Fred M. Haag sued his former employer, Infrasource Services, Inc., after he was terminated for “gross misconduct.” Pursuant to the employment contract Infra-source compelled arbitration under Pennsylvania law. The arbitrator found that Haag had accepted reimbursements for housing and other expenses to which he should have known he was not entitled. Haag’s claims were dismissed.

The district court entered a judgment that denied Haag’s motion to vacate and confirmed the arbitrator’s decision. We AFFIRM.

Review of arbitration decisions made under the Federal Arbitration Act is “extraordinarily narrow” and “exceedingly deferential.” Rain CII Carbon, LLC v. ConocoPhillips Co., 674 F.3d 469, 471-72 (5th Cir. 2012). Our review of the district court’s denial of a motion for vacatur is de novo. Laws v. Morgan Stanley Dean Witter, 452 F.3d 398, 399 (5th Cir. 2006).

There are limited grounds established by statute for vacating and modifying an arbitration award. See 9 U.S.C. §§ 10 & 11. A modification is permitted if “there was an evident material miscalculation of figures or an evident material mistake in the description of any person, thing, or property referred to in the award.” § 11(a). The statutory authority for vacating an award refers only to such defects as fraud, partiality, and misconduct or misuse of power by the arbitrator. § 10(a). Despite those limits, this court has held that “a material mistake of fact” can also be grounds for vacatur. Valentine Sugars, Inc. v. Donau Corp., 981 F.2d 210, 214 (5th Cir. 1993). The fact must be unambiguous and undisputed: ‘We interpret the term ‘undisputed’ to mean we should look to see whether there is any rational basis for disputing the truth of the fact.” Id. That mistake must also be material: “ ‘the record must demonstrate[ ] strong reliance on that mistake.’ ” Id. The parties disagree whether Valentine remains good law. We need not decide Valentine’s vitality as we conclude that Haag’s arguments for vaca-tur fail even if Valentine applies.

Haag contends that the relevant material mistake was the arbitrator’s statement *432 in his initial ruling that “[t]he facts are not in dispute that [Haag] submitted improper requests for expense reimbursement.” That statement is correct, but the statement does not apply to all of the relevant expenses. As to the housing expenses, Haag did not need to submit claims. He was reimbursed automatically with monthly deposits into his bank account. Haag’s misconduct on housing expenses was not taking steps to stop the deposits once he knew or should have known he was still receiving them after they were supposed to end.

We agree that Haag did not “submit” claims for housing reimbursement, but there is no indication that the arbitrator strongly relied on any distinction between claims improperly “submitted” versus those that were not stopped. The arbitrator found cause for termination based on Haag’s misstatement that he was paying for “all of [his] personal expenses and housing now,” “improper expense reimbursement” generally, including for travel, and a company audit that disclosed Haag “misappropriated in excess of $80,000,” in addition to the “improper” “funds [Haag] received” for housing. There was neither an unambiguous factual mistake by the arbitrator about submission of claims, nor strong or material reliance on any mistaken understanding of those facts.

This analysis is not changed by the arbitrator’s holding that Infrasource was not entitled to prevail on its counterclaims. Each of the seven counterclaims that In-frasource asserted required proof of discrete elements; the claim of fraudulent misrepresentation, for example, requires proof of a representation, that is material, made falsely, with knowledge or recklessness as to that falsity, with the intent to mislead, with justifiable reliance on that representation, and injury proximately caused by that reliance. Ira G. Steffy & Son, Inc. v. Citizens Bank of Penn., 7 A.3d 278, 290 (Pa.Super.Ct. 2010). The arbitrator found a lack of adequate proof as to the various counterclaims. The arbitrator’s finding is not inconsistent with the determination of “cause,” which under the employment agreement only required a finding of “willful engaging ... in gross misconduct materially and demonstrably injurious to the Company.”

AFFIRMED.