*1269 This appeal requires us to decide whether the employee exemption to the Anti-Kickback Statute, 42 U.S.C. §§ 1320a-7b(b)(3)(B), applies to payments that AIDS Healthcare Foundation, Inc., made to an employee tasked with referring HIV-positive patients to healthcare services offered by the Foundation. The Foundation is a nonprofit group that contracts with the State of Florida to provide an extensive array of medical services to patients with HIV/AIDS. The contracts require the Foundation to match patients who test positive for the disease with suitable providers of care. The Foundation offers financial incentives to some employees who refer patients to other healthcare services operated by the Foundation, and it offers incentives to patients who use its services. The costs of these services often are reimbursed by federal healthcare programs, such as Medicare, Medicaid, and programs funded by the Ryan White Comprehensive AIDS Resources Emergency Act. Three former employees sued the Foundation under the False Claims Act, 31 U.S.C. § 3729 et seq. , alleging that the incentives offered to employees and patients are unlawful kickbacks that render false any claims for federal reimbursement. The district court dismissed all but two of the claims for lack of particularity. And it later granted summary judgment in favor of the Foundation on the remaining claims based on the employee exemption to the Anti-Kickback Statute. The district court also denied the relators leave to file a fourth amended complaint. We affirm.

I. BACKGROUND

We divide this section in two parts. First, we describe the facts, as we must, in the light most favorable to the relators. See Chaparro v. Carnival Corp. , 693 F.3d 1333 , 1335 (11th Cir. 2012) ; Jones v. UPS Ground Freight , 683 F.3d 1283 , 1291-92 (11th Cir. 2012). Second, we describe the proceedings in the district court.

A. The Facts

AIDS Healthcare Foundation, Inc., is a national nonprofit that provides a variety of medical services to individuals with HIV/AIDS. It has contracts with the State of Florida that require it to conduct HIV testing and to match clients with positive test results to healthcare providers. To promote this goal, the Foundation offers financial incentives to certain employees who refer individuals who test positive for HIV/AIDS to other medical offerings provided by the Foundation, such as its clinic and pharmacy services. For example, the Foundation employs "Linkage Coordinators" who earn a $100 bonus for every referred patient who completes certain follow-up procedures at Foundation clinics. It also provides small incentives, such as nutrient shakes and vitamins, to patients who use its services. The Foundation receives approximately half of its revenue from federal healthcare programs, including Medicare, Medicaid, and programs established by the Ryan White Comprehensive AIDS Resources Emergency Act.

*1270 Three former employees of the Foundation, Jack Carrel, Mauricio Ferrer, and Shawn Loftis, sued the Foundation under the False Claims Act, 31 U.S.C. § 3729 et seq. They alleged that the incentives provided to employees and patients violated the Anti-Kickback Statute, 42 U.S.C. § 1320a-7b, and rendered false any claims for public reimbursement for the treatment of these patients, see id. § 1320a-7b(g). And the relators later filed a third amended complaint that alleged that the Foundation engaged in a widespread practice of submitting claims for services tainted by unlawful payments to employees and patients.

In their effort to satisfy the particularity requirement for allegations of fraud, see Fed. R. Civ. P. 9(b), the relators identified several pieces of evidence. They asserted that Foundation policies provide for incentive payments to Linkage Coordinators and employees who administer HIV tests, that the President of the Foundation has admitted to offering incentives to patients, and that the Foundation has aggressive policies for recruiting patients. The relators also pointed to a spreadsheet created by the Foundation that lists hundreds of patients, employees, test dates, and potential sources of insurance coverage, including federal healthcare programs. And they alleged that because public funds account for almost 50 percent of Foundation revenue, mathematical probability suggests that the Foundation submitted claims for unlawfully referred patients.

