MARTHA CRAIG DAUGHTREY, Circuit Judge. A jury found the defendant, Richard Williams, guilty of three counts of making and subscribing a false federal income tax return, in violation of 26 U.S.C. § 7206(1), and of 17 counts of aiding and assisting others in preparing false income tax returns, in violation of 26 U.S.C. § 7206(2).

Williams appeals, alleging that there is insufficient evidence to support the convictions, that the district court committed plain error by allowing the prosecution of charges brought beyond the statute of limitations, and that his Sixth Amendment right to a speedy trial was violated due to the lengthy delay between the entering and unsealing of the indictment. For the reasons discussed below, we find no reversible error and affirm. FACTUAL AND PROCEDURAL BACKGROUND The charges in this case stemmed from the preparation and filing of fraudulent federal income tax returns.

Defendant Williams operated SLR Corporation, which did business in Lansing and Jackson, Michigan, under the trade name Imperial Tax Services (Imperial). In 2008, the Internal Revenue Service (IRS) began to investigate income tax returns prepared by Imperial, after the IRS noticed that they disproportionately used

Schedule C (used to report profits or losses for business operated as sole proprietorships) and disproportionately claimed the earned income tax credit. Tax returns prepared by Imperial also were more likely to result in a tax refund—99% of Imperial’s clients received refunds, compared to 71% of taxpayers in Imperial’s zip code. In October 2008, Williams met with an IRS agent to discuss his company and had subsequent meetings with the agent in December 2008 and June 2009.

In April 2011, a grand jury returned an indictment charging Williams with making and subscribing a false federal income tax return for himself for the 2004 tax year, in violation of 26 U.S.C. § 7206(1), and with aiding and assisting his ex-wife, Dorothy Jones, in preparing, a false income tax return for the 2004 tax year, in violation of 26 U.S.C. § 7206(2).

The government simultaneously moved to seal this indictment, claiming that it was “concerned that the defendant may attempt to flee, destroy evidence, or intimidate witnesses if the Indictment becomes a matter of public record before the defendant is arrested.” The district court granted this motion. One year later, the government filed a superseding indictment.

This indictment incorporated the two counts from the original indictment and added two counts of violating § 7206(a), relating to Williams’s personal tax returns for 2006 and 2007, and 30 counts of violating § 7206(2), relating to Williams’s preparation of tax returns for Imperial clients for the 2005, 2006, and 2007 tax years. Again, the government successfully moved to seal this indictment, claiming the same concerns as in the previous motion to seal.

In September 2013—29 months after the original indictment was sealed and 17 months after the superseding indictment was sealed— the district court unsealed the documents at the government’s request. In January 2015, after a series of stipulations to continue the trial date, Williams proceeded to trial on 20 of the counts. The government called seven former Imperial clients, as well as the IRS caseworker assigned to the investigation. These individuals all testified that Williams reported fictitious businesses on client tax returns.

These sham businesses had common traits—the name of the business usually included the last name of the taxpayer, the businesses were all sole proprietorships, the principal business or profession listed on the

Schedule C was “unclassified,” and the business address generally was one of Williams’s previous addresses. For some clients, Williams reported substantial business losses, which reduced a client’s taxable income. For others, Williams reported fraudulent business income, enabling the client to qualify for the earned income tax credit. For the 2007 tax year, 55 percent of returns prepared by Williams involved

Schedule C, compared to the area average of seven percent. Williams obtained verification from his clients, using a Form 8879, that they had reviewed the tax return for accuracy, and that Williams was authorized to file on their behalf. However, former clients testified that Williams did not discuss or explain their tax returns to them, and one client testified that Williams did not provide her with a copy of the tax return until after it was filed. Williams collected large fees directly from a client’s anticipatory tax refund loan.

The government also presented evidence that Williams had falsified his own personal tax returns. Imperial is an 1120S corporation, or “S corporation,” and as such, any tax liability incurred by Imperial “flowed through” to Williams. Williams was required to report any income earned by Imperial on his personal tax return, using a form called

Schedule E. In 2004, Williams reported only one dollar of income earned through his work for Imperial, despite evidence that Imperial earned over $21,000 in tax preparation fees and shares of refund anticipation loan fees. In 2006, Williams reported only two dollars in income, but the government presented evidence that over $26,000 had been deposited into his bank account for preparation and loan fees. In 2007, Williams reported earning ten dollars, despite the government’s assertion that Imperial earned over $58,000. A jury found Williams guilty on all counts, and he was sentenced to 36 months in prison.

