FLOYD, Circuit Judge:

I.

Catone began working for the United States Postal Service in 1977. On August 2, 2006, he submitted a claim for federal workers' compensation benefits under the Federal Employees' Compensation Act based on injuries arising from extended periods of driving. The Office of Workers' Compensation Programs (OWCP) awarded to Catone benefits regarding his claim of temporary aggravation of obstructive sleep apnea, which he began receiving in March 2007.

To verify his continued eligibility for benefits, Catone submitted a "CA-1032" form to OWCP each year. The form instructed Catone to disclose whether, in the past fifteen months, he (1) "work[ed] for any employer"; (2) was "self-employed or involved in any business enterprise"; (3) earned "monetary or in-kind compensation" for "volunteer work"; or (4) was "unemployed for all periods." Catone submitted CA-1032 forms in April 2008 and 2009, and each time he answered "no" to the first three questions and "yes" to the fourth question. From March 2007 to September 2009, Catone received $121,729.80 in benefits from OWCP.

Catone was indicted in May 2011 on three criminal charges stemming from his receipt of federal workers' compensation benefits. The first two counts charged Catone with making false statements in connection with his receipt of benefits, in violation of 18 U.S.C. § 1920, and the third count charged him with violating 18 U.S.C. § 1001(a)(2), which makes it unlawful to "knowingly and willfully ... make[] any materially false, fictitious, or fraudulent statement" to a federal official. The indictment alleged that Catone failed to disclose that he was employed by, and received income from, Angelo's Maintenance for custodial work that he performed at Hayes Performing Arts Center (the Center) during the period that he obtained federal benefits. As relevant to the third count, the indictment alleged that Catone knowingly made false statements during an interview with federal agents when he reported that he had not earned any income while receiving compensation benefits. Instead, during that interview, he informed federal investigators that his wife was employed by Angelo's Maintenance as a custodian and that he occasionally assisted her with performing custodial tasks while she cleaned the Center.

At trial, the government elicited testimony from three former employees of the Center, whose testimony collectively established that Catone often assisted his wife in cleaning the Center; that Catone was not employed or paid by the Center; and that the Center contracted with Angelo's Maintenance to provide cleaning services. The government also proffered testimony from an employee at the bank where Catone and his wife maintained a joint checking account. According to his testimony, the Catones' account included three checks written directly to Catone from Angelo's Maintenance. Two of the checks predated Catone's receipt of workers' compensation benefits and the third check, which Catone received while also receiving workers' compensation benefits, was for $635. The jury convicted Catone on count one, which alleged a violation of § 1920 based upon the CA-1032 form that Catone submitted in April 2008, and acquitted him on the two remaining counts.

A presentence investigation report (PSR) prepared by a probation officer concluded that Catone's conviction under § 1920 carried a statutory maximum sentence of five years' imprisonment. The probation officer further found that Catone was responsible for a loss amount of $128,124.75, which constitutes the entire amount of benefits Catone received from OWCP. Based on the loss-amount calculation, the PSR added ten levels to Catone's offense level pursuant to U.S.S.G. § 2B1.1(b)(1)(F), which provides for such an enhancement when the loss amount is greater than $120,000 but not greater than $200,000. The PSR calculated Catone's total offense level as 16, which, combined with a criminal history category of I, yielded an advisory Guidelines range of twenty-one to twenty-seven months' imprisonment. Finally, the PSR also recommended that Catone pay restitution in the amount of $106,411.83, which constitutes the entire amount of a forfeiture imposed by the Department of Labor in an administrative proceeding.

Prior to his sentencing, Catone filed several objections to the PSR, two of which are relevant here. First, he objected to the PSR's conclusion that his sentence carried a statutory maximum of five years' imprisonment, claiming that his conviction was for a misdemeanor with a one-year maximum because the jury never determined that the amount of benefits falsely obtained exceeded $1000. Second, Catone objected to the loss-amount calculation. In his view, the loss amount should have been based on the difference between the amount of benefits that he actually received and the amount that he would have received but for the false statement. The district court rejected Catone's objections, sentenced Catone to a sixteen-month term of imprisonment, and imposed restitution in the amount of $106,411.83.

