LYNCH, Circuit Judge.
This case involves convictions in December 2016 for fraudulent recruitment practices from March 2006 through June 2008 by members of the U.S. Army National Guard in Puerto Rico. Defendant National Guard officers Carlos Meléndez-González and Enrique Costas-Torres carried out a scheme to procure recruitment bonuses to which they were not entitled. They were convicted after a jury trial of wire fraud, embezzlement of public money, and conspiracy. Their appeals from their convictions raise multiple issues, including tolling under the Wartime Suspension of Limitations Act, 18 U.S.C. § 3287 ; rulings by the district court as to dress in the courtroom, meant to protect the jury from prejudicial influence; sufficiency of the evidence of a conspiracy to defraud the United States; and what constitutes impermissible "overview" testimony. Finding no merit in any of defendants' many claims of error, we affirm.
I.
We review the evidence "in the light most favorable to the verdict." United States v. Van Horn, 277 F.3d 48, 50 (1st Cir. 2002) (citing United States v. Escobar-de Jesus, 187 F.3d 148, 157 (1st Cir. 1999) ).
In 2005, the Department of Defense instituted the National Guard Recruiting Assistance Program ("G-RAP") to help recruit soldiers during the ongoing conflicts in Iraq and Afghanistan. G-RAP was intended to supplement the National Guard's traditional reliance on full-time recruiters. It enabled Guard members who are not full-time recruiters to register as "Recruiting Assistants," use their personal networks to identify and nominate potential recruits and refer them to full-time recruiters, and receive bonuses if their nominees ultimately enlist. Docupak, a marketing *13company and contractor, administered G-RAP by hiring and managing Recruiting Assistants and processing bonus payments.
To become a Recruiting Assistant, an applicant completed an online application, verified his eligibility, created an online profile, and completed a mandatory training. Importantly, Recruiting Assistants were prohibited from sharing G-RAP bonuses with full-time recruiters, and this limit was emphasized in the original training module. The rules also specified, as set forth in a revised training module, that Recruiting Assistants were prohibited from receiving information about a nominee from a recruiter without the nominee's consent, and from nominating an individual they did not know.
Only upon successfully completing training (which entailed reviewing the information in the training modules and then passing a quiz) could a Recruiting Assistant begin identifying potential recruits. After making a nomination, the Recruiting Assistant would facilitate a meeting between the nominee and a full-time recruiter. The full-time recruiter would assess the nominee's qualifications, perform aptitude tests, and run a background check. The Recruiting Assistant was expected to provide support and mentorship to the nominee throughout this process. As compensation, the Recruiting Assistant would receive a $1,000 payment if the nominee enlisted and an additional $1,000 payment if the nominee progressed to basic training. Each Recruiting Assistant recorded his or her participation in the online system administered by Docupak: first by creating a profile for each nominee with the nominee's personal identifying information, then by adding entries detailing each nominee's progress.
Carlos Meléndez-González ("Meléndez"), a part-time member of the Army National Guard, became a Recruiting Assistant in 2006. Between 2006 and 2008, Meléndez received $21,000 in recruitment bonuses for twelve new National Guard enlistees recorded as his nominees on his G-RAP account.
After an Army Audit Agency review found "signs of possible fraud" in G-RAP, the Army Criminal Investigations Division ("CID") launched a nationwide investigation.
In an interview with investigators in 2013, Meléndez admitted that he did not know most of his nominees. Nor did he act as a Recruiting Assistant for any of them; the nominees were all recruited by Enrique Costas-Torres ("Costas"), a full-time recruiter who was not eligible for recruitment bonuses. Meléndez knew Costas from a previous posting. The investigation also revealed that Meléndez's G-RAP account contained various false statements, including claims that he had had meetings with nominees that in fact never occurred. Meléndez also informed investigators that he had provided his G-RAP account password to Costas.
