#### UNITED STATES of America ex rel. Dimitri YANNACOPOULOS, Plaintiff-Appellant, v. GENERAL DYNAMICS, et al., Defendants-Appellees.

No. 09-3037.

United States Court of Appeals, Seventh Circuit.

Argued Sept. 21, 2010.

Decided July 26, 2011.

*821Jeffrey I. Cummings (argued), Attorney, Miner, Barnhill & Galland, Thomas R. Meites, Attorney, Meites, Mulder *&*Glink, Chicago, IL, for Plaintiff-Appellant.

Barry Levenstam (argued), Attorney, Jenner & Block LLP, Joshua T. Buchman (argued), Attorney, McDermott, Will *&*Emery, Chicago, IL, for Defendants-Appellees.

Jeffrey A. Clair (argued), Attorney, Department of Justice, Civil Division, Appellate Staff, Washington, DC, for Amicus Curiae.

Before BAUER, SYKES, and HAMILTON, Circuit Judges.

HAMILTON, Circuit Judge.

Relator Dimitri Yannacopoulos brought this *qui torn*suit under the federal False Claims Act. He alleges that defendants General Dynamics Corporation and Lockheed Martin Corporation violated the False Claims Act in a number of ways in a sale of F-16 fighter jets to Greece, which paid for the jets with money borrowed from the United States. The district court granted summary judgment against Yannacopoulos, finding that no reasonable jury could find in his favor on any of his claims. After reviewing the voluminous record, we agree with the district court that Yannacopoulos has not shown the existence of a genuine issue of material fact. We affirm.

I. *Background*

In January 1987, General Dynamics agreed to sell to the government of Greece 40 F-16 fighters, as well as related services and equipment. The initial terms of this sale were set forth in a Letter of Intent dated March 6, 1985, to which was attached a draft contract that reflected the status of the parties’ negotiations at the time. The terms of the Greek sale were set out in “Contract Number 5/86 for the Direct Sale of F-16 C/D Aircraft” (“Contract 5/86”), executed on January 12, 1987, as well as in a number of contract amendments executed over the next several years. The total price of the Greek sale was set at $616,497,013, with a payment schedule set out in Annex AG to Contract 5/86.

The sale by General Dynamics to Greece was conducted under the United States’ Foreign Military Financing (“FMF”) program. Under that program, Greece bought the fighters and related services directly from General Dynamics, but it did so using funds that were loaned by the United States government. General Dynamics would submit invoices for payment to the United States, which then paid General Dynamics directly and assessed the amount of that payment against Greece’s trust account. The details of this arrangement were overseen by the Defense Security Assistance Agency (“DSAA”), an agency of the United States Department of Defense, which reviewed Contract 5/86 and gave the approvals needed to use FMF funds to finance the Greek sale.1

*822Several years before the Greek sale, Yannacopoulos entered into an agreement to help a General Dynamics telecommunications subsidiary market commercial telephone equipment in Greece. That consulting arrangement was maintained between the parties until October 1983, when General Dynamics released Yannacopoulos for undisclosed reasons. When Yannacopoulos later learned that Greece had agreed to purchase F-16s from General Dynamics, he claimed that he was entitled to $39 million in commissions on the sale, which General Dynamics refused to pay. Yannacopoulos then sued General Dynamics. A jury rejected Yannacopoulos’ claims, and the Eighth Circuit affirmed. See *Yannacopoulos v. General Dynamics Corp.,*75 F.3d 1298 (8th Cir.1996).

Relying, at least in part, on information obtained in the course of that lawsuit against General Dynamics, Yannacopoulos filed this suit against General Dynamics and Lockheed alleging numerous violations of the False Claims Act in relation to the Greek sale. After extensive discovery, the defendants moved for partial summary judgment. The district court granted the defendants’ motion, *United States ex rel. Yannacopoulos v. General Dynamics,*2007 WL 495257 (N.D.Ill. Feb. 13, 2007), but later reconsidered its grant of summary judgment regarding Yannacopoulos’ claim based on the Economic Price Adjustment clause proposed for Contract 5/86, *United States ex rel. Yannacopoulos v. General Dynamics,*2007 WL 1597670 (N.D.Ill. May 31, 2007). General Dynamics filed a renewed motion for summary judgment on that claim, and both defendants moved for summary judgment on the remainder of Yannacopoulos’ claims. The district court granted the defendants’ motions in their entirety. *United States ex rel. Yannacopoulos v. General Dynamics,*636 F.Supp.2d 739 (N.D.Ill.2009). This appeal followed.

II. *The False Claims Act and the Standard of Review*

The False Claims Act makes it unlawful to knowingly (1) present or cause to be presented to the United States a false or fraudulent claim for payment or approval, 31 U.S.C. § 3729(a)(1) (2006); (2) make or use a false record or statement material to a false or fraudulent claim, § 3729(a)(1)(B);2 or (3) use a false record or statement to conceal or decrease an obligation to pay money to the United States, § 3729(a)(7) (2006). Under the Act, private individuals such as Yannacopoulos, referred to as “relators,” may file civil actions known as *qui tarn*actions on behalf of the United States to recover money that the government paid as a result of conduct forbidden under the Act. *Glaser v. Wound Care Consultants, Inc.,*570 F.3d 907, 912 (7th Cir.2009). As an incentive to bring suit, a prevailing relator may collect a substantial percentage of any funds recovered for the benefit of the government. *Id.*To establish civil liability under the False Claims Act, a relator generally must prove (1) that the defendant made a statement in order to receive money from the government; (2) that the statement was false; and (3) that the defendant knew the statement was false. *E.g., United States ex rel. Gross v. AIDS Research Alliance-Chicago,*415 F.3d 601, 604 (7th Cir.2005).

*823In this appeal, Yannacopoulos claims that the defendants made a number of false statements to the United States to obtain payments for the Greek sale. We consider them in turn. First, he contends that General Dynamics lied about its use of funds loaned by the United States to capitalize a Greek business development company, as required by the terms of Contract 5/86. Next, he says that General Dynamics failed to disclose promptly to the United States its decision to delete the Economic Price Adjustment clause from the draft contract. Yannacopoulos also argues that General Dynamics made misrepresentations relating to Contract 5/86’s provisions concerning spare part purchases and an ill-fated “depot program.” Finally, he claims that after Lockheed assumed General Dynamics’ obligations under Contract 5/86, Lockheed made a number of misrepresentations in two amendments to the contract.3

We review de novo the district court’s grant of summary judgment against Yannacopoulos on these claims. *Omnicare, Inc. v. UnitedHealth Group, Inc.,*629 F.3d 697, 705 (7th Cir.2011). Summary judgment is appropriate when the pleadings and submissions in the record indicate the absence of any genuine issues of material fact, so that the moving parties are entitled to judgment as a matter of law. *Midwest Imports, Ltd. v. Coval,*71 F.3d 1311, 1317 (7th Cir.1995). As the party opposing summary judgment, Yannacopoulos is entitled to the benefit of any reasonable inferences in his favor that are supported by the record. *Jakubiec v. Cities Service Co.,*844 F.2d 470, 471 (7th Cir.1988). We may affirm the district court’s grant of summary judgment only if, upon viewing the record in this light, no reasonable jury could have rendered a verdict in Yannacopoulos’ favor. *Wilson v. Williams,*997 F.2d 348, 350 (7th Cir.1993).