The relators also highlighted their positions at the Foundation. Carrel was "the Director of Public Health" for the Southern Bureau of the Foundation between August 2012 and August 2013, Ferrer was a "Senior Program Manager" from May 2011 to August 2012, and Loftis was a "Grants Manager" from January 2013 to August 2013. They asserted that their jobs gave them insight into the "standard operating procedure at [the Foundation]" where "patients ... were referred to and received health services from [the Foundation], which included services paid for by Federal Health Care Programs." And they described various meetings with other officials where they observed discussions of financial data and incentives.

With two exceptions, the relators failed to identify specific claims submitted to the federal government that involved incentives given to patients or employees. On the contrary, the complaint conceded that "[t]he precise number of illegally referred HIV-positive patients cannot be known with certainty at this time," and it primarily relied on allegations about "the regular course of business at [the Foundation]."

The two exceptions involved "representative false claims" where the government was actually billed for services provided to referred patients. The first concerned a patient, John Doe #1, who "tested positive for HIV at [a Foundation] facility in January 2013" and was "assigned to [a Foundation] Linkage Coordinator named Julio Rodriguez who referred him to [the Foundation] for clinical services." John Doe #1 completed his follow-up visits at a Foundation clinic, and in February 2013 the Foundation "directed its accounts payable department to pay ... Rodriguez a commission for successfully linking [the] patient ... to treatment with [the Foundation]." The Foundation then informed John Doe #1 that "it was billing [the] Ryan White [Program] for his treatment," and "the Broward County Health Services Planning Council [told him] that it was paying [the Foundation] for his treatment with Ryan White funds." And the relators made parallel allegations about another patient, John Doe #2, who received health care funded by the Ryan White Program *1271 after he was referred to Foundation services by Rodriguez.

B. The Proceedings in the District Court

After the United States and Florida declined to intervene, the Foundation moved to dismiss the complaint. It argued that the complaint failed to plead the actual submission of false claims with particularity. See Fed. R. Civ. P. 9(b). And it contended that the referral fees fell within a statutory exemption to the Anti-Kickback Statute that excludes "any amount paid by an employer to an employee ... for employment in the provision of covered items or services." 42 U.S.C. § 1320a-7b(b)(3)(B).

The district court granted the motion in part and dismissed all claims except the representative claims about the John Does. It ruled that the combination of allegations that the Foundation relied on public money, that the "kickback schemes were pervasive," and that the relators had some insider knowledge about Foundation funding were insufficient to establish that the Foundation "actually submitted false claims or received payment on such claims." It also highlighted that the spreadsheet that listed patient data failed to establish that the Foundation submitted false claims because this document did "not memorialize any actual claims [the Foundation] submitted to government programs for services provided to illegally referred patients."

After discovery, the Foundation moved for summary judgment against the two remaining claims based on the employee exemption to the Anti-Kickback Statute. See id. The Foundation underscored that this exemption applies to "any amount paid by an employer to an employee ... for employment in the provision of covered items or services," id. , and that the Ryan White Act specifically provides that "referrals" are covered "services," id. § 300ff-51(e)(1)-(2); see also id. §§ 300ff-14(c)(3)(E) & (e)(1), 300ff-22(b)(3)(E) & (d)(1), 300ff-51(c)(3)(e). It concluded that this exemption applied because Rodriguez was an employee providing a statutory service when he referred the John Does to other Foundation offerings. And it highlighted that contracts with Florida required the Foundation to refer patients to medical care.

The relators then moved for leave to file a fourth amended complaint. They stated that the amended complaint had the benefit of new information gleaned from discovery and that these new findings warranted "broaden[ing] the scope of th[e] action." But the motion failed to state exactly what new information the revised 64-page complaint included or to explain how these facts could satisfy the particularity requirement.

The United States filed a statement of interest in support of the Foundation. It explained that it had "a significant interest in the proper interpretation and correct application of the False Claims Act ... and the Anti-Kickback Statute" and that the Foundation had correctly interpreted the law. It maintained that "the Ryan White Program ... explicitly includes referrals to appropriate providers as covered services," and that the relevant "statutes and regulations do not restrict grant recipients ... from paying employees to refer patients needing medical care to that same grant recipient if, as here, it is an otherwise appropriate Ryan White provider."