The investigators concluded that Meléndez and Costas had carried out a fraudulent scheme to obtain recruitment bonuses: Costas enlisted new recruits and provided Meléndez with their personal identifying information, and Meléndez pretended that the recruits were his own leads in order to collect bonuses and then to split the proceeds with Costas. On October 21, 2015, a grand jury returned an indictment charging Costas and Meléndez with conspiracy to defraud the United States, in violation of 18 U.S.C. § 371 ; conspiracy to commit wire fraud, in violation of 18 U.S.C. § 1349 ; wire fraud, in violation of 18 U.S.C. § 1343 ; and aggravated identity theft, in violation of 18 U.S.C. § 1028A(a)(1). All charges pertained to conduct that occurred between March 2006 *14and June 2008. On April 13, 2016, the grand jury returned a superseding indictment charging the same offenses plus one count of embezzling public money, in violation of 18 U.S.C. §§ 641 - 642, pertaining to the same conduct.
The two were tried jointly. Neither testified. At the close of an eight-day trial by jury, Meléndez was convicted of one count of conspiracy to defraud the United States, one count of embezzling public money, one count of conspiracy to commit wire fraud, and thirteen counts of wire fraud. Costas was convicted of three counts of wire fraud. The district court granted the defendants' motion for acquittal on one count of wire fraud and one count of aggravated identity theft. The jury found the defendants not guilty on the remaining counts.
Costas was sentenced to one year in prison, three years of supervised release, a $5,000 fine, and $3,000 in restitution. Meléndez was sentenced to time served (approximately two months), two years of supervised release, and $20,000 in restitution. The court found that Costas had the "main role" in the scheme because he was "a higher ranking officer and was the one with access to the personal and identifying information for all the recruited ... persons for which payments were processed." The court determined that Costas had not only provided his recruits' personal information to Meléndez but had also himself accessed Meléndez's G-RAP account and directly input information for certain recruits.
Costas appealed his conviction and sentence. Meléndez appealed only his conviction. Their appeals were consolidated.1
II.
We address defendants' challenges to their convictions, then dispose of Costas's challenges to his sentence. Costas's brief repeats virtually verbatim the language in Meléndez's brief and raises claims of his own. We treat the shared arguments together.2
A. Statute of Limitations and Pre-Indictment Delay
Defendants first argue that the district court erred in denying their pretrial motion to dismiss the indictment as untimely. We review this issue de novo. United States v. Ngige, 780 F.3d 497, 502 (1st Cir. 2015).
Defendants were indicted in 2015 for conduct that took place between March 2006 and June 2008. The district court held that the general five-year statute of limitations that applies to the criminal statutes under which defendants were charged, see 18 U.S.C. § 3282(a), was tolled by the *15Wartime Suspension of Limitations Act, 18 U.S.C. § 3287 ("WSLA").
As amended in October 2008,3 the WSLA tolls the statute of limitations for any offense involving, inter alia, fraud against the United States, "[w]hen the United States is at war or Congress has enacted a specific authorization for the use of the Armed Forces ... until 5 years after the termination of hostilities as proclaimed by a Presidential proclamation, with notice to Congress, or by a concurrent resolution of Congress." Id. The district court found that the 2001 Authorization for the Use of Military Force, Pub. L. No. 107-40, 115 Stat. 224 (2001) ("AUMF"), "triggered, and continues to trigger," the WSLA's tolling provisions.
On appeal, defendants renew two arguments that the district court considered and soundly rejected: (1) that the AUMF constitutes an unconstitutional delegation of legislative authority to the President in violation of separation of powers principles, and (2) that the hostilities authorized by the AUMF ended before defendants' alleged crimes occurred. We reject these arguments for substantially the same reasons. Defendants' claim is that the AUMF lacks a "sufficient statutory standard to guide the President." But defendants do not deny that tolling of the WSLA is triggered by the "enact[ment] of a specific authorization for the use of the Armed Forces" and that the AUMF indisputably qualifies as such.
The WSLA provides for tolling until the termination of hostilities is formally announced "by a Presidential proclamation, with notice to Congress, or by a concurrent resolution of Congress." 18 U.S.C. § 3287. No such formal announcement has occurred to date. The WSLA's tolling provisions remain active. See United States v. Frediani, 790 F.3d 1196, 1200-01 (11th Cir. 2015) ; United States v. Pfluger, 685 F.3d 481, 485 (5th Cir. 2012).
Defendants approach the delay issue from another angle, asserting that there was excessive pre-indictment delay. We review the district court's denial of this claim for abuse of discretion. See United States v. Bater, 594 F.3d 51, 53 (1st Cir. 2010).