In opposing summary judgment, however, Yannacopoulos could not “rest on the allegations in the pleadings,” but was required to present “evidentiary material which, if reduced to admissible evidence, may allow him to carry his burden of proof.” *Reed v. AMAX Coal Co.,*971 F.2d 1295, 1299 (7th Cir.1992). In other words, reversal would be appropriate only if Yannacopoulos’ evidence is sufficient to enable a reasonable jury to think it more likely than not that the defendants violated the False Claims Act. With that standard in mind, we turn to the merits of the claims.

III. *The HBDIC Claim*

Yannacopoulos’ primary claim on appeal concerns General Dynamics’ involvement in establishing the Hellenic Business Development and Investment Company (“HBDIC”) as part of the F-16 sale to Greece. Under Article 35 of Contract 5/86, General Dynamics agreed to “establish [HBDIC] in Greece ... for the purpose of developing and implementing Business Development projects.” HBDIC was to be incorporated in Greece, with General Dynamics as the majority shareholder and the Greek government as a minority shareholder. Once incorporated, HBDIC was to act as a venture capital company, providing seed money and loans to new companies in Greece.

*824General Dynamics agreed to capitalize HBDIC with a total of $50 million over the course of ten years after the signing of Contract 5/86. General Dynamics also agreed to provide three “in-country management and coordination personnel” for the initial ten years of HBDIC’s existence. General Dynamics admits that it paid these amounts, at least in part, using profits it made under Contract 5/86. After five years of operation, half of HBDIC’s profits were to be paid out as dividends to its shareholders. After fifteen years, HBDIC was to be dissolved (unless its funds ran out before that time and absent action to the contrary by General Dynamics and/or Greece), at which time all of its remaining assets up to $50 million, as well as half of any assets over that amount, were to revert to Greece.

Before the United States DSAA would release funds to finance the Greek sale, it required General Dynamics to execute a “Contractor’s Certification Agreement with Defense Security Assistance Agency.” General Dynamics executed two such agreements with the DSAA, one in February 1986 relating to the draft contract, and another in February 1987 relating to Contract 5/86 (collectively, the “Certification Agreement”). In the Certification Agreement, General Dynamics made a number of representations regarding the Greek sale. We discuss the relevant ones below.

Between February 1987 and August 1990, General Dynamics submitted a number of invoices to the United States for payment. On each invoice, General Dynamics certified that, “to the best of [its] knowledge and belief this invoice is in accordance with” Contract 5/86 and the Certification Agreement. These certifications are significant because a mere breach of contract does not give rise to liability under the False Claims Act. See *United States ex rel. Garst v. Lockheed-Martin Corp.,*328 F.3d 374, 378 (7th Cir.2003). If the breaching party falsely claims to be in compliance with the contract to obtain payment, however, there may an actionable false claim. *United States ex rel. Lemmon v. Envirocare of Utah, Inc.,*614 F.3d 1163, 1168 (10th Cir.2010) (describing such a statement as a “legally false request for payment”), citing *United States ex rel. Conner v. Salina Regional Health Center, Inc.,*543 F.3d 1211, 1217 (10th Cir.2008). Here, Yannacopoulos argues that General Dynamic’s certifications were false because General Dynamics allegedly violated both (1) Contract 5/86 and (2) the Certification Agreement when it “charged the HBDIC costs as part of the [Contract 5/86] price.” We address each alleged violation in turn.4

*825A. *Contract 5/86*

Yannacopoulos first argues that General Dynamics’ certifications of compliance with Contract 5/86 were false because General Dynamics breached that contract by passing on the costs of its HBDIC investment to the United States, as lender to Greece. In particular, he claims that General Dynamics breached Article 9.4 of the contract, under which General Dynamics “confirm[ed] that the material for which payment is requested are United States source end products.” Yannacopoulos interprets this provision to forbid General Dynamics from incorporating its expenditures on HBDIC stock and management personnel into the contract price because, he insists, those expenditures were not for “United States source end products.”5

For the sake of argument, we will assume that Yannacopoulos is correct that the HBDIC costs were not “United States source end products” within the meaning of Article 9.4. That is not enough, however, to show that General Dynamics breached the terms of that article, under which General Dynamics confirmed only that the *“material*for which payment is requested” was in fact “United States source end products.” In other words, General Dynamics could have falsely certified compliance with the contract only if the HBDIC costs constituted “material” within the meaning of Article 9.4.

Article 9.4 did not have such a broad reach. That article required General Dynamics to confirm the U.S. origins of the material it provided only if Greece financed “the purchase of the items to be delivered” with United States government loans. “Material” is not a freestanding contractual term. It relates back to the “items” referenced in the preceding portion of Article 9.4. See, *e.g., Delta Mining Corp. v. Big Rivers Elec. Corp.,*18 F.3d 1398, 1403 (7th Cir.1994) (noting that a court interpreting a contractual term should take account of “the context in which the word is used”).

This relationship between “materials” and “items” is reinforced by the ordinary meaning of the word “material.” See, *e.g., Rain v. Rolls-Royce Corp.,*626 F.3d 372, 379 (7th Cir.2010) (noting that courts should use the “plain and ordinary meaning” of a contractual term whenever possible). As commonly defined, a “material” is a “substance or substances out of which a thing is or can be made” or “something ... that is to be refined and made or incorporated into a finished effort.” *The American Heritage Dictionary of the English Language,*1109 (3d ed. 1992). The materials covered by Article 9.4 are the individual physical parts comprising or otherwise used in the production or provision of the “items to be delivered” under Contract 5/86 — the engines used in the fighter jets, spare parts, construction materials, etc. Thus, even if HBDIC could be deemed an “item to be delivered” under Contract 5/86 (itself an unlikely and strained reading of the contract), HBDIC’s stock or its management personnel were not “materials” as that term was used in Article 9.4. In other words, General Dynamics, by complying with its obligations regarding HBDIC, was not simultaneously violating its obligations to the United States government.

Yannacopoulos’ other arguments for a more expansive reading of Article 9.4 are misplaced. First, he makes much of General Dynamics executive Douglas Seheideman’s statement that it would have been “inconsistent with the spirit and intent of *826Contract 5/86” to pass HBDIC’s costs on to Greece.6 The language of Article 9.4 is clear on its face, however, in which case “the intent of the parties is to be derived only from the express language of the contract.” *Bratton v. Roadway Package System, Inc.,*77 F.3d 168, 173 (7th Cir.1996) (citation omitted). Even if one or more of the parties subjectively intended to bar General Dynamics from spending United States funds on the HBDIC costs, the language of Contract 5/86 simply failed to make that intent manifest.

Yannacopoulos also insists that Article 9.4 must forbid the use of the United States loan funds to capitalize HBDIC because a contrary construction “would destroy the stated contractual consideration” of Contract 5/86 — General Dynamics’ agreement to capitalize HBDIC — and would fatally undermine Article 35’s stated purpose of providing “near term and long term direct and substantial benefits to the Hellenic Industry, economy, and balance of payments.” When General Dynamics “secretly” incorporated the HBDIC costs into the price of Contract 5/86, he insists, Greece ended up “unknowingly pay[ing] for its own offset company.” But if Greece intended to pay for the HBDIC costs itself, we understand him to ask, why did it not finance the company directly without going through General Dynamics? Contract 5/86 cannot be read, he argues, to permit what he characterizes as a nonsensical result. See *FutureSource LLC v. Reuters Ltd.,*312 F.3d 281, 284 (7th Cir.2002).

