This appeal presents a montage of issues arising at a crossroads where traditional criminal law principles intersect with the marvels of modern technology. The appeal follows on the heels of a jury verdict finding defendant-appellant David Chiaradio guilty of possessing and distributing child pornography. The defendant challenges divers aspects of the indictment, trial, verdict, and sentence. After careful consideration of the well-marshaled arguments on both sides, we affirm in part and remand for further proceedings.
I. BACKGROUND
At trial, the government’s case relied in large part on testimony from agents of the *271Federal Bureau of Investigation (FBI). One agent, Joseph Cecchini, testified that on February 28, 2006, he went online in an undercover capacity to search for child pornography. Agent Cecchini’s investigation involved software known as Lime-Wire — a commercially available peer-to-peer file-sharing program that enables users to transmit files to and from other members of the LimeWire network. Users can search for files made available by other users, browse all the files made available by a particular user, and download desired files. They also may make their own files accessible for download by designating a folder on their computers that will automatically share its contents with the network.
Agent Cecchini employed a special version of LimeWire developed by the FBI, known as “enhanced peer-to-peer software” (EP2P), which was customized to assist child pornography investigations. It differs from the commercially available LimeWire program in three principal respects.
First, when a user of the commercially available version of LimeWire tries to download a file, the program seeks out all the users who are sharing the same file and downloads different pieces of that file from multiple locations in order to optimize download speed. EP2P eliminates that functionality; it allows downloading from only one source at a time, thus ensuring that the entire file is available on that source’s computer. Second, in its commercially available iteration, LimeWire responds to a search term by displaying basic information such as the names of the available files, file types, and the file sharers’ Internet Protocol (IP) addresses. EP2P displays not only that data but also the identity of the Internet Service Provider (ISP) and the city and state associated with the IP address sharing a particular file. Third, EP2P has been modified so that an agent can easily compare the hash value (essentially, the digital fingerprint) of an available file with the hash values of confirmed videos and images of child pornography. Taken together, these three modifications permit agents to download a file from a single source, learn the general location of the source, and facilitate the identification of child pornography as such.
Agent Cecchini testified that on February 28, 2006, he used EP2P to search for “pedo collection,” a term that he knew to be fancied by collectors of child pornography. His search turned up a number of files, including one being shared from an IP address in Rhode Island. He then used LimeWire’s browse function to peruse the other files being shared from that IP address and found 643 files with titles suggestive of child pornography. The agent downloaded three such files and confirmed that they contained graphic depictions of young girls.
After serving a subpoena on the ISP, Agent Cecchini traced the IP address to a residence in Westerly, Rhode Island, owned by the defendant’s father. With this information in hand, another agent, Andrew Yesnowski, obtained a search warrant.
On August 22, 2006, a search party that included Agent Yesnowski and Agent Michael Kohn executed the warrant at the Westerly dwelling. The agents seized a laptop computer from the defendant’s bedroom and a desktop computer from a spare bedroom. The defendant took responsibility for both computers and agreed to speak with agents about his computer usage. He explained that the house had a shared wireless network connecting both computers to the Internet, as well as its own internal file-sharing system enabling a user of one computer to access data and files on the other computer. In response *272to agents’ questions, the defendant admitted to installing and using LimeWire on the laptop to download music but denied that he had ever searched for, or downloaded, child pornography.
Forensic analysis revealed over 5,000 images and videos of child pornography on the desktop and nearly 2,000 on the laptop. There was some overlap between these inventories of child pornography, but the record remains tenebrous as to the details.
On May 20, 2009, a federal grand jury handed up an indictment charging the defendant with two counts of possessing child pornography, 18 U.S.C. § 2252(a)(4)(B), and one count of distributing it, id. § 2252(a)(2). After considerable pretrial skirmishing and three days of trial, a jury found the defendant guilty across the board. The district court denied the defendant’s post-trial motions for judgment of acquittal and for a new trial. Sentencing followed.
With respect to the distribution count, the district court used a base offense level of 22, see USSG § 2G2.2(a)(2), and then added 15 levels premised on various specific adjustments. Through grouping, this total offense level (37) applied to all of the counts of conviction. See id. §§ 3D1.1, 3D1.2(c), 3D1.3(a). Paired with the defendant’s criminal history category (I), this total offense level yielded a guideline sentencing range of 210-262 months.