A due process claim of excessive pre-indictment delay requires showing "both that the 'delay caused substantial prejudice to [the defendant's] right to a fair trial' and that 'the [g]overnment intentionally delayed indictment ... to gain a tactical advantage.' " Id. at 54 (alteration in original) (quoting United States v. Picciandra, 788 F.2d 39, 42 (1st Cir. 1986) ).4 Defendants have established neither. As to the second prong, they have not even argued that the prosecution intentionally delayed indictment to gain a tactical advantage. As to prejudice, they lament that it was impossible for them to retrieve relevant evidence such as the "original rules" for the G-RAP program "between 2005 and 2007" and the "Recruiters Assistants' digital files where they acknowledged, agreed to and/or were quizzed on particular updates on rules of the G-RAP program."
*16Yet the critical 2005 and 2007 G-RAP training modules (including the portions thereof setting the "rules that create criminal intention") and the contents of Meléndez's G-RAP digital account were introduced and discussed extensively at trial. And Meléndez himself admitted that he read the rules and took the training quiz when he enrolled in G-RAP.
B. Court Rulings as to Military Dress in the Courtroom
Costas argues that the district court violated his Sixth Amendment right to a public trial by partially, to use his words, "closing" the courtroom. No such thing happened. We review this claim de novo. United States v. Laureano-Pérez, 797 F.3d 45, 76 (1st Cir. 2015).
On the penultimate day of trial, just before closing arguments, the prosecution brought to the district court's attention that approximately fifteen National Guard members in the courtroom were dressed in formal National Guard Gala uniforms. The court recognized that while Guard members in fatigue uniforms had appeared "sporadically" throughout the trial, this large group in formal garb constituted a conspicuous, "overwhelming presence" in a portion of the courtroom. The judge described the scene: "all you can see are the ribbons, the golden medals on the shoulders, [and] the stripes that are with the gold ribbon as well." The Guard members so dressed confirmed to the court that they had "taken the day off" and were not (and could not be) attending the proceedings in their official capacities. The court found that the group had acted "in concert," that it was "reasonable to infer" that its uniform display was "geared to unduly influence the jury," and that "the presence of all the Gala uniforms in this fashion pose[d] a strong likelihood of influencing the jury."
In an effort to protect the jury from "undue pressure" while preserving defendants' right to a public trial, the court ruled that the Guard members could remain in the courtroom as long as they did not wear full uniforms. The court adjourned the trial until the afternoon to provide them time to change or remove their jackets and ties. The court made clear that it was willing to consider other suggestions as to how to accommodate the service members, but defense counsel offered none.
The National Guard members complied with the order. After the adjournment and closing arguments, the court described for the record that "all 15 members of the National Guard are here in court and have been here in court throughout the entire afternoon with ... half of their uniforms, that is the trousers or pants and ... the white shirt without the jacket."
Costas's public-trial claim plainly fails and is frivolous. The court did not close the courtroom at all. To the contrary, the court stressed that "the Court remains open," adjourned the proceedings to avoid excluding anyone, and ultimately verified that all Guard members had complied with its directive and remained in the courtroom through closing arguments. The court's order was thoughtfully crafted and an eminently reasonable means of maintaining courtroom decorum and protecting the jury from the risk of prejudicial influence.5
*17See United States v. Rios Ruiz, 579 F.2d 670, 674-75 (1st Cir. 1978).
C. Sufficiency of the Evidence
Defendants contend that the evidence presented at trial was insufficient to support their convictions for wire fraud and, in Meléndez's case, conspiracy. The district court rejected these claims when it denied defendants' motions for judgment of acquittal. See Fed. R. Crim. P. 29. So do we.
We review sufficiency of the evidence claims de novo. See United States v. Wyatt, 561 F.3d 49, 54 (1st Cir. 2009). "[W]e examine the evidence-direct and circumstantial-as well as all plausible inferences drawn therefrom, in the light most favorable to the verdict, and determine whether a rational fact finder could conclude beyond a reasonable doubt that the defendant committed the charged crime." Id.