This argument is not persuasive. For one thing, it was not a secret that General Dynamics charged Greece for the expenses it incurred in capitalizing HBDIC. Article 35 of Contract 5/86 explicitly required General Dynamics and its two main subcontractors to capitalize HBDIC with $50,000,000 over a ten-year period as part of the Greek sale. Anyone who read that significant term of Contract 5/86 should have realized that the $50 million or more in HBDIC costs would be incorporated into the final amount charged to Greece. Unless the sale has an element of charity, the final amount charged for a particular good or service will depend at least in part on the seller’s expenses. That is why, for example, a product purchased from an online retailer is often less expensive than the same product purchased from a brick- and-mortar store. The products are no different, but the physical store must pass on to its customers a number of expenses not incurred by the online retailer. There is no reason to believe that the Greek government or the United States government thought that General Dynamics would charitably invest millions of dollars in a Greek business for the benefit of the Greek government without somehow recouping that expense. General Dynamics’ HBDIC-related charges were not secret and were required under the contract.7

But if Greece knew of and was willing to pay for the HBDIC costs, Yannacopoulos asks, why didn’t Greece just pay those costs itself?8 The answer is simple. Greece could not have obtained a loan from the United States government specif*827ieally to capitalize HBDIC. But if General Dynamics capitalized HBDIC itself and rolled its costs for doing so into the price of Contract 5/86, Greece could obtain just such a loan from the United States as part of the larger deal to arm a NATO ally during the Cold War. General Dynamics’ involvement effectively allowed Greece to invest in HBDIC millions of American dollars that would have otherwise been unavailable. And the financial benefits Greece hoped to realize from this investment are clear: under Article 35, HBDIC was required to begin paying dividends to the Greek government after five years of operation and, if HBDIC ever dissolved, to turn over to the Greek government all of its corporate assets up to $50 million, plus half of any assets exceeding that amount. These benefits are in addition to the economic benefits that Greece might have realized from any new economic opportunities HBDIC provided to Greece.

Article 9.4 of Contract 5/86 simply did not prevent General Dynamics from capitalizing HBDIC with funds derived from the United States loans to Greece. Given the financial benefits that Greece would realize from such an arrangement, such indirect use of American funds to capitalize HBDIC was part of the consideration Greece bargained for in Contract 5/86, and the terms that the United States government approved. Because Article 9.4 permitted exactly what Yannacopoulos accuses General Dynamics of doing, General Dynamics did not breach Contract 5/86 by complying with the same contract and therefore did not falsely certify its compliance with that contract. To the extent Yannacopoulos’ claim turns on that alleged breach, summary judgment for General Dynamics was appropriate.

B. *The Certification Agreement*

Yannacopoulos argues that General Dynamics also falsely certified its compliance with the Certification Agreement, which he interprets to forbid General Dynamics from capitalizing HBDIC. In Paragraphs 4 and 6 of that agreement, General Dynamics made three certifications relevant to this appeal: (1) that “the material or components to be provided under the Purchase Agreement are predominantly of U.S. manufacture;” (2) that “all non-U.S. origin or non-U.S. manufactured items and components, and non-U.S. services procured or to be procured specifically for this Purchase Agreement are identified” in a document attached thereto; and (3) that, aside from commissions and contingent fees, any funds General Dynamics received from the United States government would “not be used to purchase services ... utilized in the execution of the Purchase Agreement from non-U.S. contractors or individuals that are not resident in the United States of America, unless the financing of such services is expressly authorized by the DSAA.” Each certification, Yannacopoulos argues, forbade General Dynamics from using United States funds to pay for the HBDIC costs without the DSAA’s prior authorization. Because each certification concerns a distinct subject matter, we address each in turn.

The first certification, referring to “material or components,” did not bar General Dynamics from spending FMF funds on the HBDIC costs. Neither stock nor management personnel can be considered “material or components,” as the first certification used those terms. As we observed in our discussion of Article 9.4, the word “material” typically refers to a substance or part from which something is made. The term “component” also does not reach the HBDIC aspects of the contract. See *The American Heritage Dictionary of the English Language,*387 (defining a “component” as “a constituent element, as of a system” or a “part of a mechanical or electrical or elec*828trical complex”). The first certification is limited to “material and components” capable of being “manufacture[d],” a description clearly inapplicable to stock and management personnel.9

Yannacopoulos contends the second certification was false because General Dynamics failed to identify the HBDIC costs among the “non-U.S. origin or non-U.S. manufactured items and components” and “non-U.S. services procured or to be procured specifically for” Contract 5/86. Turning to the second certification, we see that General Dynamics did in fact indicate that it had identified all such items, components, and services in a document attached to the Certification Agreement. General Dynamics did so by checking a box in the second certification; a box in that certification informing the DSAA that such items, components, and services could be found in Contract 5/86 was left unchecked. The document attached to the Certification Agreement made no mention of the HBDIC costs.

In arguing the falsity of the second certification, Yannacopoulos overlooks the undisputed fact that the DSAA had already been notified of General Dynamics’ payment of the HBDIC costs when it received Contract 5/86 for review. In light of that undisputed disclosure, no reasonable jury could think General Dynamics’ failure to cheek the proper box in the Certification Agreement was a material false statement, as required for liability under the False Claims Act. See *United States ex rel. Longhi v. United States,*575 F.3d 458, 467 (5th Cir.2009) (requiring that false statement on which FCA claim is based be material); *United States ex rel. Wilson v. Kellogg Brown & Root, Inc.,*525 F.3d 370, 376 (4th Cir.2008) (same); *United States ex rel. A+ Homecare, Inc. v. Medshares Management Group, Inc.,*400 F.3d 428, 443 (6th Cir.2005) (same); see *Allison Engine Co., Inc. v. United States ex rel. Sanders,*553 U.S. 662, 665, 128 S.Ct. 2123, 170 L.Ed.2d 1030 (2008) (requiring that defendant have intended that false statement “be material to the Government’s decision to pay or approve the false claim”); cf. *United States v. Rogan,*517 F.3d 449, 452 (7th Cir.2008).

The Certification Agreement relating to Contract 5/86 was signed by General Dynamics in late February 1987, weeks after Contract 5/86 was submitted to the DSAA for review. That contract required General Dynamics to pay the HBDIC costs and to provide management personnel in Greece. The best that Yannacopoulos can claim is that General Dynamics, by neglecting to refer explicitly to Contract 5/86 in the second certification, failed to remind the DSAA of what was already clear from the contract itself: that General Dynamics was paying a number of costs associated with the establishment of a foreign business development corporation. General Dynamics’ failure to remind the DSAA of information set forth in some detail in the contract it had just recently received for review could not reasonably be deemed material to the DSAA’s decision. See *Rogan,*517 F.3d at 452.

Yannacopoulos also argues that the third certification, in which General Dynamics certified that the funds it received from the United States government would “not be used to purchase services ... utilized in the execution of the Purchase Agreement from non-U.S. contractors or individuals that are not resident in the *829United States,” was false. This language says nothing about whether General Dynamics could expend any funds on HBDIC stock. Corporate stock is clearly not a “service” of any kind. Nor can this certification be read to say that General Dynamics would not expend any funds on the HBDIC management personnel. The third certification restricted General Dynamics’ use of government funds only to pay for services “utilized in the *execution*of the Purchase Agreement” (emphasis added). Such services might include, for example, the manufacture of individual components installed in the F-16s sold to Greece, or the assembly of F-16s from components manufactured in the United States or elsewhere; in other words, services General Dynamics obtained for the purpose of fulfilling the obligations it undertook under Contract 5/86. This language simply cannot reasonably be read to pertain to any services that may have been provided by the HBDIC management personnel. General Dynamics was required to certify that it was in compliance with Contract 5/86, which required it to fund and support HBDIC. The third certification cannot be interpreted to have required General Dynamics to violate Contract 5/86 itself.