Varying downward, the district court imposed concurrent 97-month incarcerative terms on each count of conviction. The court also imposed a life term of supervised release and a $100 special assessment on each count, see 18 U.S.C. § 3013(a)(2)(A). The court did not impose a fine, but it ordered the defendant to pay $10,000 to each of two victims who requested restitution. See id. § 2259. This timely appeal followed.
II. ANALYSIS
We address the defendant’s claims of error sequentially.
A. Multiplicity.
As an initial matter, the defendant challenges the government’s decision to charge him with two counts of possessing child pornography under 18 U.S.C. § 2252(a)(4)(B). These counts, he maintains, are multiplicitous; and because he has been convicted and sentenced on each count, he has been twice punished for a single crime. See U.S. Const, amend. V; Illinois v. Vitale, 447 U.S. 410, 415, 100 S.Ct. 2260, 65 L.Ed.2d 228 (1980).
The prohibition against multiplicitous prosecutions derives from “the Double Jeopardy Clause, which ‘protects against multiple punishments for the same offense.’ ” United States v. Pires, 642 F.3d 1, 15 (1st Cir.2011) (quoting Vitale, 447 U.S. at 415, 100 S.Ct. 2260). A prosecution is multiplicitous when the government charges a defendant twice for what is essentially a single crime; for example, when a felon has violated 18 U.S.C. § 922(g) by possessing a firearm, it would be multiplicitous to charge the felon with two counts simply because he had it yesterday and today. See United States v. Destefano, No. 98-2054, 1999 WL 1319192, at *1 (1st Cir. Nov. 22, 1999) (per curiam). Determining whether an indictment is multiplicitous requires an inquiring court to examine whether a particular course of illegal conduct constitutes one or multiple offenses. See Pires, 642 F.3d at 15. Congress’s intent is paramount on this point: the legislature may castigate a particular act by exposing the actor to several prosecutions and punishments, or it may specify that the act should only be subject to a single unit of prosecution. See id.; see also United States v. LeMoure, 474 F.3d *27337, 43 (1st Cir.2007) (observing that “[m]ultiple punishments for the same offense ... are permissible if the legislature so intended”).
In the case at hand, the statute of conviction prohibits “knowingly possessing] ... one or more books, magazines, periodicals, films, video tapes, or other matter which contain any visual depiction” that has traveled in, or was produced by materials which traveled in, interstate commerce if “(i) the producing of such visual depiction involves the use of a minor engaging in sexually explicit conduct; and (ii) such visual depiction is of such conduct.”1 18 U.S.C. § 2252(a)(4)(B). Here, the government seized a plethora of forbidden files during a single search of a single dwelling, yet charged the defendant with two counts of unlawful possession. The government defends its use of dual counts of possession on the ground that the proper unit of prosecution is each matter or physical medium on which images are stored. As the government would have it, the defendant’s utilization of two computers (the laptop and the desktop) exposed him to prosecution for two separate crimes. This is especially fitting, the government suggests, because the computers were located in different rooms and had different functions: the laptop was used for acquiring the pornographic images, whereas the desktop was used for storing them.
The defendant counters that section 2252(a)(4)(B), fairly read, criminalizes the possession of “one or more” computers containing offending images. It follows, the defendant says, that the government may charge only a single crime regardless of whether a defendant possesses two or 2,000 images on one or 100 computers, at least when that possession is simultaneous and under one roof. In other words, the number of “matters” (here, the number of computers) does not in itself define the proper unit of prosecution. Dividing the crime of possession into two separate crimes was especially egregious in this case, the defendant suggests, because the two computers were linked (that is, they shared an internal network through which files could freely move back and forth) and their contents overlapped (albeit to an unspecified degree).
The defendant properly preserved this issue for review, raising it by both a motion to dismiss and. a motion for judgment of acquittal. Consequently, his claim of multiplicity engenders de novo review. See United States v. Gerhard, 615 F.3d 7, 18 (1st Cir.2010). Our task is straightforward; when, as in this case, “a claim of multiplicity is premised on an indictment alleging several violations of a single statutory provision, an inquiring court must determine whether there is a sufficient factual basis to treat each count as separate.” United States v. Stefanidakis, 678 F.3d 96, 100-01 (1st Cir.2012). In making this judgment, we look to the statute of conviction to ascertain “whether Congress intended to punish each statutory violation separately.” Pires, 642 F.3d at 15 (quoting Jeffers v. United States, 432 U.S. 137, 155, 97 S.Ct. 2207, 53 L.Ed.2d 168 (1977)) (internal quotation marks omitted). The key question in this case, then, is what the legislature intended the proper unit of prosecution to be when it criminalized the possession of “one or more” matters containing illicit depictions.
