SOUTER, Associate Justice.

Sharon Bowles appeals her conviction after jury trial on five counts of theft of government funds, in violation of 18 U.S.C. § 641. We affirm.

I

Bowles was found guilty of fraudulently collecting a total of $77,379 in federal civil service retirement survivor annuity payments made in 2005 through 2009 and intended for her mother, Ann Bowles. As the surviving spouse of a civil service employee, Ann Bowles had been entitled to a monthly annuity that should have stopped after she died in 2004. After getting notice of her death from the Social Security Administration in January 2005, the United States Office of Personnel Management (OPM) sent a verification form to Ann Bowles's old mailing address, which had been and remained Sharon Bowles's as well. The form was returned to OPM signed "Ann M. Bowles," with a notation falsely indicating that Ann Bowles was still alive and eligible for the monthly payments. Twice again, in August 2005 and September 2009, the same sequence ensued: OPM sent an address verification form to Sharon Bowles's address, and the form was returned with the false notation that Ann Bowles was a living annuitant. Based on this misinformation, OPM continued to send monthly checks to Ann Bowles, each of which was negotiated with the purported signature endorsement of "Ann M. Bowles" on the back. Some of the checks also bore the spurious signature of Sharon Bowles's deceased father, some included the signature of Sharon Bowles, and some included all three. In September 2007, Sharon Bowles gave Citizens Bank a signed form (including the supposed signature of "Ann M. Bowles") with the effect of adding her mother's name as that of a joint owner on her personal bank account. Thereafter, the monthly annuity payments were deposited into this account, at first by paper check and then by electronic transfer.

The jury convicted Bowles on all counts. The district court sentenced her to time served plus 30 days of incarceration and ordered her to pay $77,379 in restitution. Bowles raises four claims of error.

II

She first contends that the district court erred in disallowing her peremptory challenge to a member of the venire and in seating the challenged individual on the jury. We review the district court's finding that counsel's challenge was motivated by the prospective juror's race, in violation of Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), for "clear error." United States v. Bergodere, 40 F.3d 512, 516 (1st Cir.1994).

At voir dire, Bowles's counsel raised a peremptory challenge to strike "Juror Number 5, Ms. Tran." The following exchange ensued:

App. 240-241.

Prior to this colloquy, there was nothing in the record apart from the strike to indicate that defense counsel's peremptory strike was motivated by race. This suggests that the district court's sua sponte initiation of a Batson enquiry into counsel's motivations was in error, "reflect[ing] a good faith, if arguably overzealous, effort to enforce the antidiscrimination requirements of [the Supreme Court's] Batson-related precedents," Rivera v. Illinois, 556 U.S. 148, 160, 129 S.Ct. 1446, 173 L.Ed.2d 320 (2009); see also Johnson v. California, 545 U.S. 162, 168, 125 S.Ct. 2410, 162 L.Ed.2d 129 (2005) (prima facie case that a party is exercising its peremptory challenges in a discriminatory manner is established "by showing that the totality of the relevant facts gives rise to an inference of discriminatory purpose.").1

That said, counsel's responses to the court do raise the scent of possible pretext. While both of defense counsel's proffered reasons for seeking to exclude Ms. Tran were race-neutral, his shifting rationale for the strike could support an inference that neither reason was genuine. See Purkett v. Elem, 514 U.S. 765, 769, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995) (focus of court's enquiry in evaluating a proffered reason for a strike is on the "genuineness of the motive" asserted by counsel). Even aside from that, counsel's second reason implicates our recognition that "facially plausible" reasons for exercising a peremptory strike may "raise a serious question of pretext where [counsel's] explanation ... is equally applicable to a juror of a different race or gender who has not been stricken." Caldwell v. Maloney, 159 F.3d 639, 651 (1st Cir.1998). Here, the district court's comments indicate that counsel's second rationale for striking Ms. Tran, her age, applied quite as well to a juror whom counsel did not challenge.