For all of these reasons, the district court correctly granted summary judgment for General Dynamics on all of Yannacopoulos’ claims related to HBDIC.

IV. *The “Economic Price Adjustment Clause” Claim*

Yannacopoulos next claims that General Dynamics violated the False Claims Act in relation to the “Economic Price Adjustment Clause” found in the draft of what eventually became Contract 5/86. Under the terms of the Greek sale, General Dynamics was to receive payments well before it provided all of the goods and services Greece purchased. Because General Dynamics would derive substantial economic benefit from these advance payments — namely, interest on the loan funds received from the United States on Greece’s behalf — the parties included in the draft contract a provision entitled “Economic Price Adjustment for Advance Payments.” Under this draft EPA clause, the total contract price was to be reduced “for imputed interest on excess contract payments” by “summing the published 90-day U.S. Treasury Bill yield rate average for each month of a calendar year and dividing the summation by 12,” then multiplying that number by “the amount defined in Annex AC” of the draft contract. Annex AC, which would define the amount needed to calculate the adjustment under the draft EPA clause, was conspicuously absent from the draft contract.

In exchange for General Dynamics’ agreement to deliver F-16s to Greece more quickly than was initially contemplated, Greece agreed to delete the EPA clause from the draft contract. On April 8,1986, General Dynamics and Greece executed Addendum One “to supplement and amend” the draft contract. General Dynamics sent DSAA a copy of Addendum One in May and July of that year. Although that addendum left the EPA clause in the draft contract, an accompanying document explained that, as a “quid pro quo for the accelerated delivery schedule,” the EPA clause was “no longer applicable” under Addendum One. At some point thereafter (the disputed date is irrelevant for reasons we discuss below), the parties deleted the EPA clause from the draft contract as a condition for General Dynamics’ accelerated delivery of aircraft. When Contract 5/86 was executed and submitted to the DSAA for review on February 3, 1987, it no longer contained the EPA clause.

By the time it executed Contract 5/86, however, General Dynamics had already submitted $70 million in invoices to DSAA *830for payment in June, September, and December 1986. Each of those invoices certified that General Dynamics was in compliance with the Certification Agreement relating to the draft contract. Yannacopoulos contends that these interim certifications were false because General Dynamics failed to provide the DSAA “direct unambiguous notice of deletion of the EPA Clause” before it executed Contract 5/86, and because these invoices falsely certified General Dynamics’ compliance with Paragraph 10 of that Certification Agreement, which required General Dynamics to “reporte ] to DSAA upon effect” any “future changes to the terms of the Purchase Agreement.”

Paragraph 10 required General Dynamics to notify the DSAA of any changes made to the EPA clause when they took effect. The deletion of a material clause constitutes a change to the contract of which the DSAA was to receive notice. Thus, Paragraph 10 of the Certification Agreement required that the DSAA be notified when the EPA clause was deleted from the draft contract. General Dynamics does not appear to dispute that the DSAA was first informed of the EPA clause’s deletion when it received a copy of Contract 5/86 for review in January 1987, some time after the invoices at issue here had been submitted for payment. Accordingly, we assume for the sake of argument that any invoices submitted for payment after the parties reached a final agreement to delete that clause, but before the DSAA received a copy of Contract 5/86, falsely certified compliance with the Certification Agreement.

But was this presumed falsehood material for the purposes of the False Claims Act? Put more precisely, could this falsehood have influenced (or naturally tended to influence) the DSAA’s decision to continue financing the Greek sale? See, *e.g., Rogan,*517 F.3d at 452. The undisputed facts show that it was not material. Before General Dynamics submitted any of the allegedly fraudulent interim invoices for payment, it sent the DSAA a letter explaining that “the provision for imputed interest in Article 11 of the Draft Contract is no longer applicable.” By sending this letter to the DSAA, General Dynamics notified the DSAA that, even though the language of the EPA clause remained in the draft contract for the time being, the parties no longer intended for that clause to have any effect.10

Having been told that the EPA clause no longer had any effect, why would the DSAA have cared if that clause were later deleted by the parties? In an attempt to answer this question, Yannacopoulos relies on former DSAA deputy director H. Diehl McKalip’s written declaration that, “had [he] been aware that the price adjustment provision had been deleted from the parties’ final contractual materials,” he would have recommended that financing of the Greek sale be suspended if General Dynamics did not “adjust[] the contract’s payment schedule in view of the deletion of the [EPA] clause.” But McKalip could not say with any certainty that he was not aware of the EPA clause’s deletion or ineffectiveness in the first place — McKalip read neither the draft contract nor Contract 5/86, and he could not recall the actual circumstances surrounding his recommendation, explaining that “the devil ... is in the details.” 11 In fact, McKalip *831could remember having approved Contract 5/86 only because “my signature is on the worksheet ... so I obviously had oversight.” 12

As a general matter, speculation like MeKalip’s is not sufficient to defeat (or win) summary judgment. See, *e.g., Chiaramonte v. Fashion Bed Group, Inc.,*129 F.3d 391, 402 (7th Cir.1997). That is particularly true here, where the undisputed facts show that, after receiving and reviewing Contract 5/86, the DSAA neither suspended General Dynamics’ financing nor required that General Dynamics alter the payment schedule to account for the absence of the EPA clause from that contract. In other words, the agency failed to take action when it actually learned of the supposed misrepresentation. In that case, speculative testimony about how that party might have acted if it had discovered that misrepresentation earlier cannot raise a genuine issue of fact as to materiality. See *American Nat. Fire Ins. Co. v. Rose Acre Farms, Inc.,*107 F.3d 451, 458 (7th Cir.1997) (affirming grant of summary judgment on grounds that defendant’s misrepresentation was not material).

If that were not enough, recall that the draft EPA clause was incomplete and could not have been given any specific content. Annex AC, which would have been needed to calculate any price reductions under the draft contract, was nowhere to be found in that draft contract. No reasonable juror could think that the DSAA would care about the deletion of an unenforceably vague contract provision. Given all of this, no reasonable juror could find that the DSAA, having taken no action when first told that the EPA clause was “no longer applicable,” and having continued to take no action when provided with a final contract lacking that clause, could have been goaded into action if only it had been told again, and a little more specifically, of the EPA clause’s deletion at some time in between. To believe this, one would have to assume that the DSAA would consider the deletion of the EPA clause from the draft contract more significant to its final approval than the absence of such a clause from the outset. A reasonable jury could not accept such an unlikely proposition.

Under the evidence presented on summary judgment, a reasonable jury could conclude only that the deletion of the “no longer applicable” EPA clause was immaterial to the DSAA’s decision regarding its funding of the Greek sale. Summary judgment for General Dynamics on Yannacopoulos’ claim regarding the EPA clause was appropriate as a matter of law.13

*832V. *The Spare Parts Claim*

Yannacopoulos next argues that General Dynamics falsely certified its compliance with the terms of the Certification Agreement in relation to the purchase of spare parts under Contract 5/86. Of the total price set out in Contract 5/86, $70 million was allocated for “Initial Support Spares” ordered by Greece. Article 8.5 went on to explain that the “total price for ... Initial Support Spares, consists of a services element and a hardware element.” While the services element was “not subject to adjustment for quantity changes,” the hardware element was “a reference planning number ... based on [Greece’s] forecast of this value” to be used “on an interim basis” until that value could be adjusted to reflect the outcome of a “spares selection conference” in January 1987. After that conference, any adjustment to the spare parts price would be incorporated into the contract “as may be appropriate prior to the [March 31, 1987] payment.” Even then, however, that price remained a mere estimate. The final price of the hardware element was to be calculated “by summing the prices of the individual items of hardware authorized by [Greece] during the life of the contract.”