When Congress added what is now section 2252(a)(4)(B) to the statute criminalizing the transportation, receipt, and distribution of child pornography, it outlawed *274the possession of “three or more books, magazines, periodicals, films, video tapes, or other matter which contain any visual depiction” of minors engaging in sexually explicit conduct. Child Protection Restoration and Penalties Enhancement Act of 1990, Pub.L. No. 101-647, § 323, 104 Stat. 4789, 4818 (current version at 18 U.S.C. § 2252(a)(4)(B)). No other section of the statute contained such a numerical limitation. From their inception, the transportation-related offenses described in section 2252(a)(1), the receipt and distribution offenses described in section 2252(a)(2), and the sale-related offenses described in section 2252(a)(3) all criminalized offending acts with respect to “any” sexually explicit depiction of a minor. See id. (current version at 18 U.S.C. § 2252(a)(3)); Protection of Children Against Sexual Exploitation Act of 1977, Pub.L. No. 95-225, § 2, 92 Stat. 7, 7-8 (current version at 18 U.S.C. § 2252(a)(1) — (2)).
In 1998, Congress changed the numerical element of section 2252(a)(4)(B) to make unlawful the possession of “one or more books, magazines, periodicals, films, video tapes, or other matter which contain any visual depiction.” See 18 U.S.C. § 2252(a)(4)(B) (emphasis supplied); Protection of Children from Sexual Predators Act of 1998, Pub.L. No. 105-314, § 203, 112 Stat. 2974, 2978. The very title of the amending legislation — “ ‘Zero Tolerance’ for Possession of Child Pornography”— makes manifest a legislative intent to punish the possession of even a single illicit image. But the legislative history contains no indication that Congress intended to permit multiple prosecutions when it used the term “one or more” in section 2252(a)(4)(B), nor is there any inkling that Congress intended to allow- prosecutors to divide simultaneous possession by a single individual of several matters containing child pornography into multiple units of prosecution, see Bell v. United States, 349 U.S. 81, 83, 75 S.Ct. 620, 99 L.Ed. 905 (1955) (observing that “[w]hen Congress has the will ... of defining what it desires to make the unit of prosecution,” it has no difficulty expressing it). We think that this is significant because, as we explain below, courts previously had treated such violations of section 2252(a)(4)(B) as comprising a single offense.
Before the 1998 amendment, the Fifth Circuit considered whether an indictment could charge a defendant who possessed numerous forbidden images with multiple offenses under section 2252(a)(4)(B). The court concluded that “the plain language of the statute’s requirement that a defendant possess ‘three or more’ items indicates that the legislature did not intend for this statute to be used to charge multiple offenses” in such a situation. United States v. Kimbrough, 69 F.3d 723, 730 (5th Cir.1995). We do not see why changing the number from “three” to “one” undermines this trenchant assessment in any way.2 Accordingly, we hold that the plain language of section 2252(a)(4)(B) memorializes Congress’s intent, at least in circumstances similar to the circumstances of this case, that one who simultaneously possesses a multitude of forbidden images at a single time and in a single place will have committed only a single offense. In this instance, the defendant may have possessed two “matters” (i.e., two computers) *275that collectively contained thousands of images, but his simultaneous possession of “one or more” matters transgressed the statute only once.
In so holding, we do not write on a pristine page. The Second Circuit answered a similar question in United States v. Polouizzi 564 F.3d 142, 153-57 (2d Cir.2009). The court found that the defendant had been impermissibly charged with eleven counts of possession when he possessed eleven files on three hard drives in two separate rooms. Id. at 155 n. 5. It examined section 2252(a)(4)(B) and relevant case law and concluded, as do we, that “Congress intended to subject a person who simultaneously possesses multiple books, magazines, periodicals, films, video tapes, or other matter containing a visual depiction of child pornography to only one conviction.” Id. at 155.
The government labors to distinguish Polouizzi on the ground that, unlike in that case, see id. at 155 n. 5, it has consistently argued the significance of dual computers in separate rooms. We find this supposed distinction unconvincing. The computers, while in separate rooms, were in the same house and were programmed so that files could move freely between them. If a defendant had multiple photo albums of images in his bedroom and living room and periodically swapped images between them, two convictions — one for each album — would not stand. This case, it seems to us, is the electronic equivalent of that situation.
