DENNIS JACOBS, Circuit Judge:

Allstate Insurance Company seeks recovery of payments to Dr. David Mun and Nara Rehab Medical, P.C. (collectively, "Defendants") on the ground that they engaged in insurance fraud. The United States District Court for the Eastern District of New York (Amon, C.J.) denied Defendants' motion to compel arbitration. On appeal, Defendants argue that the New York Insurance Law and the contract provision required by that law grant them the right to arbitrate Allstate's claims.

We conclude that the operative statute, regulation, and contract provision do not provide a right to arbitration in this context. Accordingly, we affirm.

BACKGROUND

New York's no-fault insurance regime requires that an insurer pay up to $50,000 to cover necessary health expenses for each "covered person" under a "policy of liability insurance issued on a motor vehicle." N.Y. Ins. Law §§ 5101-5109 (McKinney 2014). Covered persons may assign their no-fault benefit rights to qualified health care providers, who then seek payment directly from the insurer. See N.Y. Comp.Codes R. & Regs. tit. 11, § 65-3.11(a) (2014).

Defendants billed Allstate about $500,000 for "Electrodiagnostic Testing" purportedly performed on covered persons between October 2007 and October 2011. Because Allstate is generally required to process each no-fault claim within 30 days of submission, or then be barred from asserting defenses in any subsequent suit or arbitration, see N.Y. Ins. Law § 5106(a); Hosp. for Joint Diseases v. Travelers Prop. Cas. Ins. Co., 9 N.Y.3d 312, 849 N.Y.S.2d 473, 879 N.E.2d 1291, 1294-95 (2007), Allstate relied on Defendants' documentation and reimbursed the claims promptly.

In August 2012, Allstate filed suit against Defendants, alleging that they had fraudulently billed Allstate for testing that was fabricated or of no diagnostic value, and seeking recovery under theories of common law fraud and unjust enrichment, and under the Racketeer Influenced and Corrupt Organizations Act ("RICO"), see 18 U.S.C. § 1964(c).

Defendants moved to compel Allstate to arbitrate pursuant to the Federal Arbitration Act ("FAA"), 9 U.S.C. § 1 et seq.; the New York Insurance Law; and the arbitration provision included in Allstate policies. In April 2013, Chief Judge Amon denied the motion, citing the consensus view in the United States District Court for the Eastern District of New York that medical providers have a right to arbitrate as-yet unpaid claims, but not claims that were timely paid.1 See Allstate Ins. Co. v. Mun, No. 12 Civ. 3791(CBA)(RLM), 2013 WL 1405939, at *1-2 (E.D.N.Y. Apr. 8, 2013).

DISCUSSION

"We review de novo a district court's denial of a motion to compel arbitration." Harrington v. Atl. Sounding Co., 602 F.3d 113, 119 (2d Cir.2010).

I

Section 5106 of the New York Insurance Law provides, in relevant part:

N.Y. Ins. Law § 5106(a)-(b) (emphases added). "First party benefits" are defined as "payments to reimburse a person for basic economic loss on account of personal injury arising out of the use or operation of a motor vehicle." Id. § 5102(b).

A regulation implementing § 5106(b) requires that a "policy of liability insurance issued" on a motor vehicle include the following provision:

N.Y. Comp.Codes R. & Regs. tit. 11, § 65-1.1(a), (d) (emphases added).

The Allstate policies here included this provision, in substance. But even if an insurance contract omits the required wording, the contract is "construed as if such provisions were embodied therein." N.Y. Ins. Law § 5103(h). Defendants therefore may elect arbitration if either the Allstate policy provision or § 5106(b) provides them that right.

II

The FAA establishes that "[a] written provision in any ... contract ... to settle by arbitration a controversy thereafter arising out of such contract ... shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract." 9 U.S.C. § 2. Any "ambiguities as to the scope of the arbitration clause" are resolved in favor of arbitration. See, e.g., Mastrobuono v. Shearson Lehman Hutton, Inc., 514 U.S. 52, 62, 115 S.Ct. 1212, 131 L.Ed.2d 76 (1995) (quoting Volt Info. Scis., Inc. v. Bd. of Trs., 489 U.S. 468, 476, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989)). Nonetheless, "[w]e have applied the presumption favoring arbitration ... only where it reflects ... a judicial conclusion that arbitration of a particular dispute is what the parties intended because their express agreement to arbitrate was validly formed and ... is legally enforceable and best construed to encompass the dispute." Granite Rock Co. v. Int'l Bhd. of Teamsters, 561 U.S. 287, 130 S.Ct. 2847, 2859-60, 177 L.Ed.2d 567 (2010) (emphases added). Defendants rely on citations to the FAA; but the real question is: do Allstate's policies, which implement requirements imposed by New York law and which must be construed to satisfy those requirements, grant Defendants the right to arbitrate Allstate's fraud claims? Cf. Perry v. Thomas, 482 U.S. 483, 492 n. 9, 107 S.Ct. 2520, 96 L.Ed.2d 426 (1987) ("A court may not, then, in assessing the rights of litigants to enforce an arbitration agreement, construe that agreement in a manner different from that in which it otherwise construes nonarbitration agreements under state law.").