The district court granted summary judgment in favor of the Foundation. It ruled that the employee exemption applied because Rodriguez was an employee and the referrals were covered "services." 42 U.S.C. § 1320a-7b(b)(3)(B). And it denied the motion to amend as moot.

*1272 II. STANDARD OF REVIEW

Two standards govern our review. We review de novo both the dismissal of a complaint, Access Now, Inc. v. Sw. Airlines Co. , 385 F.3d 1324 , 1326 (11th Cir. 2004), and a summary judgment, Ellis v. England , 432 F.3d 1321 , 1325 (11th Cir. 2005). And we review a denial of leave to amend a complaint for abuse of discretion. Carruthers v. BSA Advertising, Inc. , 357 F.3d 1213 , 1217 (11th Cir. 2004).

III. DISCUSSION

We divide our discussion in three parts. First, we explain that the payments to Rodriguez fell within the employee exemption to the Anti-Kickback Statute. Second, we explain that the district court correctly dismissed the relators' other claims for lack of particularity. Third, we explain that the relators waived their argument about amendment.

A. The Referral Payments to Rodriguez Fell Within the Employee Exemption.

To determine whether the Foundation was entitled to pay Rodriguez for referring patients to other Foundation services, we must consider the texts of three statutes: the False Claims Act, the Anti-Kickback Statute, and the Ryan White Act. A careful review of their relevant provisions and related regulations establishes that the Foundation was entitled to pay its employee for referring patients to its services. And the relators' arguments about congressional intent fail.

The False Claims Act, 31 U.S.C. § 3729 et seq. , creates liability for individuals "who present or directly induce the submission of false or fraudulent claims" to the government, Universal Health Servs., Inc. v. United States ex rel.Escobar , --- U.S. ----, 136 S.Ct. 1989 , 1996, 195 L.Ed.2d 348 (2016) ; see also 31 U.S.C. § 3729 (a)(1)(A), (B), (G) (forbidding specific fraudulent acts). It also "permits, in certain circumstances, suits by private parties on behalf of the United States against [violators]." Hughes Aircraft Co. v. United States ex rel. Schumer , 520 U.S. 939 , 941, 117 S.Ct. 1871 , 138 L.Ed.2d 135 (1997) (citing 31 U.S.C. § 3730 (b) ). Florida has enacted a parallel statutory scheme with similar provisions. See Fla. Stat. §§ 68.082 (2)(a), (b), (g), 68.083(2).

The Anti-Kickback Statute, which broadly forbids kickbacks, bribes, and rebates in the administration of government healthcare programs, see 42 U.S.C. § 1320a-7b(b), provides that "a claim that includes items or services resulting from a violation of [the Anti-Kickback Statute] constitutes a false or fraudulent claim for purposes of [the False Claims Act]," id. § 1320a-7b(g). The Anti-Kickback Statute creates liability for anyone who "knowingly and willfully offers or pays any remuneration ... to any person to induce such person ... to refer an individual to a person for the furnishing ... of any item or service for which payment may be made in whole or in part under a Federal health care program." Id. § 1320a-7b(b)(2) (emphasis added). Notwithstanding its general prohibition on paying for "refer[rals]," id. , the Anti-Kickback Statute exempts "any amount paid by an employer to an employee (who has a bona fide employment relationship with such employer) for employment in the provision of covered items or services ," id. § 1320a-7b(b)(3)(B) (emphasis added). And the statute exempts "any payment practice specified by the Secretary [of the Department of Health and Human Services] in regulations." Id. § 1320a-7b(b)(3)(E). A regulation provides a parallel exemption for "any amount paid by an employer to a[ ] [bona fide] employee ... for employment in the furnishing of any item or service for which payment *1273 may be made in whole or in part under Medicare, Medicaid, or other Federal health care programs." 42 C.F.R. § 1001.952 (i).