Williams was also ordered to pay $60,594 in restitution. DISCUSSION Sufficiency of the Evidence Williams contends that his convictions under 26 U.S.C. § 7206(1) and § 7206(2) were not supported by sufficient evidence. We review a sufficiency-of-the-evidence challenge de novo, and the relevant inquiry is whether, “viewing the evidence in the light most favorable to the prosecution,' any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Fisher, 648 F.3d 442, 450 (6th Cir. 2011) (quoting Jackson v.

Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original)). Williams’s 2004 Tax Return First, Williams challenges the sufficiency of the evidence as to Count 1, which alleges that he filed a false personal tax return for the 2004 tax year, in violation of 26 U.S.C. § 7206(1).

To convict under § 7206(1), the government must prove: (1) that the defendant willfully made and subscribed a return, statement, or other document, (2) that contained a written declaration that it was made under penalties of perjury, and (3) that the defendant did not believe to be true and correct as to every material matter. United States v. Tarwater, 308 F.3d 494, 504 (6th. Cir. 2002). “[T]he failure to report income or other items necessary to the computation of tax is material.” United States v. Anderson, 353 F.3d 490, 499 (6th Cir. 2003) superseded by statute on other grounds.

Williams does not dispute the charge that he willfully made and subscribed a return containing a written declaration that was made under penalty of perjury. He does dispute the finding that he did not believe the return to be true and correct, and he challenges the sufficiency of the evidence as to this element. Williams contends that the information he listed on his 2004 tax return was the “literal truth/’ which negates any possibility that he did not believe the return to be true and correct. In 2004, Williams reported that Imperial experienced a loss of $745 on the company’s corporate tax return.

He reported one dollar of income on his personal income return, using Form 1040. According to Williams, because Imperial’s tax return showed that “the corporation did not report any income, [he] did not have an affirmative duty to report a positive income figure on his individual Form 1040 return.” This argument is untenable. “Section 7206 is a perjury statute that criminalizes lying on any document filed with the IRS.” Tarwater, 308 F.3d at 504 (emphasis added).

If an individual lies on a corporate tax return, he cannot copy that false information onto a personal tax return and claim it as “literal truth.” Rather, the tax return would contain information known to be untrue. Williams correctly points out that the government did not charge him with preparing false returns on behalf of the corporation, but because Imperial’s income flows through to Williams, evidence of corporate earnings is relevant to determining Williams’s personal income.

At trial, an IRS agent testified that he found unreported income for Williams for the 2004 tax year, explaining that he found a number of deposits made into Imperial’s bank account in 2004 totaling over $21,000. The jury was shown a

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schedule of these deposits, and the agent testified that these deposits were income from tax-preparation services. The agent further testified that Williams was the only individual who was involved with Imperial, or who obtained any financial benefit from Imperial. Finally, the agent testified that Imperial’s corporate tax return for 2004 did not explain the one dollar reported by Williams on his personal tax return, despite the fact that Williams claimed that the one dollar was earned in connection with Imperial.

This testimony provided a sufficient basis from which the jury—or any rational trier of fact—could have found beyond a reasonable doubt that Williams knew that his tax return for 2004 was not true and correct as to every material matter. Williams’s 2006 and 2007 Tax Returns Williams also disputes the sufficiency of the evidence regarding Counts 2 and 3 of the superseding indictment, which allege that Williams filed false income tax returns for 2006 and 2007, respectively.

Again, Williams denies that the evidence established that he did not believe that the returns were true and correct as to every material matter. “A matter is ‘material’ if it has a natural tendency to influence, or is capable of influencing or affecting, the ability of the IRS to audit or verify the accuracy of a tax return.” Tarwater, 308 F.3d at 505 (citing Neder v. United States, 527 U.S. 1, 16, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999)). In 2006 and 2007, Williams filed his taxes using Form 1040EZ, rather than using Form 1040.

He reported earning two dollars in 2006 and ten dollars in 2007, which the government contends was a vast understatement. Williams’s sole argument is that Form 1040EZ does not ask for business income, so he did not report his business income. He bases this argument on United States v.

Borman, a Seventh Circuit case holding that to be guilty of a § 7206(1) violation, “the untruth must be found in a statement of some material information called for by the form itself, and any implication drawn from the filing of a particular form—-that the taxpayer had received no income requiring the use of a different form—is simply not enough.” 992 F.2d 124, 126 (7th Cir. 1993). Based on this decision, Williams contends that he cannot be convicted under a theory that he should have reported his taxes using Form 1040, which does inquire about business income.