The evidence presented at trial established that Meléndez used the personal identifying information of a dozen new National Guard enlistees to obtain recruitment bonuses; that he did not help recruit his purported nominees and did not know most of them; and that his G-RAP account entries reported fictitious meetings between him and his purported nominees. It was Costas who had recruited these enlistees, and Costas was the one, unlike Meléndez, who had access to their private personal information. Shortly after many of the $1,000 recruitment bonuses were wired to Meléndez's account, Meléndez made $500 cash withdrawals. Finally, Meléndez knew from his training (to the extent it was not self-evident) that he was prohibited from nominating persons he did not know. A jury could readily infer that Meléndez willfully entered into a scheme to defraud the National Guard by feigning eligibility for recruitment bonuses.
As to Costas, the evidence supported the conclusion that he committed wire fraud by giving Meléndez the personal information of enlistees he had recruited, with the intent that Meléndez use it to fraudulently apply for recruitment bonuses. Costas was ineligible for such bonuses, he knew Meléndez, and at least three of Meléndez's nominees had given their information only to Costas. Costas emphasizes that the prosecution did not present any direct evidence that he received kickbacks. Meléndez's frequent $500 cash withdrawals provide circumstantial evidence, though, that he was splitting his bonuses with whomever was providing him with the necessary information. Regardless, the prosecution did not need to prove that Costas actually received any kickbacks. It was sufficient to show that Costas, by giving Meléndez the personal information of enlistees, purposefully caused him to use that information fraudulently to procure unearned bonuses. See United States v. Carrington, 96 F.3d 1, 7 (1st Cir. 1996) (holding that "[t]he crime of wire fraud does not require that the defendant's object be attained" and that the crime is "completed" upon transmission of the requisite "wire communication").
Finally, Meléndez challenges his conspiracy conviction. He argues that he could not possibly be found guilty because Costas, the only co-conspirator named in the superseding indictment, was acquitted of the conspiracy charges. The prosecution suggests in response that the jury could have found that Meléndez entered into a conspiracy with one of the "unknown" co-conspirators described in the superseding indictment. The evidence-that Meléndez did not have access to the private personal information he submitted online and that he repeatedly made cash withdrawals of exactly one half the amount of his recruitment bonuses-was *18sufficient to prove that Meléndez had conspired with someone. "[S]o long as there is 'sufficient evidence to sustain a rational verdict of guilt beyond a reasonable doubt' for a conspiracy charge, 'an inconsistent verdict should stand.' " United States v. Rios-Ortíz, 708 F.3d 310, 317 (1st Cir. 2013) (quoting United States v. Figueroa-Encarnación, 343 F.3d 23, 30 n.4 (1st Cir. 2003) ). Meléndez's conviction stands.
D. Evidentiary Challenges
Defendants raise a variety of evidentiary challenges. We address below only the one sufficiently substantial to warrant discussion. The other arguments are "insufficiently developed, patently meritless, or both." United States v. George, 841 F.3d 55, 61 (1st Cir. 2016).
1. Claim of Improper Overview Testimony from Agent De Jesús
Defendants argue that one of the prosecution's witnesses, CID Agent André de Jesús, provided improper and prejudicial overview testimony. Agent De Jesús conducted the investigation that led to Costas's and Meléndez's indictment. As the prosecution's sixth witness at trial, De Jesús testified regarding the origins of the CID's investigation of the G-RAP program; the procedure his office followed in conducting G-RAP-related investigations; and the steps he took when investigating defendants, including interviewing Meléndez's purported nominees. Costas (but not Meléndez) contemporaneously objected that De Jesús was providing improper overview testimony and "painting a picture of guilt for the defendants" by using words like "fraud" and "investigation." He also objected on hearsay grounds to De Jesús's reporting on statements Meléndez's nominees made to him. The court overruled the objections.
We review Costas's claims for abuse of discretion. United States v. Rodriguez, 525 F.3d 85, 95 (1st Cir. 2008). Because Meléndez did not contemporaneously object, he bears the burden of establishing plain error. Id.; see also United States v. Leon-Delfis, 203 F.3d 103, 113 (1st Cir. 2000) (explaining that this court "typically require[s] defendants in joint criminal trials to raise their own objections at trial" and relaxes this rule "only when the district court specifically states that an objection from one defendant will be considered an objection for all defendants").