II.

We first address Catone's challenge to his conviction. Catone argues that his conviction under § 1920 should be vacated because the government failed to disclose, in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), evidence that undermined the government's theory that Catone willfully concealed the work he performed for Angelo's Maintenance. Because Catone did not raise this issue below, we review the claim for plain error. See United States v. Vinyard, 266 F.3d 320, 324 (4th Cir.2001). To establish plain error, Catone must show (1) that the court erred, (2) that the error is clear and obvious, and (3) that the error affected his substantial rights, meaning that it "affected the outcome of the district court proceedings." United States v. Olano, 507 U.S. 725, 732-34, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). Even when this burden is met, we retain discretion whether to recognize the error and will deny relief unless the district court's error "seriously affects the fairness, integrity or public reputation of judicial proceedings." Id. at 736, 113 S.Ct. 1770 (brackets omitted) (internal quotation marks omitted).

Catone bases his Brady claim on a "CA-7" form that he submitted to the Department of Labor in March 2007, which disclosed that he had performed a total of 14.6 hours of work for Angelo's Maintenance at a rate of $12.00 per hour. In his view, the CA-7 form undermined the government's theory that he had been willfully concealing from the OWCP the work that he performed for Angelo's Maintenance. Catone thus argues that the government's failure to produce the form as part of discovery constitutes a Brady violation that should be noticed on plain-error review.

To prevail on a Brady claim, a defendant must show that (1) the evidence is either exculpatory or impeaching, (2) the government suppressed the evidence, and (3) the evidence was material to the defense. United States v. McLean, 715 F.3d 129, 142 (4th Cir.2013). No Brady violation exists when the evidence is "available to the defense from other sources" or through a "diligent investigation by the defense." United States v. Higgs, 663 F.3d 726, 735 (4th Cir.2011) (internal quotation marks omitted). Accordingly, "[p]ublicly available information which the defendant could have discovered through reasonable diligence cannot be the basis for a Brady violation." United States v. Willis, 277 F.3d 1026, 1034 (8th Cir.2002) (internal quotation marks omitted). Evidence is "material" only if it is "likely to have changed the verdict." United States v. Bartko, 728 F.3d 327, 338 (4th Cir.2013).

Catone's Brady violation claim fails for numerous reasons. First, to establish a Brady violation, the exculpatory material must be known to the government but not to the defendant. See United States v. Roane, 378 F.3d 382, 402 (4th Cir.2004) ("[I]nformation actually known by the defendant falls outside the ambit of the Brady rule."). As Catone is the individual who completed the CA-7 form and submitted it to the Department of Labor, the document was already known to him. Second, the CA-7 form is a publicly available document and could have been uncovered by a diligent investigation. As a senior claims examiner at the Department of Labor testified, Catone could have obtained a copy of his entire claims file by simply submitting a written request to the Department of Labor. See United States v. Wilson, 901 F.2d 378, 381 (4th Cir.1990) (observing that "where the exculpatory information is not only available to the defendant but also lies in a source where a reasonable defendant would have looked, a defendant is not entitled to the benefit of the Brady doctrine"). Third, Catone is unable to show that had the CA-7 form been disclosed, it would have likely changed the verdict. Instead of undermining the government's theory of intent, the CA-7 form demonstrates that Catone — in a separate benefits claim — knew that he was required to disclose his employment with Angelo's Maintenance but nevertheless failed to do so with respect to the benefits he received in connection with the underlying charges. Catone has failed to establish plain error with respect to his Brady claim.

III.