We can, however, bypass the question whether the district court acted within its discretion, because any error was harmless. See Rivera, 556 U.S. at 160, 129 S.Ct. 1446 (affirming application of harmlessness standard of review to trial court's error in denying a defendant his right to a peremptory strike under state law). Although our own pre-Rivera precedent held that the mistaken refusal to accept a defendant's exercise of peremptory challenges was structural error requiring automatic reversal of a conviction, see United States v. Vargas, 606 F.2d 341, 346 (1st Cir.1979), we have since recognized that "the Supreme Court [in Rivera] ... disavowed the sort of reasoning used in Vargas and ... indicated that mistaken denials of peremptory challenges do not ordinarily warrant automatic reversal."2 United States v. Gonzalez-Melendez, 594 F.3d 28, 33 (1st Cir.2010) (applying harmlessness review to district court's erroneous failure to designate which jurors are alternates before allowing the parties an additional peremptory challenge pursuant to Fed.R.Crim.P. 24(c)(4)). Every one of our sister circuits to have considered the question has similarly held that, under Rivera, error in sustaining a Batson challenge is subject to harmless error analysis. See Jimenez v. City of Chicago, 732 F.3d 710, 715 (7th Cir.2013) (civil); United States v. Williams, 731 F.3d 1222 (11th Cir.2013) (criminal); Alaska Rent-A-Car, Inc. v. Avis Budget Group, Inc., 709 F.3d 872, 880 (9th Cir.2013) (civil); Avichail v. St. John's Mercy Health System, 686 F.3d 548, 552-53 (8th Cir.2012) (civil).

As Bowles's counsel conceded at oral argument, nothing in the record indicates that Ms. Tran was biased or otherwise unqualified to serve on the jury. Accordingly, any error by the district court in seating her was harmless, as it did not "affec[t] the defendant's substantial rights." United States v. Maryea, 704 F.3d 55, 74 (1st Cir.2013); see also Rivera, 556 U.S. at 158-59, 129 S.Ct. 1446 (right to impartial jury satisfied where no member of the jury was removable for cause).

III

Next, Bowles says the district court violated the rule against hearsay by admitting into evidence photocopies of the annuity checks that were deposited into her bank account. "We review a district court's decision to admit or to exclude evidence for abuse of discretion." See United States v. Scott, 270 F.3d 30, 46 (1st Cir.2001).

Bowles does not object to the admission of the checks themselves,3 but rather contends that the signature endorsements on the backs of the checks were the inadmissible hearsay. The objection fails for two reasons. First, the large majority of the endorsements in question purport to represent the signatures of Bowles's deceased parents. See App. 68-179. These endorsements were all written after Bowles's parents had died, are indisputably false, and therefore cannot have been offered to prove the truth of what they implicitly state. See Fed.R.Evid. 801 (defining "hearsay" as a "statement ... offer[ed] in evidence to prove the truth of the matter asserted"); United States v. Vigneau, 187 F.3d 70, 74 (1st Cir.1999) ("Whoever wrote the name `Patrick Vigneau' on the [money order forms] was stating in substance: `I am Patrick Vigneau....'").

Second, the endorsements were offered as one step in proving fraudulent action (i.e., check issued to predeceased person, endorsement by someone pretending to be that person, evidence indicating defendant wrote endorsement and received money). Each signature endorsement was thus a legally operative verbal act of imposture for a fraudulent purpose, see Fed. R.Evid. 801(c), advisory committee's note (the hearsay definition excludes "the entire category of `verbal acts' ... in which the statement itself affects the legal rights of the parties...."), an integral step in what the law has traditionally called the actus reus of the repeated theft offense charged. See United States v. Pang, 362 F.3d 1187, 1192 (9th Cir.2004). In this respect, the endorsements are comparable to words offering a bribe or making a threat, which we have recognized as verbal acts that are not hearsay. United States v. Diaz, 597 F.3d 56, 65 n. 9 (1st Cir.2010).