Prior to the spares selection conference in January 1987, Greece decided to purchase a number of spare parts from suppliers other than General Dynamics. Despite this news, Greece and General Dynamics did not adjust the spare parts line item in Contract 5/86 before the March 31, 1987 payment. General Dynamics submitted a number of invoices to the DSAA for payment in relation to the spare parts line item. Those invoices represented that General Dynamics was in compliance with the Certification Agreement, under which General Dynamics had agreed to report to the DSAA “any future changes to the terms of the Purchase Agreement ... upon effect.”

Yannacopoulos claims that General Dynamics falsely certified its compliance with the Certification Agreement by failing to inform the DSAA of what he calls “the parties’ understanding that they would not abide by the deadline in Article 8.5” when it submitted these invoices. Yannacopoulos has no evidence of any formal agreement (written or otherwise) between the parties. His claim is that the parties reached an implicit, informal agreement that they would “disregard” the violation of Article 8.5 that he says (and that we will assume, for the sake of argument) resulted when they failed to change the price of the spare parts line item after Greece decided to purchase spare parts from other suppliers.

To succeed on this claim, Yannacopoulos must show that, when General Dynamics filed the invoices relating to spare parts, it knew that it had failed to comply with Article 8.5. See *United States ex rel. Lamers v. City of Green Bay,*168 F.3d 1013, 1018 (7th Cir.1999) (observing that “it is impossible to meaningfully discuss falsity without implicating the [False Claims Act’s] knowledge requirement”). The False Claims Act does not penalize all factually inaccurate statements, but only those statements made with knowledge of their falsity. “Innocent mistakes or negligence are not actionable under this section.” *Hindo v. University of Health Sciences/The Chicago Medical School,*65 F.3d 608, 613 (7th Cir.1995); see 31 U.S.C. § 3729(a)(2) (requiring that false statement be made “knowingly”). For General Dynamics to have known of its failure to comply with Article 8.5, however, it also had to know that Article 8.5 required an alteration to the spare parts line item prior to the March 31, 1987 payment. Article 8.5 required such an alteration only if the initial estimate regarding the price of the spares to be purchased was incorrect. If General Dynamics did not know that Greece’s estimate regarding the price of *833the spare parts line item was no longer correct, then it could not have known that it had failed to comply with Article 8.5 and could not be held liable under the False Claims Act. See, *e.g., Hindo,*65 F.3d at 613.

To avoid summary judgment on this claim, Yannacopoulos needed to present evidence sufficient to allow a reasonable jury to conclude that, by March 1987, General Dynamics knew of facts conclusively establishing that the initial $70 million estimate was incorrect. By basing the initial spare parts line item on a flexible estimate rather than a firm price, General Dynamics and Greece admitted their uncertainty about what that line item’s price should be. Faulty calculations are not actionable under the False Claims Act. *Lamers,*168 F.3d at 1018. Yannacopoulos needed to offer evidence that General Dynamics knew by March 31, 1987 that Greece would never order $70 million in spare parts over the long life of Contract 5/86. See *United States ex rel. Owens v. First Kuwaiti Gen. Trading & Contracting Co.,*612 F.3d 724, 733-34 (4th Cir.2010) (explaining that an estimate is fraudulent for purposes of the FCA if that estimate is made by an individual who knows of “facts that *preclude*that estimate” (emphasis added)); *United States ex rel. Siewick v. Jamieson Science & Engineering, Inc.,*214 F.3d 1372, 1378 (D.C.Cir.2000) (same); *United States v. Foster Wheeler Corp.,*447 F.2d 100, 101 (2d Cir.1971) (“Inflated cost estimates are quite different from fraudulent estimates.”); cf. *Lamers,*168 F.3d at 1018 (noting that “promises of future compliance” are knowingly false only if the party making that promise “never intended to comply”).14

Yannacopoulos’ theory is that because General Dynamics knew that Greece had decided to purchase at least some spares from other suppliers, it also had to know that a reduction in the original spare parts estimate was necessary. This assumption, crucial to Yannacopoulos’ claim, is simply not borne out by the record. Greece did not base its initial $70 million estimate “on a set quantity of spares” to be purchased, but merely provided that estimate without any explanation. Unaware of the basis for Greece’s initial estimate, General Dynamics would have been hard pressed to know how that estimate was affected, if at all, by Greece’s decision to purchase some spare parts from other suppliers. Only complicating matters is the early date^ — March 1987 — by which Yannacopoulos claims General Dynamics must have known that the $70 million estimate was incorrect. So early in the parties’ contractual relationship, General Dynamics could only speculate about any effect the events of the next decade would have on the total value of spare parts Greece would wish to purchase.15 Further, it is hard to see how General Dynamics could have known that *834the initial estimate was incorrect after Greece said that it wanted to “keep the price of the spares line item roughly at the same level it was initially,” despite purchasing some spare parts from other suppliers.

Given this evidence, no reasonable jury could have concluded that General Dynamics knew that Greece would never purchase $70 million of spare parts over the lifetime of Contract 5/86. We can assume that General Dynamics, upon learning that Greece intended to purchase spares from other suppliers, suspected that Greece might purchase fewer spare parts from General Dynamics than initially estimated. But especially where the initial estimate was so arbitrary, a suspicion is a far cry from actual knowledge that the initial arbitrary estimate was no longer reliable. To prove this claim, Yannacopoulos had to come forward with evidence that General Dynamics knew the estimate was incorrect before the March 31, 1987, payment, nearly a decade before the final price for the spare parts was decided. He has failed to do so. Summary judgment against Yannacopoulos on his spare parts claim was appropriate.

VI. *The Depot Claim*

Yannacopoulos also claims that General Dynamics falsely certified its compliance with the terms of the Certification Agreement in relation to Contract 5/86’s depot program. Article 8.2 of Contract 5/86 contained a $49,887,435 line item for a “depot program,” relating to materials and equipment for use in repairing and maintaining the F-16s. Article 8.11 explained that the depot program was “subject to reassessment” by Greece until no later than 12 months after Contract 5/86’s effective date. During the time period for “reassessment,” General Dynamics agreed to “limit the cost[s] incurred” for the depot program to those “required to maintain the contract delivery schedule,” which were “anticipated to include the depot site survey, preparation of recommended lists and schedules and preparation for and support of the depot working conference(s).” Greece never authorized General Dynamics to begin work on the depot program, and the parties ultimately cancelled that program in July 1995.

General Dynamics submitted a number of invoices relating to the depot program, each of which certified General Dynamics’ compliance with Contract 5/86 and the Certification Agreement. As in his spare parts claim, Yannacopoulos contends that these certifications were false because General Dynamics “failed to report to [the] DSAA ... that it had reached an [implicit] understanding with Greece to disregard the timetable imposed by Article 8.11.” Under this “timetable,” he says, Greece had until April 25, 1987 “to either ‘delete’ the depot program in whole or in part, or [to] select the depot work it wanted and authorize GD to begin performance.”

We disagree with this strained interpretation of Article 8.11, which rests on a reading of select language from that article without regard for its context. Although Article 8.11 provided a limited period of time in which Greece could “reassess” the depot program, that time limit must be read in conjunction with the contractual language found immediately thereafter. See *Delta Mining Corp.,*18 F.3d at 1403. That language required General Dynamics to “limit the cost[s] incurred” on that depot program during “the period of time allowed for reassessment.” Article 8.11 did nothing to limit the Greek government’s ability to “reassess” its interest in the depot program at any time. Rather, that article gave the Greek government a year in which it could reassess its interest in that program without having to worry about incurring unnecessary costs for a program that it had decided not to purchase. Greece could reassess its *835interest in buying the depot program after the Article 8.11 deadline had passed, but it would do so at its own risk. After that deadline passed, General Dynamics was no longer prohibited from incurring costs beyond those specifically delineated in that article, costs that we presume were assessed against Greece like any other costs under Contract 5/86.