Catone next challenges the imposition of his sixteen-month felony sentence, claiming that his conviction under § 1920 resulted in a misdemeanor rather than a felony conviction. Because Catone properly raised this issue during his sentencing hearing, we review his claim de novo. See United States v. Mackins, 315 F.3d 399, 405 (4th Cir.2003).

Section 1920 of the criminal code makes it unlawful to "knowingly and willfully ... make[] ... a false, fictitious, or fraudulent statement or representation ... in connection with the application for or receipt of compensation or other benefit or payment" under a federal program. 18 U.S.C. § 1920. The statute further provides that any individual convicted of violating § 1920

Id. Although the jury found that Catone knowingly and willfully made a false statement in connection with his receipt of federal workers' compensation benefits, it made no finding that the offense led to more than $1000 in "falsely obtained" benefits. Construing the "amount of the benefits falsely obtained" as an element necessary to sustain a felony conviction under § 1920, Catone argues that the district court violated his Sixth Amendment right to trial by a jury by imposing a felony sentence. The government counters that Catone's felony conviction does not violate the Sixth Amendment prohibition against judicial fact finding because the language and structure of § 1920 indicate that the amount of benefits falsely obtained is not an essential element for felony liability. In any event, the government claims that any Sixth Amendment error is harmless.

A.

Whether a particular fact must be submitted to the jury and found beyond a reasonable doubt turns on whether the fact constitutes an element of the charged offense. See United States v. O'Brien, 560 U.S. 218, 224, 130 S.Ct. 2169, 176 L.Ed.2d 979 (2010) ("Elements of a crime must be charged in an indictment and proved to a jury beyond a reasonable doubt."). Although this Court has not previously addressed whether the amount of benefits falsely obtained is an element of a § 1920 offense, we have found that the government must prove loss amount as an element of a felony conviction under 18 U.S.C. § 641 — the statute dealing with theft of federal property — which employs analogous language, and a nearly identical structure, as § 1920. See United States v. Wilson, 284 F.2d 407, 408 (4th Cir.1960). In Wilson, we observed that, in effect, § 641 "creates two separate crimes with different penalties." Id. "In order to sustain the imposition of the higher penalty," we concluded, "it [i]s incumbent upon the Government to prove a value in excess of the stated amount — then, $100. Id. Thus, because punishment for a § 641 offense varies depending on the value of the stolen property, we reasoned that value is a substantive element of the aggravated offense.

Our analysis in Wilson is consistent with, and supported by, the Supreme Court's recent Sixth Amendment jurisprudence. In Apprendi v. New Jersey, the Supreme Court held that, "[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to the jury, and proved beyond a reasonable doubt." 530 U.S. 466, 490, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). The Court subsequently extended the reasoning of Apprendi to mandatory minimum sentences, explaining that when a finding of fact "aggravates the legally prescribed range of allowable sentences, it constitutes an element of a separate, aggravated offense that must be found by the jury, regardless of what sentence the defendant might have received if a different range had been applicable." Alleyne v. United States, 133 S.Ct. 2151, 2162 (2013); id. at 2155 ("Any fact that, by law, increases the penalty for a crime is an `element' that must be submitted to the jury and found beyond a reasonable doubt."). Under Apprendi and its progeny, therefore, any fact that increases either the statutory maximum or mandatory minimum constitutes "an element of a distinct and aggravated crime" that must be found by the jury beyond a reasonable doubt. Id. at 2162-63.

Section 1920 establishes two levels of sentencing depending on the amount of benefits that a defendant "falsely obtained." Absent a finding that a defendant received more than $1000 in falsely obtained benefits, the maximum sentence for a § 1920 offense is one year of imprisonment. If a defendant is found to have received more than $1000 in falsely obtained benefits, the statutory maximum increases to five years' imprisonment. Because a finding that the amount of falsely obtained benefits exceeds $1000 increases the maximum punishment to which a defendant is exposed, it constitutes a substantive element for a felony offense that must be submitted to the jury and proven beyond a reasonable doubt. See Alleyne, 133 S.Ct. at 2162-63 ("The essential point is that the aggravating fact produced a higher range, which, in turn, conclusively indicates that the fact is an element of a distinct and aggravated crime. It must, therefore, be submitted to the jury and found beyond a reasonable doubt.").