The government’s reliance on case law approving the charging of multiple possession counts under section 2252A(a)(5)(B), see, e.g., United States v. Hinkeldey, 626 F.3d 1010, 1014 (8th Cir.2010); United States v. Planck, 493 F.3d 501, 503-05 (5th Cir.2007), is equally misplaced. Section 2252A, enacted after section 2252, criminalizes trafficking in and possessing all “child pornography,” a term broad enough to include otherwise unobjectionable images of children that have been manipulated to appear pornographic. See 18 U.S.C. §§ 2252A(a), 2256(8); Child Pornography Prevention Act of 1996 § 1(13), Pub.L. No. 104-208, § 121, 110 Stat. 3009, 3009-027. With respect to possession offenses, section 2252A(a)(5)(B) prohibits knowingly possessing “any book, magazine, periodical, film, videotape, computer disk, or any other material that contains an image of child pornography.” 18 U.S.C. § 2252A(a)(5)(B) (emphasis supplied). The use of the word “any” contrasts sharply with section 2252(a)(4)(B), which criminalizes possessing “one or more ” matters containing any image. Id. § 2252(a)(4)(B) (emphasis supplied). ■
The possession provisions of section 2252A and section 2252 are, thus, materially different. This difference — between “any” and “one or more” — is of decretory significance. The phrase “one or more,” unlike the word “any,” strongly suggests Congress’s intent that multiple matters be included in a single unit of prosecution.3 See Hinkeldey, 626 F.3d at 1014; see also Kimbrough, 69 F.3d at 730 & n. 6 (explaining that the difference between “any” and “three or more” is what “distinguishes the *276offense of possession of child pornography from the offenses of transporting and receiving child pornography for purposes of the multiplicity argument”). For aught that appears, the government could have charged the defendant with multiple counts of possession under section 2252A(a)(5)(B). But it did not do so, and we cannot permit the government to emphasize the superficial affinities between these two laws and gloss over their differences in order to salvage an improvident charging decision.
The government also cites case law dealing with drug and gun possession offenses in support of its argument that section 2252(a)(4)(B) contemplates multiple units of prosecution in this type of child pornography case. None of the statutes underpinning those prosecutions uses the term “one or more.” See, e.g., 18 U.S.C. § 922(g) (“It shall be unlawful for any person [under certain enumerated circumstances] to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition____” (emphasis supplied)); 21 U.S.C. § 841(a)(1) (making it unlawful to possess “a controlled substance” (emphasis supplied)). For this reason, the cases cited shed no light on the appropriate unit of prosecution under section 2252(a)(4)(B).
The short of it is that, on the facts of this case, the defendant’s unlawful possession of a multitude of files on two interlinked computers located in separate rooms within the same dwelling gave rise to only a single count of unlawful possession under section 2252(a)(4)(B). Yet, the government charged the defendant with multiple counts of possession. His simultaneous convictions and sentences on those counts violated his constitutional right to be free from double jeopardy. See United States v. Rivera-Martinez, 931 F.2d 148, 153 (1st Cir.1991). While other cases, on different facts, might appropriately give rise to multiple possession charges under section 2252(a)(4)(B), the facts of this case do not support such an outcome.
B. Discovery.
We turn next to the defendant’s contention that the district court should have granted his pretrial motion to compel production of the source code of the EP2P program (essentially, the human-readable version of the instructions used by a computer running EP2P). In the district court, the defendant claimed that he was entitled to the source code on several grounds. The court denied the motion. The only point that warrants discussion involves Federal Rule of Criminal Procedure 16(a)(1)(E), which requires the government to permit the defendant to examine and copy documents, data, and objects in its control if the items are material to preparing the defense or if the government plans to use them in its case in chief.4
We review district court determinations under Rule 16 for abuse of discretion. United States v. Correa-Alicea, 585 F.3d 484, 493 (1st Cir.2009). Reversible error may not be found unless the objecting party can show prejudice. See United States v. Spinosa, 982 F.2d 620, 631 (1st Cir.1992).
