to engage in arbitration, § 4." Moses H. Cone Mem'l Hosp., 460 U.S. at 22, 103 S.Ct. 927. Under § 3, a district court must grant a party's motion to stay further proceedings if (1) the court is "satisfied that the issue . . . is referable to arbitration" pursuant to "an agreement in writing for such arbitration," and (2) the "applicant for the stay is not in default in proceeding with such arbitration." 9 U.S.C. § 3. The circumstances giving rise to default under the FAA "are limited and, in light of the federal policy favoring arbitration, are not to be lightly inferred." Maxum Founds., Inc. v. Salus Corp., 779 F.2d 974, 981 (4th Cir.1985). A party is in default only if it has "so substantially utiliz[ed] the litigation machinery that to subsequently permit arbitration would prejudice the party opposing the stay." Id.

Section 4 provides that "[a] party aggrieved by the alleged failure, neglect, or refusal of another to arbitrate under a written agreement may petition [a] district court . . . for an order directing that such arbitration proceed." 9 U.S.C. § 4. If the court determines "that an agreement for arbitration was made in writing," it must "make an order summarily directing the parties to proceed with the arbitration in accordance with the terms thereof." Id.

If a party's motion under §§ 3 or 4 presents unresolved questions of material fact, the FAA "call[s] for an expeditious and summary hearing" to resolve those questions. Moses H. Cone Mem'l Hosp., 460 U.S. at 22, 103 S.Ct. 927; see also 9 U.S.C. § 4 ("If the making of the arbitration agreement or the failure, neglect, or refusal to perform the same be in issue, the court shall proceed summarily to the trial thereof."). Thus, "[o]ne thing the district court may never do is find a material dispute of fact does exist" and then deny the motion without holding "any trial to resolve that dispute of fact." Howard v. Ferrellgas Partners, L.P., 748 F.3d 975, 978 (10th Cir.2014) (emphasis omitted).

Section 16 authorizes immediate appeal from an order "refusing a stay of any action under section 3 . . . [or] denying a petition under section 4 . . . to order arbitration to proceed." 9 U.S.C. § 16(a)(1). "Congress's purpose in creating appellate jurisdiction for these orders was to effectuate a `strong policy favoring arbitration' through appeal rules, whereby `an order that favors litigation over arbitration. . . is immediately appealable, even if interlocutory in nature.'" Rota-McLarty v. Santander Consumer USA, Inc., 700 F.3d 690, 696 (4th Cir.2012) (quoting Stedor Enterprises, Ltd. v. Armtex, Inc., 947 F.2d 727, 730 (4th Cir.1991)). Against this background, we now turn to the issues before us.

B.

Our first determination is whether we have jurisdiction. Dillon argues that the Banks are appealing an interlocutory order denying motions for reconsideration—rather than an order denying motions seeking arbitration under §§ 3 or 4 of the FAA—and therefore that § 16(a) of the FAA, which would otherwise confer jurisdiction, does not apply. We disagree. Because the Renewed Motions by their very terms sought enforcement of Dillon's purported arbitration agreements, we have jurisdiction over this appeal regardless of the district court's characterization of those motions.

We determine whether the Renewed Motions are petitions under either §§ 3 or 4, and thus whether § 16(a) affords us jurisdiction, by looking to whether they "evidence[] a clear intention to seek enforcement of an arbitration clause." Rota-McLarty, 700 F.3d at 698. We conclude below that the motions did so.

BMO Harris and Bay Cities each labeled their motions as a "RENEWED MOTION TO COMPEL ARBITRATION AND TO STAY LITIGATION." J.A. 298, 375. The terms "compel" and "stay" invoke §§ 4 and 3, respectively. The two banks thus employed the "first, simplest, and surest way to guarantee appellate jurisdiction under § 16(a)." Wheeling Hosp., Inc. v. Health Plan of the Upper Ohio Valley, Inc., 683 F.3d 577, 585 (4th Cir.2012) (quoting Conrad v. Phone Directories Co., 585 F.3d 1376, 1385 (10th Cir. 2009)). Indeed, we generally do not look beyond the caption of a denied motion when determining our jurisdiction under the FAA unless we "suspect[] that the motion has been mis-captioned in an attempt to take advantage of § 16(a)." Id. (quoting Conrad, 585 F.3d at 1385). There is no basis for suspicion here: BMO Harris and Bay Cities both made clear in their respective motions that they were seeking enforcement of arbitration clauses. See J.A. 299-300 (BMO Harris repeatedly describing its motion as one "to compel arbitration"); J.A. 376 (Bay Cities asking the court to enter an "order compelling plaintiff James Dillon . . . to arbitrate each of [his] claims" and "staying this action pending arbitration").

Unlike BMO Harris and Bay Cities, Generations moved to dismiss Dillon's claims against it. We have previously held that a motion to dismiss is an appropriate vehicle to "invoke the full spectrum of remedies under the FAA, including a stay under § 3." Choice Hotels Int'l, Inc. v. BSR Tropicana Resort, Inc., 252 F.3d 707, 710 (4th Cir.2001). We determine whether we have appellate jurisdiction over such a motion by asking whether the movant "made it clear within the four corners of its motion to dismiss that it was seeking enforcement of the arbitration agreement." Wheeling Hosp., 683 F.3d at 586. Here, Generations asked the district court to dismiss Dillon's claims against it because Dillon "agreed that any disputes related to the Loan Agreement . . . would be determined exclusively . . . through arbitration." J.A. 317. This language makes clear that Generations moved to enforce an arbitration agreement.