Our conclusion that the amount of benefits falsely obtained is a substantive element for a felony conviction under § 1920 is consistent with the Eleventh Circuit's interpretation of § 1920. See United States v. Hurn, 368 F.3d 1359, 1362 (11th Cir.2004) ("Under Apprendi, for a defendant to be subject to a 5-year rather than a 1-year maximum sentence under § 1920, the jury must determine that the amount of benefits she `falsely obtained' exceeds $1,000."). We acknowledge that some of our sister circuits have reached the opposite conclusion, opining that loss amount should be treated as a sentencing consideration rather than an essential element of the offense. See United States v. Webber, 536 F.3d 584, 595 (7th Cir.2008) (intimating in dictum that "the language and structure of [§ 1920]" indicate that "the amount of benefits falsely obtained is not a substantive element of the offense but a statutorily mandated punitive sentencing factor"); United States v. Henry, 164 F.3d 1304, 1307-08 (10th Cir.1999); United States v. Grillo, 160 F.3d 149, 150 (2d Cir.1998) (per curiam). The Supreme Court, however, has expressly repudiated the notion that "there is a constitutionally significant difference between a fact that is an `element' of the offense and one that is a `sentencing factor.'" S. Union Co. v. United States, ___ U.S. ___, 132 S.Ct. 2344, 2356, 183 L.Ed.2d 318 (2012); see also Apprendi, 530 U.S. at 494, 120 S.Ct. 2348 ("[T]he relevant inquiry is one not of form, but of effect — does the required finding expose the defendant to a greater punishment than that authorized by the jury's guilty verdict?"). Thus, because we believe that the Eleventh Circuit's approach in Hurn comports with the Supreme Court's recent Sixth Amendment cases associated with Apprendi, as well as this Circuit's decision in Wilson, we decline to follow the few decisions in other circuits that view loss amount as a punitive sentencing factor.

B.

The government concedes that Catone's felony conviction is not supported by a jury finding that the offense led to more than $1000 in falsely obtained benefits, but it argues that the error is harmless. As with all nonstructural constitutional errors, an Apprendi error does not mandate reversal if the government can establish that the error is harmless. United States v. Brown, 757 F.3d 183, 189-90 (4th Cir.2014). An Apprendi error is harmless "where a reviewing court concludes beyond a reasonable doubt that the omitted element was uncontested and supported by overwhelming evidence, such that the jury verdict would have been the same absent the error." Neder v. United States, 527 U.S. 1, 17, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999); United States v. Strickland, 245 F.3d 368, 380 (4th Cir.2001) (observing that Neder "articulat[es] the particular test for when an omitted instruction on an element of an offense is harmless").

The government contends that, in this case, the Apprendi error is harmless because there is overwhelming evidence establishing that Catone received more than $100,000 in federal workers' compensation benefits. In its view, to obtain a felony conviction under § 1920, the jury need only find that the defendant received more than $1000 in benefits without distinguishing between benefits flowing from a defendant's false statement and those legally obtained.