Because Yannacopoulos’ claim regarding the depot program rests on an incorrect interpretation of Article 8.11, the claim fails as a matter of law. The district court was correct to grant summary judgment for General Dynamics on that claim.

VII. *The Modifications Five and Six Claims*

In March 1993, defendant Lockheed acquired General Dynamics’ Fort Worth Division and assumed all of General Dynamics’ rights and obligations under Contract 5/86. Following its assumption of those responsibilities, Lockheed and Greece executed two modifications to Contract 5/86, both of which Yannacopoulos now contends were “reverse false claims.”

A. *The Modification Five Claim*

Yannacopoulos’ first claim against Lockheed concerns Amendment H0005 to Contract 5/86 (“Modification Five”), executed on March 17, 1993. In February 1987, Greece had exercised its option under Article 35 of Contract 5/86 to participate in a co-production program with General Dynamics. Under that program, General Dynamics was to provide technical support and materials to Hellenic Aerospace Industry. The price of the co-production program was based on a projection regarding the amount of support work the Hellenic Aerospace Industry would require over the course of the program. Each year after the first four years of that program, Greece and General Dynamics were to “review the level of coproduction support to be provided” to the Hellenic Aerospace Industry. The contract provided that, if Hellenic Aerospace Industry’s “actual performance” was “such that the level of [General Dynamics’] support [could] be reduced, the support will be reduced and the coproduction price ... will be reduced accordingly.” The parties agreed to “work out the details for the implementation of [this article] during the fourth year after the signature of [the] Contract.”

The agreed price for the co-production program was $53,693,555. Because Hellenic Aerospace Industry produced fewer F-16 components than originally anticipated, however, less support was required to produce those components than was initially anticipated. By late September or October 1990, General Dynamics had collected $47,693,487 for its co-production work, though Greece had authorized only about $24 million worth of co-production work by that time. In March 1993, Greece and Lockheed executed Modification Five to Contract 5/86, which maintained the price of the coproduction program line item at $53,693,555. Lockheed made no refund to the United States until 1996, when it made a refund of $7,042,940 related to the co-production charges.

Under the False Claims Act, a “reverse false claim” is a false statement used not to obtain payments from the government, but to “conceal, avoid, or decrease an obligation to pay or transmit money or property to the Government.” 31 U.S.C. § 3729(a)(7) (2006); see *United States ex rel. Bahrani v. Conagra, Inc.,*465 F.3d 1189, 1194-95 (10th Cir.2006).16*836Yannaeopoulos contends that Modification Five “was a reverse false claim because it concealed and avoided [Lockheed’s] contractual obligation to make a coproductionrelated refund by maintaining the price of the coproduction line item unchanged at $53,693,555.” In trying to prove this, Yannacopoulos argues that, because General Dynamics had been overpaid for its work on the co-production line item, it had an obligation to pay the amount of that overpayment to the United States government, an obligation he says Lockheed concealed when it submitted Modification Five to the government without mentioning that overpayment.

Assuming that such an obligation existed, however, and assuming that Modification Five concealed that obligation, Yannacopoulos’ claim can succeed only if Modification Five was false. See, *e.g., Gross,*415 F.3d at 604; 31 U.S.C. § 3729(a)(7) (2006). Despite this, Yannacopoulos failed to argue the falsity of Modification Five in his opening brief. Only after Lockheed pointed out this omission in its response brief did Yannacopoulos offer an explanation as to how a mere contract modification — an agreement between two parties altering their contractual obligations to one another — could be false. First, he claims that Modification Five’s $53,693,555 price tag for the co-production line item was “false and inflated.” Second, he argues that Modification Five was false because “the U.S. Government recoupment line item” in that Modification was priced at $29,047,706, when nearly $23 million of that amount had already been repaid to the United States. We address in turn these alleged falsehoods, neither of which is sufficient to give rise to liability under the False Claims Act.17

1. *Modification Five’s Co-production Program Line Item*

Showing the objective falsity of the price contained in Modification Five’s co-production program line item, however, is not as simple a task as establishing the falsity of a statement of historical fact. A statement may be deemed “false” for purposes of the False Claims Act only if the statement represents “an objective falsehood.” *Wilson,*525 F.3d at 376, citing *Lamers,*168 F.3d at 1018. Although a breached contractual term may be considered a falsehood in a looser sense — a false promise — a mere breach of a contractual duty does not satisfy this standard. See *United States ex rel. Garst v. Lockheed-Martin Corp.,*328 F.3d 374, 378 (7th Cir.2003) (observing that a mere “fail[ure] to keep one’s promise is just breach of contract,” not fraud); *Harrison v. Westinghouse Savannah River Co.,*176 F.3d 776, 789 (4th Cir.1999) (affh'ming dismissal where allegations showed only “poor and inefficient management of contractual duties”). Nor do mere “differences in interpretation growing out of a disputed legal question” involving the terms of a con*837tract. See *Lamers,*168 F.3d at 1018. To establish the objective falsity of the co-production line item price in Modification Five, Yannacopoulos needed to present evidence showing that Greece did not in fact agree “to pay [that amount] for the items and services to be delivered” under the co-production line item.18

None of the evidence on which Yannacopoulos relies is sufficient to show either the falsity of the coproduction line item price in Modification Five or Lockheed’s knowledge of that falsity. Much of that evidence shows, at best, that General Dynamics and Greece reached other agreements regarding the co-production program before Modification Five was executed. But nothing about those agreements prevented Lockheed and Greece from reaching a new agreement when they negotiated the final terms of Modification Five. The parties to the original agreement were not bound to follow that agreement even after both agreed that it was not in their best interests to do so. Yannacopoulos also claims that General Dynamics collected millions of dollars for work on the co-production program that was not yet completed at the time Modification Five was signed, but we fail to see how this goes to show that Greece did not actually agree to pay the price set forth in that modification. The remainder of the evidence on which he relies — the decrease in demand for F-16 parts and General Dynamics’ decision to no longer submit invoices in relation to the co-production program — suffer from that same failing. None of it could enable a reasonable jury to conclude that the price of the co-production program line item in Modification Five was objectively false, in the sense that Greece did not actually agree to pay the price set forth in that line item.

2. *Government Recoupment Line Item Price*

In his reply brief, Yannacopoulos takes issue with the fact that a $29,047,706 line item for “U.S. Government recoupment” was included in the total contract price set forth in Modification Five.19 This was false, he says, because a later amendment to Contract 5/86 states that most of this money had already been repaid to the United States. Moreover, he claims that Article 8.7 of Contract 5/86 prohibits this line item — accurate or not — from being included in the contract price in the first place. By placing an inaccurate price for the government recoupment line item into the total price of Contract 5/86, Yannacopoulos says, Lockheed “inflat[ed] the contract’s total price and concealed] the fact that [it had retained] millions of dollars of [loan] funds that defendants had been paid for the value of work they never performed.”