We conclude that § 16(a) provides us with jurisdiction over this interlocutory appeal because the "the essence of the requested relief [in the Renewed Motions] `is that the issues presented be decided exclusively by an arbitrator and not by any court.'" Rota-McLarty, 700 F.3d at 699 (quoting Wheeling Hosp., 683 F.3d at 585) (internal quotation marks omitted). We therefore deny Dillon's motion to dismiss this appeal for lack of jurisdiction.

C.

We turn now to the merits of this appeal, reviewing the district court's order denying the Renewed Motions de novo. See Patten Grading & Paving, Inc. v. Skanska USA Bldg., Inc., 380 F.3d 200, 203-04 (4th Cir.2004). We proceed mindful that, "as a matter of federal law, any doubts concerning the scope of arbitrable issues should be resolved in favor of arbitration, whether the problem at hand is the construction of the contract language itself or an allegation of waiver, delay, or a like defense to arbitrability." Moses H. Cone Mem'l Hosp., 460 U.S. at 24-25, 103 S.Ct. 927.

We are compelled to conclude that the district court erred by construing the Renewed Motions as motions for reconsideration and then denying them on that basis. The district court did not elaborate beyond concluding that the motions sought reconsideration of a previously decided question. We see two possible bases for the court's approach, but neither is availing. The court could have refused to consider the Renewed Motions on the merits because it believed that the Banks had only one opportunity to invoke the FAA's enforcement mechanisms. Or, alternatively, the court could have relied on the law of the case doctrine to deny the Renewed Motions if resolution of those motions turned on a rule of law that the court had already decided. We briefly consider each rationale.

First, no authority—not the FAA, the Federal Rules of Civil Procedure, or any other source of law of which we are aware—limits a party to only one motion under §§ 3 or 4 of the FAA.7 Section 4 provides that a party seeking to enforce an arbitration agreement "may petition" the court for an order compelling arbitration. 9 U.S.C. § 4. And § 3 states that courts "shall on application of one of the parties stay the trial of the action" if certain conditions are met. Id. § 3. Indeed, the FAA lists only one circumstance under which "a party may lose its right to compel arbitration," Rota-McLarty, 700 F.3d at 702: when that party "is in default in proceeding with such arbitration," id. (quoting 9 U.S.C. § 3). The district court's order cannot rest upon this ground because the court did not find that the Banks were in default.

Second, because the Renewed Motions presented different issues than did the Initial Motions, the district court could not have relied on the law of the case doctrine to deny the Renewed Motions. That doctrine "posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case." L.J. v. Wilbon, 633 F.3d 297, 308 (4th Cir.2011) (emphasis added) (quoting TFWS, Inc. v. Franchot, 572 F.3d 186, 191 (4th Cir.2009)). It does not apply here because the court's order denying the Initial Motions contained no rule of law that dictated the resolution of the Renewed Motions.

In the Initial Motions, the Banks maintained, not unreasonably, that because Dillon's complaint was based on and incorporated by reference the very loan agreements that the Banks sought to introduce, the pleadings themselves established Dillon's agreement to arbitrate. Although the district court disagreed, ruling that the pleadings were insufficient because authenticated loan agreements were necessary, the Banks did not challenge this ruling in their Renewed Motions. Rather, they attempted to cure the evidentiary deficiencies the court relied on and asked the court to determine whether Dillon actually agreed to submit his claims to arbitration. The court's prior ruling—that the pleadings did not establish arbitrability—did not determine whether Dillon consented to arbitration. Accordingly, the district court should have resolved the Renewed Motions on the merits.

At bottom, neither the fact that the district court denied the Initial Motions nor the court's reasoning for doing so dictated the resolution of the Renewed Motions. Rather than resolving "any doubts concerning the scope of arbitrable issues . . . in favor of arbitration," Moses H. Cone Mem'l Hosp., 460 U.S. at 24-25, 103 S.Ct. 927, the district court impermissibly denied the Renewed Motions without considering their merits. We must therefore vacate the court's order as inconsistent with the "emphatic federal policy in favor of arbitral dispute resolution." Mitsubishi Motors Corp., 473 U.S. at 631, 105 S.Ct. 3346.

On remand, the district court must determine whether Dillon's claims are "referable to arbitration under an agreement in writing for such arbitration," unless it finds that the Banks are "in default in proceeding with such arbitration." 9 U.S.C. § 3. And, with respect to the two banks that seek orders compelling arbitration, the court must decide whether those banks are "aggrieved by the . . . failure, neglect, or refusal of [Dillon] to arbitrate under a written agreement for arbitration." Id. § 4. If unresolved questions of material fact prevent the court from ruling on the Renewed Motions, the court shall hold "an expeditious and summary hearing" to resolve those questions. Moses H. Cone Mem'l Hosp., 460 U.S. at 22, 103 S.Ct. 927.

III.

For the foregoing reasons, we vacate the district court's order and remand for further proceedings.

VACATED AND REMANDED.