The Ryan White Act establishes that the referral of patients with HIV/AIDS is a standalone compensable "service." The Act permits funding of "core medical services," 42 U.S.C. § 300ff-14(a)(2)(A) ; see also id. § 300ff-22(a)(1), a definition that includes "[e]arly intervention services," id. § 300ff-14(c)(3)(E) ; see also id. §§ 300ff-14(e)(1), 300ff-22(b)(3)(E) & (d)(1). In turn, the Act explains that these early intervention services include "referrals of individuals with HIV/AIDS to appropriate providers of health and support services, including ... to entities receiving [funding under the Ryan White Act] for the provision of such services." Id. § 300ff-51(e)(2); see also id. § 300ff-51(e)(1)(C).

The texts of these laws make clear that the Foundation was entitled to pay Rodriguez for referring the John Doe patients. As the district court ruled and the relators concede, Rodriguez was an employee of the Foundation. The Anti-Kickback Statute permits payments to employees for their "employment in the provision of covered items or services." Id. § 1320a-7b(b)(3)(B). And the Ryan White Act defines "[c]ore medical services," id. § 300ff-51(c)(3), to include "referrals of individuals with HIV/AIDS to appropriate providers of health ... services," id. § 300ff-51(e)(2); see also id. §§ 300ff-14(c)(3)(E) & (e)(1), 300ff-22(b)(3)(E) & (d)(1), 300ff-51(c)(3)(e). The relators do not dispute that the Foundation is an "appropriate provider." And they admit that contracts between the Foundation and Florida "required [the Foundation] to refer HIV [positive] patients into medical care." Because referrals are compensable medical services under the Ryan White Act, the Foundation was entitled to pay Rodriguez for referring the John Does.

Despite the plain text of the statutes and regulation, the relators contend that Congress and the agency did not really mean what they wrote. Instead, they assert that drafting history, policy concerns, and tangentially related regulations and caselaw implicitly bar the Foundation from "buying" referrals on a per-capita basis. They also suggest that, even if certain kinds of referral arrangements are covered by the exemption, the exemption implicitly excludes the "purchase" of referrals that direct patients to a particular provider instead of to any provider in a nondiscriminatory fashion. And they colorfully argue that there is a "yawning difference between the appropriate provision of referral services to people with HIV/AIDS and the corrupt purchase of patient referrals."

The relators cite the drafting history and general purpose of the Anti-Kickback Statute and its regulatory exceptions for the proposition that "buy[ing]" referrals categorically violates the principle of honesty in medical services. They assert that Congress intended for the statute to prohibit "financial incentives to induce referrals of program business" and the "steering of patients to particular providers, thus violating the policy of freedom of choice." The relators also underscore that the statute requires the agency to consider factors such as "patient freedom" and "competition among health care providers" when it promulgates safe harbors, id. § 1320a-7d(a)(2), and that the agency consequently stated in a proposed rule that safe harbors should "encourage competition, innovation[,] and economy." The relators maintain that these general principles of freedom and neutrality establish that referral programs-particularly those that pay on a per-capita basis and those that pay employees only when they refer patients to a *1274 medical program run by the payor-are unlawful.

We lack the authority to ignore the texts of these laws in the service of general purposes and selective legislative history. Although the relators complain that paid referrals threaten "freedom of choice" and introduce market inefficiencies, the employee exemption plainly covers the payments to Rodriguez. And the relevant statutes say nothing to forbid payment on a per-capita basis or to require nondiscriminatory referrals to any available healthcare provider. Indeed, the employee exemption covers " any amount paid by an employer to an employee" without specifying the terms, method, or frequency of payment, id. § 1320a-7b(b)(3)(B) (emphasis added), and the Ryan White Act requires only that referrals be made to an "appropriate provider[ ]," id. § 300ff-51(e)(2). And that another regulatory exemption to the Anti-Kickback Statute specifically excludes the kind of "volume"-based compensation that the relators complain about, 42 C.F.R. § 100.952 (f)(2), implies the lack of similar language in the regulation about the employee exemption permits payment on a per-capita basis, see id. § 100.952(i).