The FBI developed EP2P as an investigatory tool. Its source code is closely held; it is not shared with or accessible to the agents who use the program, *277let alone the public. The defendant argues that he had to obtain the source code in order to determine whether he could credibly challenge the reliability of the technology and, thus, block the expert testimony proffered by the government on the EP2P program and how it implicated the defendant. See Fed.R.Evid. 702; see also Daubert v. Merrell Dow Pharm., Inc., 509 U.S. 579, 597, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993) (calling on courts to ensure that an expert’s testimony “rests on a reliable foundation and is relevant to the task at hand”). In his view, his inability to examine the source code prevented him from mounting such a challenge.5
Faced with the defendant’s motion to compel, the district court convened an evidentiary hearing. The court heard testimony from Agent P. Michael Gordon, the government’s proposed EP2P expert. Agent Gordon had been involved in the testing of the program, had instructed other agents about its use, and had participated in over eighty investigations in which EP2P was employed. He demonstrated, among other things, how to check the results of an EP2P investigation manually to ensure that the files transferred had in fact come from the location identified through EP2P. He vouchsafed that, in his wide experience, no EP2P investigation had ever yielded a false positive. The district court denied the motion to compel and concluded that Agent Gordon’s testimony passed Daubert muster.
We need not linger long over the denial of the motion to compel. Even if the source code were discoverable under Rule 16 — a matter on which we take no view— the defendant cannot demonstrate prejudice from its nondisclosure. The government gave the defendant a digital file recording the transfer from the defendant’s laptop to Agent Cecchini’s computer. It also gave the defendant a copy of the FBI guide detailing how to reconstruct an EP2P session manually (using only the recording and publicly available programs). The government presented testimony indicating that its agents had used these materials to reconstruct the transfer and had verified that the files downloaded by Agent Cecchini came from the defendant’s computer. The defendant neither contradicted nor cast the slightest doubt upon this testimony. This evidence makes it pellucid that the forbidden files were located on the defendant’s computers and transferred to Agent Cecchini. Consequently, any error in the application of the EP2P program was harmless.
Relatedly, the defendant — who does not challenge Agent Gordon’s qualifications as an EP2P expert — nevertheless contends that it was error for the court to allow his expert testimony. In this regard, the defendant asserts that the EP2P technology was too untested to form an adequate foundation for the agent’s attestations. In making its Daubert determination, the district court acknowledged that the technology had not been independently tested. Relying on a compendium of other facts, however, it found sufficient evidence of EP2P’s reliability to permit Agent Gordon’s testimony. We review this ruling for abuse of discretion. See Ruiz-Troche v. Pepsi Cola of P.R. Bottling Co., 161 F.3d 77, 83 (1st Cir.1998).
Evidence Rule 702 provides that if “scientific, technical, or other specialized *278knowledge will help the trier of fact to understand the evidence or to determine a fact in issue,” “[a] witness who is qualified as an expert by knowledge, skill, experience, training, or education may testify [thereto] in the form of an opinion or otherwise” so long as certain requirements are met. Fed.R.Evid. 702. In evaluating whether proposed expert testimony satisfies those requirements, the district court must look to “a number of factors, including but not limited to the verifiability of the expert’s theory or technique, the error rate inherent therein, whether the theory or technique has been published and/or subjected to peer review, and its level of acceptance within the scientific community.” Samaan v. St. Joseph Hosp., 670 F.3d 21, 31-32 (1st Cir.2012) (internal quotation marks omitted).
The defendant concedes that the evidentiary hearing held on his motion to compel was the functional equivalent of a Daubert hearing. Although Agent Gordon was not a programmer, did not know the program’s authors, and had never seen the source code, he had significant specialized experience with both EP2P and the manual re-creation of EP2P sessions. He testified that the program, with respect to identifying the source of particular files, had no error rate. He also demonstrated how the results of an EP2P investigation could be independently verified and made it clear that EP2P had never yielded a false positive. These showings sufficiently evinced the reliability of EP2P. Consequently, permitting Agent Gordon to testify at trial about the program was well within the district court’s discretion.
In an effort to blunt the force of this reasoning, the defendant laments that EP2P has not been subjected to peer review in the scientific community. This is true as far as it goes — but it does not take the defendant very far. The Daubert factors are not a “ ‘definitive checklist or test,’ but form the basis for a flexible inquiry into the overall reliability of a proffered expert’s methodology.” Ruiz-Troche, 161 F.3d at 81 (quoting Daubert, 509 U.S. at 593, 113 S.Ct. 2786). Here, moreover, there is a credible explanation for the absence of peer review. The record shows that the source code is purposely kept secret because the government reasonably fears that traders of child pornography (a notoriously computer-literate group) otherwise would be able to use the source code to develop ways either to evade apprehension or to mislead the authorities. This circumstance satisfactorily explains the absence of any peer review. Cf. Puerto Rico v. United States, 490 F.3d 50, 64 (1st Cir.2007) (recognizing “a qualified privilege for law enforcement techniques and procedures”); United States v. Cintolo, 818 F.2d 980, 1002 (1st Cir.1987) (discussing qualified privilege for confidential government surveillance information where “discoverability of this kind of information will enable criminals to frustrate future government surveillance and perhaps unduly jeopardize the security of ongoing investigations”).