Accordingly, the only remaining hurdle to admitting the endorsements into evidence is the burden on the government, as proponent, to authenticate each endorsement as the defendant's act, that is, to establish a reasonable likelihood that the proffered "item is what the proponent claims it is." Fed.R.Evid. 901(a); see United States v. Savarese, 686 F.3d 1, 11 (1st Cir.2012). Here, it is undisputed that the checks had been mailed to Bowles's home address after her mother's death and then deposited in Bowles's personal bank account. This circumstantial evidence is more than sufficient to establish a reasonable likelihood that the endorsements on the checks were written by Bowles. See United States v. Gonzalez-Maldonado, 115 F.3d 9, 20 (1st Cir.1997) ("[C]ircumstantial evidence is permitted to authenticate [an] item.").

On top of that, there were two documents admitted without objection that included examples of Bowles's handwriting and signature. See App. 56-57. It therefore would have been within the district court's discretion to admit the endorsements based on the evidence of authenticity apparent from those comparable examples of Bowles's signature already in the record. See Fed.R.Evid. 901(b)(4) (Evidence may be authenticated by its "appearance, contents, substance, internal patterns, or other distinctive characteristics, taken in conjunction with circumstances.").

IV

Bowles's third argument is that the district court abused its discretion by admitting into evidence a copy of a Massachusetts Registry of Motor Vehicles record of information about her driver's license. The Registry record, which contains the apparent signature of Sharon Bowles as well as her personal information, was admitted to give the jury an additional example for comparing Bowles's handwriting with the signature endorsements on the checks. See 28 U.S.C. § 1731 ("The admitted or proved handwriting of any person shall be admissible, for purposes of comparison, to determine genuineness of other handwriting attributed to such person."). Bowles conceded the Registry record's authenticity at trial, see App. 215, but says it should not have been admitted into evidence without "some element of proof that the signature [on the Registry record] was [hers]." Appellant's Br. 29.4

The argument lacks merit. First, Bowles herself admits that the "proof" she seeks could have consisted of "evidence... establish[ing] that it might be the custom or requirement of the Registry" to compel persons acquiring driver's licenses "to sign the license." Id. But no such evidence was needed because Massachusetts law provides that "[e]very person licensed to operate motor vehicles ... shall endorse [her] name in full in a legible manner on the margin of the license, in the space provided for the purpose, immediately upon receipt of such license...." Mass. Gen. Laws Ann. ch. 90 § 8. This suffices to establish a reasonable likelihood that the signature on Bowles's license is what it purports to be. Second, and more broadly, the Registry record is a prototypical public record that is self-authenticating under the Federal Rules. The mandate for a licensee's immediate signature on receipt makes it reasonable to infer that the photo of the signature is as much a part of the "record" as any notation of fact contained within it. See Fed.R.Evid. 902(4) ("A copy of an official record" is self-authenticating "if the copy is certified as correct by ... the custodian or another person authorized to make the certification."). Here, the Registry record is on its face "a true copy of the records" held by the Registry, and was certified as such by the then-Registrar of Motor Vehicles. App. 35-36. Third, for the same reason discussed above with respect to the signature endorsements on the checks, the district court would have been within its discretion to find the signature on the Registry record authentic based on a comparison with the examples of Bowles's signature that were already in the record. See Fed.R.Evid. 901(b)(4).

V

Finally, Bowles contends that it was error for the district court to deny her post-trial motion for a judgment of acquittal. But her argument is that, excluding what she terms the erroneously admitted checks and the Registry record, there was insufficient evidence from which the jury could find that she committed the charged offenses. Since that evidence was properly admitted, that is the end of the issue, though we note that the evidence of Bowles's guilt was overwhelming: OPM forms were three times sent to Bowles's address, and three times returned with fraudulent notations indicating that Ann Bowles was alive and eligible to receive annuity payments; all of these payments were deposited into Bowles's personal bank account; and the several examples of Bowles's handwriting and signature were an ample basis for the jury to find that she had written the fraudulent signature endorsements on the annuity checks. There was no error in concluding that a reasonable jury could find Bowles guilty of stealing government funds.

VI

The judgment of the district court is affirmed.

It is so ordered.