But the plain language of the statute indicates just the opposite: whether a conviction under § 1920 results in a felony or a misdemeanor turns on whether "the amount of the benefits falsely obtained" exceeds $1000. Had Congress intended for the degree of punishment to be based on the total amount of benefits that a defendant received, as the government contends, Congress could have so provided by omitting the word "falsely" from the statute, so as to deliver a felony conviction when "the amount of benefits obtained" exceeds $1000. Instead, Congress chose to make the degree of punishment for § 1920 offenses hinge upon the amount of "benefits falsely obtained." 18 U.S.C. § 1920 (emphasis added); see United States v. Tupone, 442 F.3d 145, 158 n. 9 (3d Cir.2006) (Stapleton, J., dissenting) ("Congress chose ... to limit punishment in accordance with the amount of `benefits falsely obtained.'"); Hurn, 368 F.3d at 1362 (observing that the plain language of § 1920 requires the government to prove a causal link between the defendant's false statement and the receipt of more than $1000 in benefits); see also Lowe v. SEC, 472 U.S. 181, 207 n. 53, 105 S.Ct. 2557, 86 L.Ed.2d 130 (1985) ("[W]e must give effect to every word that Congress used in the statute."). Consistent with the plain language of § 1920, we believe that Congress intended to impose harsher punishment based upon the amount of benefits received as a result of a defendant's false statements rather than the total amount of benefits obtained. To hold otherwise would punish a defendant for obtaining benefits that he lawfully was entitled to receive.

Although it is uncontested that Catone received more than $100,000 in federal workers' compensation benefits, the evidence regarding the portion of benefits Catone falsely obtained is far from overwhelming and uncontroverted. Evidence adduced at trial shows that Catone received a single check — in the amount of $635 — from Angelo's Maintenance during the period he received federal workers' compensation benefits. And the government's own witness testified that an individual may continue to receive benefits despite earning small amounts of income. Notably, the government fails to point to any probative evidence that could reasonably support a finding that Catone received more than $1000 in benefits as a result of his false statement. We therefore are unable to find that the Apprendi error is harmless.

Because the jury made no finding that the amount of benefits falsely obtained exceeded $1000, and we are unable to locate "overwhelming evidence" in the record to support such a conclusion, Neder, 527 U.S. at 17, 119 S.Ct. 1827, Catone's felony conviction cannot stand. Accordingly, we vacate Catone's felony conviction and direct the district court to impose a misdemeanor sentence on remand.

IV.

Last, Catone challenges the district court's application of a ten-level sentencing enhancement to his base offense level under Section 2B1.1(b)(1)(F) of the Guidelines, as well as the district court's restitution order. We review the district court's application of the Guidelines de novo and its factual findings for clear error. United States v. Quinn, 359 F.3d 666, 679 (4th Cir.2004). We review the district court's restitution award for an abuse of discretion. United States v. Grant, 715 F.3d 552, 556-57 (4th Cir.2013).

Section 2B1.1(a) of the Guidelines provides the base offense level for crimes involving fraud or deceit. That Section also calls for various increases to a defendant's base offense level depending on the specific loss amount at issue. U.S.S.G. § 2B1.1(b). The government must prove the amount of loss by a preponderance of evidence. United States v. Pierce, 409 F.3d 228, 234 (4th Cir.2005). The district court, though it need not reach a precise figure as to loss, must make a "reasonable estimate" of loss based on the "available information" in the record. U.S.S.G. § 2B1.1 cmt. n. 3 (C); see also United States v. Miller, 316 F.3d 495, 503 (4th Cir.2003).

As a general rule, the Guidelines instruct that "loss is the greater of actual loss or intended loss." U.S.S.G. § 2B1.1 cmt. n. 3(A). A different rule applies, however, for government-benefits offenses like Catone's. We have held that, when a defendant obtains both proper and improper benefits, the amount of loss is calculated based on "the difference between the amount of benefits [the defendant] actually received and the amount he would have received had he truthfully and accurately completed the [CA-]1032 forms." United States v. Dawkins, 202 F.3d 711, 715 (4th Cir.2000).

After our decision in Dawkins, the Sentencing Commission adopted the following commentary to § 2B1.1:

U.S.S.G. § 2B1.1 cmt. n. 3(F)(ii). Consistent with our case law, Comment Note 3(F)(ii) distinguishes a defendant's loss amount from the total amount of benefits obtained. It further instructs that, when a defendant is the intended recipient of some amount of government benefits, the proper loss calculation is based on the amount of benefits received as a result of the defendant's fraudulent representation.