Borman, however, is inapplicable—aside from the fact that it has not been adopted by this Circuit—because unlike the defendants in that case, Williams did make an untrue statement directly on • his Form 1040EZ.

The form—which has changed since the Borman decision—requires filers to swear that, “Under penalties of perjury, I declare that I have examined this return and, to the best of my knowledge and belief, it is true, correct, and accurately lists all amounts and sources of income I received during the tax year.” (Emphasis added.) The information discussed in this declaration, specifically the amount and source of income, are material matters, as they undoubtedly-influence “the ability of the IRS to audit or verify” the truth and accuracy of the return. Tarwater, 308 F.3d at 505.

At trial, an IRS agent testified that he uncovered unreported income for Williams for both the 2006 and 2007 tax years. The agent explained that over $26,000 was deposited into Williams’s bank account in 2006, and over $58,000 was deposited in 2007. Again, the jury was shown

summary schedules of these deposits, and the agent testified that the deposits were income from tax-preparation services. Former Imperial clients testified that Williams had prepared their taxes in 2006 and 2007, for a fee. The jury also heard that in 2006, Williams purchased a Jaguar and reported earning $4,000 a month as an accountant at Imperial on the car loan application.

This testimony clearly provided a sufficient basis from which the jury—or any rational trier of fact—could have found beyond a reasonable doubt that Williams knew that his tax returns for 2006 and 2007 were not true and correct as to every material matter.

Client Tax Returns Finally, Williams contends that there is insufficient evidence to support his convictions for aiding and abetting the preparation of false tax returns, in violation of 26 U.S.C. § 7206(2). “An offense under § 7206(2) has three essential elements: (1) that defendant aided, assisted, procured, counseled, advised or caused the preparation and presentation of a return; (2) that the return was fraudulent or false as to a material matter; and (3) that the act of the defendant was willful.” United States v. Goosby, 523 F.3d 632, 637 (6th Cir. 2008).

Williams believes that the government failed to present sufficient evidence that he willfully prepared false tax returns. He argues on appeal, as he did at trial, that his clients gave him written verification that the information in their tax returns was true and correct. He explains that he relied on those verifications and did not submit any false returns deliberately. At trial, however, the government presented ample evidence that Williams included false tax information without client direction or consent.

Seven former Imperial clients testified that Williams listed nonexistent businesses on their tax returns. They denied telling Williams that they owned businesses, or directing Williams to include business profits, losses, or expenses on their tax returns. Several former clients testified that Williams did not discuss or explain their tax returns to them, and one client testified that she was not given a copy of the tax return before it was filed.

Another client testified that when she confronted Williams after the IRS required her to pay over $10,000 in back taxes, Williams told her that he had been “trying to help,” which she understood to mean help her and her husband get a higher tax refund. The jury was also presented evidence of the similar characteristics of the fictitious businesses. See United States v. Rozin, 664 F.3d 1052, 1059 (6th Cir. 2012) (“Willfulness may be established by evidence that is entirely circumstantial.”) (internal quotation marks and citation omitted).

Considering the evidence presented by the government, we conclude that a rational trier of fact could have found beyond a reasonable doubt that Williams willingly included false information on the tax returns at issue. Williams’s challenges to the sufficiency of the evidence adduced to convict him thus are without merit. Statute of Limitations Williams next contends, for the first time on appeal, that the district court improperly sealed both the original and superseding indictments and, therefore, that the statute of limitations for the counts listed in the indictments was not tolled.

Williams further asserts that by the time the indictment was unsealed, the statute of limitations had run for the majority of the counts therein, including 14 counts for which he was found guilty at trial. But Williams fails to address the threshold question. Before considering the merits of his arguments regarding the sealing of the indictment and tolling of the limitations bar, we must determine whether his failure to present the statute-of-limitations defense to the district court prevents him from successfully arguing it on appeal.

Previously, we have allowed statute-of-limitations bars to be raised for the first time on appeal and have reviewed such arguments for plain error. See United States v. Singer, 782 F.3d 270, 278 (6th Cir. 2015); see also United States v. Crossley, 224 F.3d 847, 858 (6th Cir. 2000), superseded by statute other grounds.

Since these decisions were issued, however, the Supreme Court has ruled that a statute-of-limitations bar may not be raised successfully for the first time on appeal, not even for plain-error review: [A] statute-of-limitations defense becomes part of a case only if the defendant puts the defense in issue. When a defendant presses a limitations defense, the Government then bears the burden of establishing compliance with the statute of limitations by presenting evidence that the crime was committed within the limitations period or by establishing an exception to the limitations period.