III

The arbitration provision in the Allstate policies appears quite broad. It contemplates arbitration if the claimant and insurance company "do not agree regarding any matter relating to the claim." N.Y. Comp.Codes R. & Regs. tit. 11, § 65-1.1(d); see J.A. 146-47. But it is not as broad as it may seem.

An arbitrable dispute is one between the insurance company and a "person making a claim for first-party benefits." N.Y. Comp.Codes R. & Regs. tit. 11, § 65-1.1(d). Defendants are no longer "making a claim." They made a claim; they made many claims. And those claims were promptly paid by Allstate. Allstate's fraud suit therefore does not raise a dispute between it and a person "making a claim for first-party benefits." The arbitration provision does not apply.

IV

A

Because the Allstate policies are construed to conform to § 5106(b), see N.Y. Ins. Law § 5103(h), we must also decide whether arbitration under these circumstances is required by statute.

Like the policy wording, § 5106(b) appears broad. It provides a right to arbitrate "any dispute involving the insurer's liability to pay first party benefits." N.Y. Ins. Law § 5106(b) (emphasis added).

Critically, however, § 5106(b) provides such an arbitration right only to a "claimant" embroiled in a "dispute involving the insurer's liability to pay first party benefits." Id. "Claimant" is not defined in the statute but necessarily references "a person who claims something"2 — here, "first party benefits."

Defendants were "claimants" for "first party benefits" when they submitted their claims. If Allstate had disputed those claims without paying them promptly, disputes contemplated by the statute would have arisen. But Allstate paid Defendants' claims in full. Now, years later, when Allstate seeks recovery for losses caused by Defendants' alleged fraud, Defendants are no longer "claimants" asserting a right to first party benefits, and there is no "dispute involving the insurer's liability to pay first party benefits." This dispute involves the medical provider's liability to the insurer, under a fraud theory, for what the provider already recovered in the claims process.

Section 5106(b)'s reference to § 5106(a) is telling. Subsection (b) provides an arbitration right only in a "dispute involving the insurer's liability to pay first party benefits, ... the amount thereof or any other matter which may arise pursuant to subsection (a) of this section." N.Y. Ins. Law § 5106(b) (emphasis added). The limitation to "matter[s] which may arise pursuant to subsection (a)" modifies all of the antecedents,3 and therefore limits the scope of arbitration to matters arising under subsection (a). Subsection (a), in turn, requires that payments of first party benefits "be made as the loss is incurred" and that those payments become "overdue if not paid within thirty days after the claimant supplies proof of the fact and amount of loss sustained." Id. § 5106(a). Section 5106(b)'s arbitration right therefore applies only to disputes arising from the insurer's non-payment during the initial 30-day claims process, not to insurer fraud suits brought later.

B

The linkage between the 30-day reimbursement process in subsection (a) and the arbitration right in subsection (b) is a feature, not a bug. Section 5106 creates a no-fault "[f]air claims settlement" procedure. See id. § 5106. Subsection (a) defines when insurance companies must pay claims; subsection (b) makes arbitration available for disputes stemming from those claims. They work together to "create a simple, efficient system that ... provide[s] prompt compensation to accident victims without regard to fault, and in that way reduce[s] costs for both courts and insureds." State Farm Mut. Auto. Ins. Co. v. Mallela, 372 F.3d 500, 502 (2d Cir.2004). "The primary aims of [the no-fault] system were to ensure prompt compensation for losses incurred by accident victims without regard to fault or negligence, to reduce the burden on the courts and to provide substantial premium savings to New York motorists." Med. Soc'y v. Serio, 100 N.Y.2d 854, 768 N.Y.S.2d 423, 800 N.E.2d 728, 731 (2003) (citation omitted).