At sentencing, both Catone and the government agreed that the framework established by Dawkins controlled. And both parties asserted that the Dawkins analysis could be made based on the facts in the existing record. Citing Dawkins, the government contended that, if Catone had truthfully and accurately completed his CA-1032 forms, "he would not have received any benefits" at all. J.A. 343. Thus, the government asserted that the loss amount was $128,124.75, the entire amount of the benefits he received. Id. at 342-43. In support, the government cited "the jury's guilty verdict and the evidence presented at trial." Id. at 343.

In contrast, Catone asserted that the loss amount under Dawkins was less than $1,000. Id. at 307-08. Like the government, he also cited evidence presented at trial: namely, the testimony of two federal employees, who stated that Catone's benefits likely would have been reduced — but not completely terminated — had he properly disclosed his work as a custodian on the CA-1032 forms. Id. at 51-52, 78-79. Indeed, one of the government's witnesses testified that it was possible that small amounts of reported outside income would not reduce the benefit amount at all. Id. at 78. According to these employees, the precise amount of any reduction would be calculated under a so-called "Shadrick Formula" published by the U.S. Department of Labor. Id. at 51-52. Catone asserts that under the Shadrick Formula — which he contends is consistent with Dawkins — his benefits would have been reduced by less than $1,000.

The district court ultimately accepted the government's position, but did not perform the calculation required by Dawkins and the Guidelines. J.A. 281. Rather, it simply adopted the PSR's conclusion that the loss amount equaled the entire amount of benefits that Catone received. Id. The PSR in turn is devoid of any analysis under Dawkins or Comment Note 3(F)(ii) of the Guidelines. Id. at 324.

As the government concedes on appeal, the district court failed to apply the analysis required under Dawkins, and its loss-amount calculation therefore was erroneous. Accordingly, we must vacate Catone's sentence and remand for resentencing.

As Catone argues, however, the record is devoid of any evidence that could reasonably support a finding of loss in excess of $5,000, as is required for any offense-level enhancement under the Guidelines. See U.S.S.G. § 2B1.1(b)(1)(A) (no increase in offense level for loss of $5,000 or less). The evidence presented at trial established that disability benefits are calculated under the Shadrick Formula, that the Shadrick Formula would also be used to calculate any reduction in benefits resulting from Catone's outside income, and that it was possible that Catone's benefits might not have been reduced at all. The government, however, failed to present any evidence at trial or at sentencing showing how the Shadrick Formula would be applied in this case, nor did it present any other evidence otherwise establishing the amount of benefits Catone would have been entitled to receive had he truthfully reported his outside income. While a sentencing court need only make a "reasonable estimate" of loss based on the "available information" in the record, U.S.S.G. § 2B1.1 cmt. n.3(C), an estimate that is unsupported by any evidence cannot be reasonable.

The government bears the burden of proving the loss amount, see Dawkins, 202 F.3d at 714, yet it failed to present the evidence necessary for the district court to make that determination. Because there is no evidence in the record that could support a loss amount exceeding $5,000, we direct the district court on remand to resentence Catone under U.S.S.G. § 2B1.1(b)(1)(A), without any offense-level enhancements for loss amount.*

Finally, because the district court erred in calculating Catone's loss amount, we also must vacate the district court's award of restitution in the amount of $106,411.83, which represents the amount of a forfeiture imposed by the Department of Labor. As we explained in Dawkins, the restitution amount in a government-benefits case depends on the loss amount calculated under the Guidelines. See Dawkins, 202 F.3d at 715. In light of the district court's erroneous loss-amount calculation, we vacate the restitution order and remand for recalculation consistent with this opinion.

V.

For the reasons provided above, we affirm Catone's conviction, vacate his sentence, and remand for further proceedings consistent with this opinion.

AFFIRMED IN PART, VACATED IN PART, AND REMANDED.