When a defendant fails to press a limitations defense, the defense does not become part of the case and the Government does not otherwise have the burden of proving that it filed a timely indictment. When a defendant does not press the defense, then, there is no error for an appellate court to correct—and certainly no plain error. Musacchio v. United States, — U.S. —, 136 S.Ct. 709, 718, 193 L.Ed.2d 639 (2016) (emphasis in original) (citation omitted). Because Williams did not “press the defense” in the district court, we find no error, plain or otherwise, in the prosecution of the allegedly time-barred claims.

Right to a Speedy Tidal Next, Williams contends that the lengthy delay between the issuance and unsealing of the indictments violated the Speedy Trial Clause of the Sixth Amendment. “In determining whether a defendant’s [Sixth Amendment] right to a speedy trial has been violated, this court reviews questions of law de novo and questions of fact under the clearly erroneous standard.” United States v. Williams, 753 F.3d 626, 632 (6th Cir. 2014) (quoting United States v. Jackson, 473 F.3d 660, 664 (6th Cir. 2007)).

However, Williams raises this issue for the first time on appeal, and we therefore review it for plain error only, United States v. Olano, 507 U.S. 725, 732-37, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). In Barker v. Wingo, the Supreme Court identified four factors to consider when analyzing a potential speedy-trial violation: (1) the length of the delay; (2) the reason for the delay; (3) the defendant’s assertion of his right, and (4) prejudice to the defendant. 407 U.S. 514, 530, 92 S.Ct. 2182, 33 L.Ed.2d 101 (1972). Length of Delay The first Barker factor—the length of the delay—is a threshold inquiry. Doggett v.

United States, 505 U.S. 647, 651-52, 112 S.Ct. 2686, 120 L.Ed.2d 520 (1992). “Simply to trigger a speedy trial analysis, an accused must allege that the interval between accusation and trial has crossed the threshold dividing ordinary from ‘presumptively prejudicial’ delay....” Id. (citing Barker, 407 U.S. at 530-31, 92 S.Ct. 2182). “[I]n calculating the length of the delay, only those periods of delay attributable to the government or the court are relevant to [the defendant’s] constitutional claim.” United States v.

Howard, 218 F.3d 556, 564 (6th Cir. 2000); see also Barker, 407 U.S. at 529, 92 S.Ct. 2182 (“We hardly need add that if delay is attributable to the defendant, then his waiver may be given effect under standard waiver doctrine.”). Williams and the government jointly requested on four separate occasions that the district court delay the trial date, and, as a result, the trial began almost a year later than initially scheduled. Hence, the 11-month period from February 2014 to January 2015 cannot be included in the length of the delay for purposes of this analysis.

Determining the length of the delay also requires us to identify the date on which the speedy-trial right attached. “The length of delay is measured from the earlier of the date of indictment or arrest to the defendant’s trial.” United States v. Bass, 460 F.3d 830, 836 (6th Cir. 2006) (citing Maples v. Stegall, 427 F.3d 1020, 1026 (6th Cir. 2005)). As the government points out, our circuit has not ruled definitively whether the right attaches when the indictment is entered, or, in cases where the indictment is initially under seal, when the indictment is unsealed.

After subtracting the 11-month delay that can be attributed partially to Williams, 34 months passed between the return of the first indictment and trial, and 22 months passed between the filing of the superseding indictment and trial. Because a delay of one year or more is “presumptively prejudicial,” Williams, 753 F.3d at 632, these delays trigger further analysis. However, only five months can be attributed to possible government delay after the indictment was unsealed. “A delay of five months is not per se excessive under the Sixth Amendment,” and, therefore, does not trigger further analysis.

Howard, 218 F.3d at 564 Our sister circuits are split on this issue. In the Second Circuit, for example, “the speedy trial right under the Sixth Amendment attaches not when a sealed indictment is filed but when it is unsealed (or when the Government arrests the defendant or otherwise apprises him of the charges against him).” United States v. Watson, 599 F.2d 1149, 1156 (2nd Cir. 1979). The First Circuit, however, has rejected adopting a “bright-line rule that the relevant time period for purposes of the right to a speedy trial begins to run only once the indictment is unsealed.” United States v.