The relators cannot complain that this interpretation of the exemption is absurd. On the contrary, incentive-based referral arrangements are logical in the light of the urgent need to ensure that people with HIV/AIDS receive prompt care before their conditions worsen. Congress may well have concluded that it preferred that patients receive any care-even if not from the optimal provider-as quickly as possible. And paid incentives logically further this goal. Indeed, the statement of interest submitted by the government in the district court states "that Congress embraced the notion of 'one stop shopping' for patients with HIV/AIDS."

The relators next cite a variety of unrelated regulatory exemptions to the Anti-Kickback Statute for the same proposition that pay-per-referral arrangements are inherently abusive and implicitly excluded from the employee exemption. For example, they point out that different exemptions for referral arrangements may not apply if compensation is "based ... on the volume or value of any referrals ... or [the] business otherwise generated," 42 C.F.R. § 1001.952 (f)(2) (emphasis added), or if the referrals are not accompanied by disclosures, see id. § 1001.952(f)(4) ; see also generally id. § 1001.952 (outlining other regulatory exemptions). The relators conclude that because these other safe harbors were promulgated "after enactment of the Ryan White Program," their principles of fairness and disclosure somehow implicitly limit the scope of the employee exemption.

We disagree. That other exemptions to the Anti-Kickback Statute may not apply to the payments that the Foundation made to Rodriguez is irrelevant to whether the John Doe referrals were statutorily exempted "covered items or services," 42 U.S.C. § 1320a-7b(b)(3)(B), under the plain terms of the Ryan White Act, see id. § 300ff-51(e). Indeed, many of the other regulatory exemptions cited by the relators apply to business relationships that are completely different from an employee-employer relationship. See, e.g. , 42 C.F.R. § 1001.952 (b) (concerning "payment[s] made by a lessee to a lessor"); id. § 1001.952(c) (concerning "[e]quipment rental"); id. § 1001.952(d) (concerning "[p]ersonal services and management contracts"). In short, unrelated regulatory provisions cannot eviscerate a distinct statutory exemption that plainly applies to the actions of the Foundation.

The relators also cherry-pick statements from caselaw to suggest that paid referrals *1275 are inherently unlawful. For example, they cite United States v. Starks , where we held that the Anti-Kickback Statute reached a scheme where a publicly-funded drug-treatment program paid unaffiliated public-health workers tasked with "advis[ing] pregnant women about possible treatment for drug abuse" to refer these women to the drug-treatment program. 157 F.3d 833 , 836 (11th Cir. 1998) ; see also id. at 835-36 . In upholding the convictions against a void-for-vagueness challenge to the statute, we explained that "even if [the defendants] believed that [the workers] were bona fide employees [of the program], they were not providing 'covered items or services.' " We explained that one of the workers "received payment ... only for referrals and not for any legitimate service for which the Hospital received any Medicare reimbursement." Id. at 839 . And we pointed out that the program "did not at any time pay [the workers] for any of their time, effort, or business expenses, or for any covered Medicare service." Id. at 836 . The relators contend that the employee exemption categorically "does not protect payments made only for referrals."

The relators' argument misses the mark. Unlike the payments in Starks that were made to non-employees in exchange for referrals not contemplated by a healthcare program, the payments that the Foundation made to Rodriguez were in exchange for referrals that were both a standalone compensable service under the Ryan White Act and demanded by its contracts with Florida. The relators cannot avoid the plain text of the statutory exemption.