The majority of De Jesús's testimony covered his investigation of defendants, of which he had first-hand knowledge. "Where an officer testifies exclusively about his or her role in an investigation and speaks only to information about which he or she has first-hand knowledge, the testimony is generally ... permissible." United States v. Rose, 802 F.3d 114, 121 (1st Cir. 2015). Contrary to Costas's argument, De Jesús never expressed a view as to defendants' guilt. De Jesús used the word "fraud" only when explaining that the CID's nationwide investigation of the G-RAP program began after an Army Audit Agency review found "indications of possible fraud" in the program. De Jesús was merely providing context for his own investigation.
As the prosecution has conceded on appeal, De Jesús did delve into hearsay testimony when he testified about statements Meléndez's purported recruits made to him in interviews. Specifically, De Jesús reported that all of his interviewees denied having received assistance from Meléndez during the enlistment process and that six of them claimed not to know Meléndez. However, we find the admission of this testimony harmless. The interviewees later testified at trial consistent with De Jesús's *19summary. There is no indication in the record that De Jesús attempted to vouch for them. Nor was there any need for such endorsement: none of the interviewees had credibility or bias problems, and they provided only straightforward and unproblematic testimony concerning their interactions (or the lack thereof) with defendants during their recruitment. Defendants suffered no prejudice.
E. Costas's Sentencing
Costas challenges his sentence as procedurally and substantively unreasonable. We find no abuse of discretion. See United States v. Ayala-Vazquez, 751 F.3d 1, 29 (1st Cir. 2014).
On the procedural front, Costas argues that the district court erred in applying a four-level enhancement based on a loss amount of $20,000 under United States Sentencing Guidelines § 2B1.1, and a two-level enhancement for abuse of a position of trust under § 3B1.3. The abuse-of-trust enhancement was plainly appropriate. Costas abused the "professional or managerial discretion" he possessed as a Sergeant Major and full-time recruiter when he misused the personal information of his recruits. See United States v. Sicher, 576 F.3d 64, 72-73 (1st Cir. 2009) (quoting U.S.S.G. § 3B1.3 cmt. n.1).
As to the loss amount, Costas asserts that the court should have considered only the $3,000 in bonus payments resulting from the three wire-fraud counts of which Costas was convicted. Instead, the court took into account all of the bonuses Meléndez obtained, including those tied to wire-fraud counts of which Costas was acquitted. A district court may rely on acquitted conduct in sentencing "so long as that conduct ha[s] been proved by a preponderance of the evidence." United States v. Martí-Lón, 524 F.3d 295, 302 (1st Cir. 2008). Here, the evidence showed that Meléndez collected at least $20,000 in bonuses for nominating twelve recruits who were all in fact recruited by Costas; that those recruits provided their personal information only to Costas; and that that information was nevertheless somehow input into Meléndez's G-RAP account. Additional evidence not admitted at trial (but properly considered at sentencing) showed that Meléndez provided his password to Costas and that Costas himself had directly input information into Meléndez's account. The district court had a sufficient basis to deem Costas responsible, by a preponderance of the evidence, for all of Meléndez's fraudulently procured bonuses.
Next, Costas asserts that his sentence was substantively unreasonable because Meléndez, who was convicted on many more counts, received a lesser sentence. Costas "is not entitled to a lighter sentence merely because ... his co-defendant[ ] received [a] lighter sentence[ ]." United States v. Torres-Landrúa, 783 F.3d 58, 69 (1st Cir. 2015) (quoting United States v. Dávila-González, 595 F.3d 42, 50 (1st Cir. 2010) ). And we have no reason to second-guess the district court's conclusion that Costas had the "main role" in the scheme because he was "a higher ranking officer and the one with access to the personal and identifying information for all of the recruited ... persons for which the payments were processed." See Ayala-Vazquez, 751 F.3d at 33-34 ("Determinations as to the relative culpability amongst codefendants are best made by the district judge....").
For the first time on appeal, Costas attempts to challenge as unfounded the district court's statement during sentencing that Costas "tried to manipulate the jury by basically causing ... other members ... of the military force to come here *20dressed up in their Gala uniforms...." The argument is waived.
III.
We affirm each of defendants' convictions.