Yannacopoulos waived this argument for purposes of this appeal. Unlike his argument regarding the coproduction program line item — the falsity of which Yannacopoulos also argued only in his reply brief— Yannacopoulos failed to present any facts or argument regarding the government recoupment line item anywhere in his opening briefs discussion of Modification Five. The argument was waived. Eg., *United States v. Diaz,*533 F.3d 574, 577 (7th Cir.2008).20

*838B. *The Modification Six Claim*

Yannacopoulos’ final claim on appeal is that Amendment H0006 to Contract 5/86 (“Modification Six”), executed on February-26, 1996, was also a reverse false claim. In Modification Six, Lockheed agreed to refund to Greece $29,926,515. Of that amount, $22,883,575 related directly to the aircraft sale and $7,042,940 related to the co-production program — an amount that Lockheed later paid to the United States to be credited to the Greek trust fund account. On appeal, Yannacopoulos contends that Modification Six constituted a reverse false claim designed to conceal Lockheed’s purported “obligation to refund tens of millions of ... unearned [loan] funds” to the United States government, among other things.

To establish a reverse false claim, Yannacopoulos must first show that Modification Six was objectively false in some way. See *Wilson,*525 F.3d at 376. He asserts that Modification Six was false in two separate respects. First, he claims that Annex AK to Modification Six was false because it “states that [the] defendants paid to the Government ... $29,047,706 GD collected from Greece for recoupment,” despite the fact that $1,891,146 in “additional facilities rental recoupment” charges included in that amount was allegedly unpaid by that time. Second, he argues that Annex AG to Modification Six was false because it “did not ... *truthfully*reconcile the payments received by [the] defendants with the value of the work they performed.” Rather, it set forth “new payment schedules ... to collect additional [loan] funds for the remaining contract work as if [the defendants’] had retained no advance payments.” We address each of these claims in turn, finding neither sufficient to defeat summary judgment.21

1. *The Annex AK Claim*— Additional *Facilities Rental*

In Article 8.3 of Modification Six, Lockheed and Greece agreed that line item 14, entitled “U.S. Government Recoupments,” would be in the amount of $6,097,706. (A. 408). As explained in Article 8.7 of Modification Six, this line item represented “the amount of recoupment that the U.S. Government has directed to be collected by” Lockheed from Greece. This amount was to be “collected by [Lockheed] and paid to the U.S. Government and is not included in the Contract Price nor ... in the Payment Schedule.” Article 8.7 went on to say that the “method of payment, the frequency of paymenty and other payment terms and information are included in ANNEX AK— U.S. GOVERNMENT RECOUPMENTS.” Turning to Annex AK of Modification Six, one finds, as of September 30, 1991, a total recoupment amount of $29,047,706. This amount was comprised of two discrete components: (1) $1,891,146 for what Annex AK calls “Additional Facility Rental Recoupment”; and (2) $27,156,560 for “Item Delivery Recoupment.” At issue here is the amount for “Additional Facility Rental Recoupment,” which was a charge owed to *839the United States government for use of the United States’ Fort Worth facility to produce F-16 aircraft for Greece.

Yannacopoulos argues that, because Article 8.7 discussed Annex AK in terms of “payment” rather than “collection,” we must read that Annex as a representation that the defendants had paid the entire $29,047,706 recoupment amount to the United States Government by the time the parties executed Modification Six. But see *Lamers,*168 F.3d at 1018 (noting that “imprecise statements” are not actionable false statements). Because General Dynamics allegedly never paid the $1,891,146 amount for “Additional Facilities Rental Recoupment,” Yannacopoulos insists that Annex AK was false.

Yannacopoulos misreads the language of Modification Six. While Annex AK says that, between March 31,1989 and September 30, 1991, General Dynamics had collected from Greece $29,047,706 in funds designated for recoupment, it cannot be read to say that this entire amount had already been repaid to the United States government. Footnote 4 to that Annex states that, out of that amount, “$22,950,-000 [was] refunded to the Greece commercial sales account of the [FMF] trust fund on [May 17, 1991].” That amount related solely to “Item Delivery Recoupment,” though, and not the “Additional Facility Rental” amount that Yannacopoulos says was never paid. Footnote 5 to Annex AK went on to explain that the remaining $6,097,706 recoupment amount — $1,891,146 for “Additional Facility Rental” and $4,206,560 for “Item Delivery Recoupment” — “has been paid and moved below the line under [line item] 14.”

Footnote 5 — the crucial provision of Modification Six — cannot reasonably be understood to say, falsely or otherwise, that the $6,097,706 in line item 14 had already been repaid to the United States government by the time Modification Six was executed. Line item 14 was the amount designated by the United States for collection from Greece. By saying that this amount “has been paid,” footnote 5 indicates that this designated amount has already been paid by Greece, not by Lockheed.22 Because Modification Six never says that the $1,891,146 for facility rental had already been paid to the United States, it is irrelevant whether such a statement would have been false if it had actually been made.

2. *The Annex AG*Claim— *Reconciliation of Payments*

Finally, Yannacopoulos argues that Annex AG of Modification Six “implicitly represented” that an agreed-upon refund of $29,926,515 to the United States government “was the totality of [the loan] funds that [the] defendants had been paid for the value of ... work that they never performed.” 23 This “implicit” representation, he says, was false because Lockheed “secretly retained over $21 million in advance payments for the value of work it never performed.”

As noted above, a claim under the False Claims Act requires proof of an objective falsehood. See *Wilson,*525 F.3d at 376. *840In the context of a contractual agreement such as Modification Six, an objective falsehood requires proof that the parties did not actually reach the agreement set forth therein. Yannacopoulos does not claim that Lockheed and Greece did not actually agree to the refunds set forth in Modification Six, however. Instead, he says only that they “implicitly” represented that the refunds provided for in that modification were the only funds that Lockheed had been paid for work it had not completed. But see *Lamers,*168 F.3d at 1018 (noting that “imprecise statements” are not actionable false statements). Yannacopoulos provides no evidentiary support for such a strained reading between the lines of Modification Six, apparently believing that a bald assertion about that modification’s meaning should suffice. It does not. See, *e.g., Drake v. Minn. Min. & Mfg. Co.,*134 F.3d 878, 887 (7th Cir.1998) (“Rule 56 demands something more than the bald assertion of the general truth of a particular matter, rather it requires ... specific concrete facts establishing the existence of the truth of the matter asserted.”) (quotation omitted).

At its core, Yannacopoulos’ complaint is that Lockheed and Greece reached an agreement that allowed Lockheed “to collect additional [loan] funds for the remaining contract work as if it had retained no advance payments.” But this is nothing more than an argument that the parties should have agreed in Modification Six to refund more than a mere $29,926,515. Even if that may be true as a matter of contract law and sound public policy, that would not make Modification Six false. And absent evidence of a knowing falsehood, Yannacopoulos’ final claim stumbles right out of the gate.24

The judgment of the district court is Affirmed.

1

. In 1998, the Department of Defense renamed the DSAA as the Defense Security Co*822operation Agency. We use here the original DSAA designation in the record.

2

. In 2009, Congress amended the False Claims Act, Pub. L. 111-21, § 4(a)(1), making those amendments generally applicable only to conduct occurring on or after May 20, 2009, Pub. L. 111-21, § 4(f). The one exception is the amendment to section 3729(a)(1)(B), which applies to cases, such as this, that were pending on or after June 7, 2008. *Id.*

3

. The False Claims Act was enacted in 1863, in the midst of the Civil War, in response to flagrant frauds committed against the government, such as selling defective rifles and artillery shells filled with sawdust instead of explosives. See J. Randy Beck, *The False Claims Act and the English Eradication of Qui Tam Legislation,*78 N.C. L. Rev. 539, 555 (2000). The claims here, arising from a complex, long-term contract involving many contingencies, allowances, predictions, and amendments, are considerably more difficult to prove than those simpler frauds.