B. The Relators' Other Allegations Fail for Lack of Particularity.

Federal Rule of Civil Procedure 9(b) requires a party "alleging fraud or mistake ... [to] state with particularity the circumstances constituting fraud or mistake." To satisfy this particularity standard in a qui tam action, a relator must allege the actual "submission of a [false] claim" because "[t]he False Claims Act does not create liability merely for a health care provider's disregard of [g]overnment regulations or improper internal policies unless ... the provider ... asks the [g]overnment to pay amounts it does not owe." United States ex rel. Clausen v. Lab. Corp. of Am. , 290 F.3d 1301 , 1311 (11th Cir. 2002). The complaint also must offer "some indicia of reliability ... to support the allegation of an actual false claim for payment being made to the [g]overnment." Id. It is not enough that a relator "merely ... describe[s] a private scheme in detail [and] then ... allege[s] simply and without any stated reason ... his belief that claims requesting illegal payments must have been submitted, were likely submitted[,] or should have been submitted." Id. Nor may he point to "improper practices of the defendant[ ]" to support "the inference that fraudulent claims were submitted" because "submission ... [can]not [be] inferred from the circumstances." Corsello v. Lincare, Inc. , 428 F.3d 1008 , 1013 (11th Cir. 2005). Indeed, even if the relator is an insider who alleges awareness of general billing practices, an accusation of "[u]nderlying improper practices alone [is] insufficient ... absent allegations that a specific fraudulent claim was in fact submitted to the government." Id. at 1014 (emphasis added); see also United States ex rel. Sanchez v. Lymphatx, Inc. , 596 F.3d 1300 , 1302 (11th Cir. 2010). In short, he must "allege the 'who,' 'what,' 'where,' 'when,' and 'how' of fraudulent submissions." Corsello , 428 F.3d at 1014 .

For example, in Clausen we held that the relator's "descri[ptions of] the various schemes [the defendant company] allegedly implemented to generate unneeded or duplicative medical tests on unsuspecting ... patients" were insufficient because he *1276 "merely offer[ed] conclusory statements ... and d[id] not adequately allege when-or even if-the schemes were brought to fruition" by the actual submission of false claims. 290 F.3d at 1312 . Although the relator generally alleged that false bills were submitted for unnecessary tests, "[n]o amounts of charges were identified," "[n]o actual dates were alleged," "[almost no] policies about billing or even second-hand information about billing practices were described," and "[n]o copy of a single bill or payment was provided." Id. And in United States ex rel. Atkins v. McInteer , we held that "detail[ed]" allegations of "an elaborate scheme for defrauding the government by submitting false claims" were insufficient when the relator failed to "show[ ] that the defendants actually submitted reimbursement claims for the services he describe[d]." 470 F.3d 1350 , 1359 (11th Cir. 2006). Although the relator was an insider "psychiatrist responsible for the provision of medical care," we explained that he lacked "firsthand knowledge of the defendants' submission of false claims" because he was "not a billing and coding administrator responsible for filing and submitting the ... claims" and relied instead on "rumors from staff and observ[ations of] records of what he believed to be the shoddy medical and business practices of two other psychiatrists." Id. ; see also Sanchez , 596 F.3d at 1302 .

To be sure, "we are more tolerant toward complaints that leave out some particularities of the submissions of a false claim if the complaint also alleges personal knowledge or participation in the fraudulent conduct." United States ex rel. Matheny v. Medco Health Solutions, Inc. , 671 F.3d 1217 , 1230 (11th Cir. 2012). For example, in Matheny we held sufficient allegations that the defendant had submitted false "[d]iscovery [s]amples" when the relator "allege[d] personal involvement in ... the creation of [an] actual [d]iscovery [s]ample," alleged when the discovery sample was submitted, id. at 1230 , and "allege[d] in detail who made the [d]iscovery [s]amples ..., who approved and directed the process ..., and how various employees, including [the] [r]elator ..., altered the patient accounts to produce a false [d]iscovery [s]ample," id. at 1229 . And in United States ex rel. Walker v. R&F Properties of Lake County, Inc. , we held sufficient allegations of fraudulent billing when the realtor was a nurse practitioner who had personally used incorrect billing codes on a consistent basis and had been told by the "office administrator" that the defendant healthcare provider " ' never ' billed [these fraudulent services] in another manner." 433 F.3d 1349 , 1360 (11th Cir. 2005) (emphasis added). Although the relator failed to specify when the defendant actually submitted the false claims that were based on the fraudulent billing methods, we held that her pertinent insider information was "sufficient to explain why [she] believed [that the defendant] submitted false or fraudulent claims." Id. at 1360 . Nonetheless, we have made clear that even if a relator "assert[s] ... direct knowledge of [a] defendant['s] billing and patient records," she still must allege "specific details" about false claims to establish "the indicia of reliability necessary under Rule 9(b)." Sanchez , 596 F.3d at 1302 (internal quotation marks omitted).