C. Suppression.
Following the denial of his motion to compel, the defendant moved to suppress the fruits of the FBI’s search, alleging that the affidavit in support of the warrant was inadequate. The district court denied this motion.
The defendant’s arguments in support of his motion to suppress bear a strong family resemblance to his arguments in support of his motion to compel. He posits that EP2P is largely untested and insists that the affidavit filed in support of the search warrant did not sufficiently demonstrate its reliability.
The Fourth Amendment provides that “no Warrants shall issue, but *279upon probable cause, supported by Oath or affirmation.” U.S. Const, amend. IV. Probable cause exists when “the affidavit upon which a warrant is founded demonstrates in some trustworthy fashion the likelihood that an offense has been committed and that there is sound reason to believe that a particular search will turn up evidence of it.” United States v. Aguirre, 839 F.2d 854, 857-58 (1st Cir.1988). The issuing magistrate must examine the totality of the circumstances to determine the existence of probable cause. United States v. Schaefer, 87 F.3d 562, 565 (1st Cir.1996). This prescription binds reviewing courts, but the issuing magistrate’s determination “should be paid great deference.” Illinois v. Gates, 462 U.S. 213, 236, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983) (quoting Spinelli v. United States, 393 U.S. 410, 419, 89 S.Ct. 584, 21 L.Ed.2d 637 (1969)) (internal quotation marks omitted).
When reviewing a district court’s denial of a motion to suppress, the scrutiny afforded by the court of appeals must be tempered by yet another level of deference: we assess the district court’s factual findings for clear error. See United States v. Garcia-Hernandez, 659 F.3d 108, 111 (1st Cir.2011). Withal, we assay the district court’s rulings of law de novo. See id.
In this case, the circumstances, viewed in their totality, leave no doubt that there was -probable cause to support the warrant. The supporting affidavit chronicled Agent Cecchini’s investigation and spelled out how it led to the defendant’s IP address and, in turn, his abode. In the process, it described the EP2P technology that the FBI had developed for such investigations and had used in this case.
The defendant objects to these references to EP2P on the basis that the technology was too untested to meet the requirements of the Federal Rules of Evidence. This argument mixes plums and pomegranates; the Federal Rules of Evidence do not apply to proceedings surrounding the issuance of a search warrant. See Fed.R.Evid. 1101(d)(3). Instead, the issuing magistrate must “make a practical, common-sense decision whether ... there is a fair probability that contraband or evidence of a crime will be found in a particular place.” Gates, 462 U.S. at 238, 103 S.Ct. 2317. In this instance, the magistrate made a sensible determination, based on a detailed affidavit, that a search of the defendant’s residence was likely to turn up illicit images. Because probable cause “does not require scientific certainty,” Roche v. John Hancock Mut. Life Ins. Co., 81 F.3d 249, 254 (1st Cir.1996), no more was exigible.
The defendant tries to attack the affidavit in yet another way, suggesting that it contained knowing or reckless material omissions about the reliability of EP2P. In particular, he focuses again on the absence of peer review. This attack is easily repulsed. Here, the allegedly omitted statements — what the FBI knew about the reliability of EP2P, including, but not limited to, the absence of peer review — would, if included in their entirety, tend to show that EP2P was reliable. Thus, the alleged omissions in the supporting affidavit were not material: had the omitted statements been added, they would not have diluted the affidavit’s showing of probable cause. See United States v. Rumney, 867 F.2d 714, 720 (1st Cir.1989).
Put in the simplest of terms, had the affiant included the additional statements describing what was known about EP2P’s reliability, those statements would have served no purpose except to strengthen the affidavit. It would be wildly illogical to suppress the fruits of a search on the ground that the warrant application omit*280ted statements that, if included, would have increased the affidavit’s persuasive force. Cf. United States v. Bynum, 293 F.3d 192, 198-99 (4th Cir.2002) (observing that an omission in an affidavit will not be fatal “just because the officer fails to include in th[e] affidavit all of the information known to him supporting a finding of probable cause”).