4

. Yannacopoulos also argues that the Arms Export Control Act, 22 U.S.C. § 2751*et seq.,*as interpreted by the DSAA, forbids the use of United States funds for indirect offsets such as HBDIC. In his reply brief, however, he admits that General Dynamics "never certified compliance with [that statute]____ Of course it did not.” But if General Dynamics never certified compliance with the Arms Export Control Act, then any violations of that act would not support a claim under the False Claims Act. See *United States ex rel. Main v. Oakland City University,*426 F.3d 914, 917 (7th Cir.2005); *United States ex rel. Lamers v. City of Green Bay,*168 F.3d 1013, 1020 (7th Cir.1999) ("The FCA is a fraud prevention statute; violations of ... regulations are not fraud unless the violator knowingly lies to the government about them.”); *United States ex rel. Thompson v. Columbia/HCA Healthcare Corp.,*125 F.3d 899, 902 (5th Cir.1997); *United States ex rel. Hopper v. Anton,*91 F.3d 1261, 1266 (9th Cir.1996) ("Violations of laws, rules, or regulations alone do not create a cause of action under the FCA. It is the false *certification*of compliance which creates liability when certification is a prerequisite to obtaining a government benefit.”). To the extent Yannacopoulos' claims are based on the theory that General Dynamics violated the Arms Export Control Act, summary judgment was proper.

5

. For ease of reference, we refer to the HBDIC stock and management personnel coilectively as the “HBDIC costs.”

6

. Scheideman’s precise statement was that it would have been "outside the spirit and intent" of Contract 5/86 to add "a separate contract line item ... invoicing Greece for the capitalization costs to HBDIC.”

7

. The DSAA provided a control by evaluating whether the prices charged for the items in Contract 5/86 were reasonable.

8

.In his previous lawsuit against General Dynamics, Yannacopoulos made essentially the same argument, claiming that HBDIC was "of de minimis value” and "valueless to the Greek government” as it was structured in Contract 5/86. *Yannacopoulos,*75 F.3d at 1302 &n. 3.

9

. This is consistent with the DSAA's October 1985 and February 1987 "Guidelines for FMS Loan Financing of Direct Commercial Contracts,” which state that "items purchased must be manufactured in the U.S. and be composed mainly of U.S. made items, components!,] and services.” The February 1989 and July 1991 Guidelines differ only in that they further clarify that the items must be “U.S. manufactured and assembled.”

10

. Yannacopoulos argues that General Dynamics’ communications to the DSAA merely "expressed GD's negotiating position” or "communicat[ed] that Greece's ... version of the EPA Clause modification was 'no longer applicable.' ” He calls our attention to nothing in the record, however, that supports that strained interpretation.

11

. If McKalip had been able to recall the DSAA’s approval of Contract 5/86, he might *831have recalled, for instance, that the DSAA had been told that the EPA clause was “under consideration for being taken out” in exchange for "accelerated aircraft deliveries” well before that clause was actually deleted.

12

. This may explain why McKalip’s declaration does not address a former DSAA official’s testimony that (1) the EPA clause had nothing to do with the DSAA's approval of the draft contract; and (2) that the DSAA disliked that clause because it provided for money to be returned directly to Greece, rather than to the United States government.

13

. Yannacopoulos also argues that his due process rights were violated because the district court allowed General Dynamics to present additional evidence in support of its renewed motion for summary judgment on the EPA clause claim without allowing him to present additional evidence of his own. Yannacopoulos gives no reason, however, that he was unable to include this additional evidence with the substantial amount of evidence he attached to his objection to General Dynamics' request for leave to file its renewed motion. Regardless, summary judgment for General Dynamics on the EPA clause claim was appropriate even in light of the additional evidence described in Yannacopoulos’ briefs.

14

. Under the FCA, a defendant lacking actual knowledge of a falsehood will still be deemed to have known of that falsehood if he acted in (1) deliberate ignorance; or (2) reckless disregard of that falsehood. 31 U.S.C. § 3729(b). Here, however, Yannacopoulos argues only that General Dynamics and Greece actually knew of the inaccuracy of their initial estimate and agreed to disregard the provisions of Contract 5/86 that purportedly required them to rectify that inaccuracy by March 1987.

15

. In fact, it took several years before the final price of *the*spare parts line *item*was agreed upon, with a number of price adjustments taking place during that time. The first adjustment to that line item occurred in 1988, when the price of the spares was reduced to $69,000,000. It was again reduced to $30,288,097 in 1990. Ultimately, the spares line item was reduced to the final price of $24,359,722 in 1996.

16

. The 2009 amendments to the False Claims Act make it unlawful to "knowingly conceal[] or knowingly and improperly avoid[] or decrease[] an obligation to pay or transmit money or property to the Government,” apparently regardless of whether such actions *836involve an a falsehood. Pub. L. 111-21, § 4(a)(1). This amendment does not apply here, however, because it applies only to conduct occurring on or after May 20, 2009. See Pub. L. 111-21, § 4(f).

17

. We reject Lockheed’s argument that, because any amounts that should have been refunded in Modification Five were allegedly later refunded in Modification Six, discussed below, Yannaeopoulos has no standing to bring his claim regarding Modification Five. Even if those funds were later returned, the United States was presumably harmed when it was denied the opportunity to collect interest on the funds in its possession. And even if the United States was not actually harmed by the loss of any such interest funds, we may not dismiss a suit for lack of standing “just because the plaintiff fails to prove injury.” See, *e.g., MainStreet Organization of Realtors v. Calumet City,*505 F.3d 742, 745 (7th Cir.2007).

18

.Even if he could meet this burden, Yannacopoulos would also have to show that Lockheed knew that Greece did not really agree to pay the amount set out in the co-production line item, despite the fact that Greece specifically said as much by signing Modification Five.

19

. Government recoupment was described by one deponent as encompassing such things as the cost to the U.S. Government for developing the F-16.

20

. By contrast, the facts allegedly showing the falsity of the coproduction line item were all discussed in Yannacopoulos' opening brief. He failed to connect the dots adequately in *838that brief, but a finding of waiver on that issue would not be appropriate. See *Hernandez v. Cook County Sheriff's Office,*634 F.3d 906, 913 (7th Cir.2011) ("While arguments made for the first time in a reply brief are generally treated as waived, it does not necessarily follow that arguments that are better developed in a reply brief are waived.”). On this issue, however, we simply had no dots to connect until we received Yannacopoulos’ reply brief, too late to have given Lockheed notice it might need to justify the recoupment line item.

21

. Lockheed argued in its response brief that Modification Six contained no objectively false statements. In his reply, Yannacopoulos could articulate only two alleged falsehoods. To the extent he may believe that Modification Six was false in some other respects, Yannacopoulos has waived any argument on those points.

22

. This is consistent with the minutes of Greece's and Lockheed’s June 1995 negotiations regarding Modification Six, which state that the modification "credits $22,950,000 against Annex AK and [line item] 14” while the "remaining amount of U.S. $6,097,706 consists of $4,206,560 in reserve and U.S. $1,891,146 *committed for payment*to the U.S. Government for facility rental.” (Emphasis added.)

23

. This $29,926,515 refund should not be confused with the $29,047,706 recoupment amount set out in Annex AK.

24

. Because we conclude that Yannacopoulos has failed to adduce sufficient evidence showing that Modifications Five and Six were false, we do not reach the United States’ argument that the defendants had an "obligation” to return money to the United States as required for a reverse false claim.