New York's arbitration process for no-fault coverage is an expedited, simplified affair meant to work as quickly and efficiently as possible. See N.Y. Comp.Codes R. & Regs. tit. 11, § 65-4.5 (setting out "[s]pecial expedited arbitration" procedures). Discovery is limited or non-existent. See id. Complex fraud and RICO claims, maturing years after the initial claimants were fully reimbursed, cannot be shoehorned into this system.

Allowing the providers to elect arbitration in these actions would also undercut anti-fraud measures that the New York legislature encouraged. The state requires insurers to file plans "for the detection, investigation and prevention of fraudulent insurance activities." N.Y. Ins. Law § 409(a). These plans must provide for the "coordination with other units of an insurer for the investigation and initiation of civil actions" to recover amounts paid in medical provider frauds. Id. § 409(c)(4) (emphasis added).

Our reading of § 5106 allows insurers to actively combat fraud without impairing the system of prompt insurer reimbursement. In an informal letter opinion, the New York Insurance Department agrees, and contemplates "actions" (i.e., court proceedings) to recover money paid on fraudulent claims4:

Letter from Lawrence Fuchsberg, Supervising Attorney, N.Y. Ins. Dep't, to Francis J. Serbaroll, Cadwalader, Wickersham & Taft, Appellee's Br. at ADD-1-2 (Nov. 29, 2000) (emphases added) (citations omitted).

C

Defendants rely on state court cases that are inapposite or of dubious value. One case rules that waiver of a substantive right under a contract does not also waive a right to arbitrate under the same contract, a point with no bearing on this appeal. See Riese v. Local 32B-32J, Serv. Emps. Int'l Union, No. 74-11, 1986 WL 84814, at *1-2 (Sup.Ct.N.Y.Cnty. Oct. 15, 1986). Others, such as Nyack Hospital v. Government Employees Insurance Co., 139 A.D.2d 515, 526 N.Y.S.2d 614, 615 (1988), involve only the initial claims process, not a later recovery action. And a Short Form Order that Defendants attach to their reply brief is based entirely on an unspecified "applicable automobile insurance contract" and provides almost no relevant analysis because the insurer's arguments were rejected as untimely. See Short Form Order, Am. Transit Ins. Co. v. Elzanaty, Index No. 601543/13 (N.Y. Sup. Ct. Nassau Cnty. Oct. 9, 2013) (Appellant's Reply Br. at Addendum B). Defendants are left to rely on a Civil Court opinion from 1983, which is distinguishable, incompatible with more recent precedent, and issued by a court of limited jurisdiction. See Country-Wide Ins. Co. v. Frolich, 119 Misc.2d 1089, 465 N.Y.S.2d 446 (Civ.Ct. Kings Cnty.1983).5

The weight of New York authority holds that the 30-day process in § 5106(a) does not constrain later insurer actions seeking recovery for fraud. See Lincoln Gen. Ins. Co., 917 N.Y.S.2d at 811 ("[W]here, as here, an insurer timely pays a claim within the 30-day claim determination period, the insurer is not foreclosed from affirmatively commencing an action to recover the amounts paid on the claim when the insurer later discovers that the claim is fraudulent." (citations omitted)); Fair Price Med. Supply Corp. v. Travelers Indem. Co., 9 Misc.3d 76, 803 N.Y.S.2d 337, 340 (App. Term 2d Dep't 2005) ("[A]n insurer precluded from defending a claim based on provider fraud is not without remedy; after paying such a claim, the insurer, for example, may have an action to recover benefits paid under a theory of fraud or unjust enrichment...."), aff'd, 42 A.D.3d 277, 837 N.Y.S.2d 350 (2007), aff'd 10 N.Y.3d 556, 860 N.Y.S.2d 471, 890 N.E.2d 233 (2008); Carnegie Hill Orthopedic Servs. P.C. v. GEICO Ins. Co., 19 Misc.3d 1111(A), 2008 WL 852488, at *5-6 (N.Y. Sup.Ct. Nassau Cnty.2008) (allowing insurer to bring fraud counterclaim outside 30-7 day period).

New York courts hold that insurer fraud suits may be pressed long after the 30-day period for processing claims. And as § 5106(b) provides, the right to demand arbitration exists only during and within that process. It follows that Defendants have no right to elect arbitration of Allstate's fraud claims under § 5106.

CONCLUSION

For the foregoing reasons, the order of the district court is affirmed.