Casas, 356 F.3d 104, 112 (1st Cir. 2004). But, because the remaining Barker factors largely weigh against Williams, we see no need to decide whether the right to a speedy trial attaches before or after an indictment is unsealed in order to find that there was no plain error involving Williams’s Sixth Amendment right to a speedy trial.

Reason for Delay The second Barker factor is the reason for the delay. “Governmental delays motivated by bad faith, harassment, or attempts to seek a tactical advantage weigh heavily against the government, while neutral reasons such as negligence are weighted less heavily, and valid reasons for a delay weigh in favor of the government.” United States v. Robinson, 455 F.3d 602, 607 (6th Cir. 2006). Williams contends that the delay was motived by the government’s attempts to seek a tactical advantage in sealing the indictment simply as a way to extend the statute of limitations.

However, in support of this theory, Williams points only to the fact that the government included no particularized findings or affidavit with their motion to seal. Further, Williams argues that the government cited “flight risk” concerns in their motion to seal, despite having evidence that he was not a flight risk based on his previous cooperation with the IRS agent. Despite Williams’s contention to the contrary, the record before us is silent as to the reasons for the actual delay between the sealing and unsealing of the indictment, and the reasons provided by Williams are largely conjecture.

The record includes the reasons provided by the government in its motion to seal but does not include any additional information as to why the indictment remained sealed for such a long period of time. As the government points out, the record’s silence is largely due to the fact that Williams did not bring a speedy-trial claim at or before trial. Because the record contains no information regarding the actual reasons for this period of delay, we are unable to determine if this delay was due to a valid reason, negligence, or something more sinister.

As a result, this factor of the speedy-trial analysis does not weigh in favor of either party. Assertion of Right The third Barker factor concerns the defendant’s assertion of his or her right to a speedy trial.

Because “[t]he more serious the deprivation, the more likely a defendant is to complain,” the assertion of one’s right to a speedy trial “is entitled to strong evidentiary weight in determining whether the defendant is being deprived of the right.” Barker, 407 U.S. at 531-32, 92 S.Ct. 2182 (‘We emphasize that failure to assert the right will make it difficult for a defendant to prove that he was denied a speedy trial.”).

Williams concedes that this factor seems to weigh against him, but he suggests that it be given minimal weight because “his attorney never gave any serious thought to the issue.” The fact that Williams and his attorney previously gave no “serious thought” to the pretrial delay sends a strong signal that the severity of any deprivation experienced was minimal, at best. This factor, we conclude, weighs against Williams. Prejudice The final factor in the speedy-trial analysis is whether and how the pretrial delay prejudiced Williams.

When evaluating prejudice, we consider the three purposes served by the speedy-trial right: “(

i) to prevent oppressive pretrial incarceration; (ii) to minimize anxiety and concern of the accused; and (iii) to limit the possibility that the defense will be impaired.” Williams, 753 F.3d at 634 (quoting Barker, 407 U.S. at 532, 92 S.Ct. 2182). “Of these, the most serious is the last, because the inability of a defendant adequately to prepare his case skews the fairness of the entire system.” Id. Williams was not subject to pretrial incarceration, nor was he subjected to inordinate anxiety and concern because the indictment entered against him was sealed for the majority of the delay at issue.

Additionally, Williams does not argue that the delay impaired his defense at all, and he makes no effort to explain how the lengthy delay prejudiced him at trial.

Con-cededly, “impairment of one’s defense is the most difficult form of speedy trial prejudice to prove because time’s erosion of exculpatory evidence and testimony can rarely be shown.” Doggett, 505 U.S. at 655, 112 S.Ct. 2686 (internal quotation marks and citation omitted). “When a defendant is unable to articulate the harm caused by delay, the reason for the delay (factor 2) will be used to determine whether the defendant was presumptively prejudiced,” United States v. Mundt, 29 F.3d 233, 236 (6th Cir. 1994), but, as discussed above, the record does not explain the reason for the delay.

Williams claims that “[h]is level of cooperation with the case agent precludes a finding that he shares any responsibility for the delay between the filing and unsealing of the indictments,” but even if true, it is not enough to explain whether any delay attributable to the government was in bad faith, simply negligent, or innocent. Absent evidence that any of the three purposes served by the speedy-trial requirement were subverted due to this delay, this final factor also weighs against Williams.

Not only has Williams failed to assert his right to a speedy trial, but also the record on appeal does not support his claim of prejudice. As a result, Williams has not shown the plain error necessary to prevail on this issue. CONCLUSION For the reasons set out above, we AFFIRM the district court’s judgment.