The relators contend that the district court erred when it dismissed their broad allegations of widespread misconduct. They maintain that they pleaded with sufficient particularity their sweeping claims that the Foundation sought reimbursement after it paid employees for unlawful referrals and enticed patients with free food, gift cards, cash, and other perks. Although they admit ignorance of "the exact number of illegally referred patients for whom [the Foundation] submitted *1277 claims for payment with government funds," they assert "direct knowledge that [the Foundation] does so." We disagree.

The complaint failed to allege fraud with particularity. Most importantly, the relators failed to offer sufficient "indicia of reliability ... to support the allegation [that] actual false claim [ s ] for payment [were] made to the [g]overnment." Clausen , 290 F.3d at 1311 . Although the relators allege a mosaic of circumstances that are perhaps consistent with their accusations that the Foundation made false claims-such as that the Foundation provided incentives to certain patients and employees, that the Foundation frequently requested reimbursement from federal healthcare programs, and that Foundation policies focused on aggressive patient recruitment-the relators fail to allege with particularity that these background factors ever converged and produced an actual false claim where the Foundation both violated the Anti-Kickback Statute when it unlawfully recruited a patient and then billed the government for the services provided to that patient. Indeed, the relators conceded in their complaint that "[t]he precise number of illegally referred HIV-positive patients cannot be known with certainty at this time."

To be sure, the relators made particular allegations about the John Doe representative claims, but these claims cannot help the relators because they involved no fraud. As explained above, the payments to Rodriguez fell squarely within the employee exemption, so these defective allegations hardly suggest other instances of actual fraud. Indeed, that the referrals cited by the relators were covered "services" under the Ryan White Act only undercuts the notion that the Foundation was engaged in rampant illegal conduct in other transactions that the relators failed to identify with specificity. We will not infer fraud from instances of perfectly lawful conduct.

Nor can the relators rely on mathematical probability to conclude that the Foundation surely must have submitted a false claim at some point. Again, a relator must allege an " actual false claim for payment" that was presented to the government. Id. Speculation that false claims "must have been submitted" is insufficient. Id. If anything, the relators' mathematical guesswork cuts the other way. They concede that less than 50 percent of Foundation funding comes from public coffers, so it is entirely possible that even if certain patients and employees received incentives, the ensuing treatment was untethered from government funding. Cf. Matheny , 671 F.3d at 1227 (explaining that "the [r]elators ... alleged the existence of federal funds with particularity" when the "[c]omplaint specifie[d] the Medicare or Medicaid invoice number or reimbursement check and the [billing] code for accounts alleged to contain [o]verpayments" and included exhibits that "identif[ied] the Medicare or Medicaid claim invoice number ... or the government reimbursement check number" (internal quotation marks omitted)). The relators failed to establish that the Foundation ever submitted a claim for an unlawfully referred patient.

The relators also cannot rely on their "personal knowledge or participation" in the alleged fraud. Id. at 1230 . Carrel pointed to his position as a "Director of Public Health" and his attendance at "monthly financial review meetings with the ... Finance Manager." And Ferrer and Loftis highlighted their managerial positions and possession of nondescript information that "patients who were illegally referred ... would, as a matter of course, receive various [reimbursed] health services from the [F]oundation" and that public "funding was used in [Foundation] operations."

*1278 But the relators failed to explain how their access to possibly relevant information translated to knowledge of actual tainted claims presented to the government. Indeed, that the relators supposedly had access to pertinent data and still were unable to pinpoint specific false claims other than meritless accusations about the John Does suggests that they lack any meaningful "personal knowledge or participation in the fraudulent conduct." Id. To be sure, Ferrer asserted that he personally saw Foundation workers offer gift cards to "employees who secured and referred clients" and that he knew that the Foundation gave incentives like "milkshakes and vitamins" to patients. But these allegations about exchanges at unspecified times are untethered to any particular transaction or claim that actually involved government funding. In short, the relators' general allegations of "standard operating procedure[s]," "standard business practice[s]," and the "course of ... operations" at the Foundation hardly establish that the Foundation ever "ask[ed] the [g]overnment to pay amounts it [did] not owe." Clausen , 290 F.3d at 1311 .

The relators also unpersuasively point to a Foundation spreadsheet that lists various patients, employees, test dates, and other medical and referral information, and they highlight that this sheet identifies public healthcare programs-such as Medicaid and the Ryan White program-as funding sources for some of these patients. According to the relators, this document suggests that the Foundation unlawfully claimed government funding for these patients. But the notations on the spreadsheet about possible sources of funding fail to establish that the relevant claims " actual [ ly ] ... [were] made to the [g]overnment." Id. Indeed, the relators admit that the spreadsheet reflects "what potential governmental sources of funding were available for medical care." As the district court explained, the "[s]preadsheet is neither a billing form nor a record of actual reimbursements" and it "does not memorialize any actual claims [the Foundation] submitted to government programs for services provided to illegally referred patients." And again, that the Foundation was entitled to pay for at least some referrals covered by the Ryan White Act dilutes any inference of fraud from this record.

The relators also cite statements made by Foundation executives and excerpts of company documents that suggest that the Foundation took an aggressive approach to patient recruitment, but this evidence fails to identify actual false claims. For example, the president of the Foundation allegedly has admitted to "[t]he provision of small incentives to patients" and the payment of referral fees to employees. But that the Foundation supposedly made such expenditures at unknown times and places again fails to establish specific instances where the Foundation wrongfully demanded payment from the government. The relators also point to an internal financial presentation where the Foundation listed referral figures, which they conclude "evidences [the Foundation's] intense interest in tracking its success in channeling patient referrals." But this information again fails to tie the referral program to specific, fraudulent claims submitted to the government.

In sum, the general allegations that the Foundation sometimes claimed public reimbursement for services, sometimes offered incentives to employees and patients, and sometimes served patients eligible for government programs is not a specific allegation of the " presentment of [a false] claim." Id. Absent more exact allegations that these factors converged into actual false claims, even accusations that "the practices of [the Foundation were] unwise or improper ... [do not establish] actionable damage to the public fisc as required under the False Claims Act." Id. The relators *1279 cannot rely on their sweeping accusations that lack the " 'who,' 'what,' 'where,' 'when,' and 'how' " of the supposedly fraudulent submissions. Corsello , 428 F.3d at 1014 .

C. The Relators Waived Their Argument About Amendment.

The relators briefly argue that the district court abused its discretion when it denied as moot their motion to file a fourth amended complaint. They allege that the new complaint contained unspecified "additional details of the organization-wide kickback scheme," and they argue that the employee exemption does not bar amendment because Medicare and Medicaid, unlike the Ryan White Act, "do not reimburse for referral services." We are unpersuaded.

The relators' opening brief contains only a single paragraph of abstract arguments about why they should be permitted to amend, and we have consistently explained that "argument[s] ... briefed in the most cursory fashion ... [are] waived." In re Globe Mfg. Corp. , 567 F.3d 1291 , 1297 n.3 (11th Cir. 2009). This failure to clearly identify relevant arguments and supporting factual allegations is particularly significant in the light of the heightened pleading requirement of Rule 9(b). More specifically, the relators are demanding that we comb through the 64-page fourth amended complaint, identify new allegations, and determine sua sponte whether these accusations are sufficiently particular. We reject this invitation to do the relators' work for them.

IV. CONCLUSION

We AFFIRM .