D. Jury Instructions.
The defendant presents twin claims of instructional error. We deal with them one by one.
He first asserts that he was entitled to a “lesser included offense” instruction on the distribution count. In his view, distribution necessarily entails possession. Thus, possession must be a lesser included offense of distribution, and the jury should have been instructed accordingly. See Fed.R.Crim.P. 31(c)(1).
We review de novo the trial judge’s decision about whether to give a lesser included offense instruction. United States v. Boidi, 568 F.3d 24, 27 (1st Cir.2009) (citing United States v. Flores, 968 F.2d 1366, 1367-68 (1st Cir.1992)). The defendant “is entitled to such an instruction where (1) the lesser offense is included in the offense charged, (2) a contested fact separates the two offenses, and (3) the evidence would permit a jury rationally to find the defendant guilty of the lesser offense and acquit him of the greater.” Id. (alterations, citations, and internal quotation marks omitted).
Our inquiry here can stop at the first step of this pavane. In deciding whether an offense is necessarily included in the offense charged, we apply “an elements test, under which one offense is not necessarily included in another unless the elements of the lesser offense are a subset of the elements of the charged offense.” Carter v. United States, 530 U.S. 255, 260, 120 S.Ct. 2159, 147 L.Ed.2d 203 (2000) (quoting Schmuck v. United States, 489 U.S. 705, 716, 109 S.Ct. 1443, 103 L.Ed.2d 734 (1989)) (internal quotation marks omitted). “To pass the test, all the elements of the lesser included offense must be elements of the charged offense — but the charged offense must include at least one additional element.” Flores, 968 F.2d at 1369.
We have stated, albeit in the context of drug trafficking, that “[w]hile ‘possession’ is certainly helpful in proving distribution, it is technically not a necessary element.” United States v. Sepulveda, 102 F.3d 1313, 1317 (1st Cir.1996). The same is true in this child pornography case. One can envision circumstances in which an individual could be guilty of distribution without ever obtaining possession of (or even coming into contact with) the contraband. For example, the broker of a deal between a person who has child pornography and a person who wishes to procure it may be guilty of distribution but not guilty of possession. Cf. United States v. Brunty, 701 F.2d 1375, 1381 (11th Cir.1983) (observing, in drug context, that distribution may consist of “arranging or supervising the delivery” of contraband or “negotiating for or receiving the purchase price” of contraband). Accordingly, possession is not a necessary element of distribution in a child pornography case, and the district court did not err in refusing to give the requested lesser included offense instruction.
The defendant’s second claim of instructional error contemplates that the district court should have embraced his proposed carve-out to its instruction on distribution. This carve-out stated in pertinent part that proof of “possession of child pornography and even possession of child pornography with the intent to distribute child pornography is not sufficient *281to prove distribution.” Where, as here, a trial court refuses to give a requested instruction, its refusal is erroneous “only if the requested instruction was (1) correct as a matter of substantive law, (2) not substantially incorporated into the charge as rendered, and (3) integral to an important point in the case.” United States v. McGill, 953 F.2d 10, 13 (1st Cir.1992).
We have canvassed the instructions as a whole. See Cintolo, 818 F.2d at 1003. After conducting this canvass, we are satisfied that the instructions given covered substantially the same ground as the instruction requested. The court’s charge adequately communicated the disparate elements of possession and distribution, satisfactorily illuminated the difference between the two, and made plain what the government needed to prove to convict on each offense. While the defendant may have wanted the court to put the distinction in his chosen words, the court was under no obligation to “parrot the exact language that the defendant prefers.” McGill, 953 F.2d at 12. The court’s instructions constituted a fair and reasonably complete statement of the applicable law. Our jurisprudence requires no more.
E. Judgment of Acquittal.
We now address the defendant’s plaint that the government introduced insufficient evidence of distribution and that, therefore, the court should have granted his motion for judgment of acquittal on the distribution count. See Fed.R.Crim.P. 29. We review the denial of a motion for judgment of acquittal de novo. See United States v. Dwinells, 508 F.3d 63, 72 (1st Cir.2007). In this exercise, we examine “whether, after assaying all the evidence in the light most amiable to the government, and taking all reasonable inferences in its favor, a rational factfinder could find, beyond a reasonable doubt, that the prosecution successfully proved the essential elements of the crime.” United States v. O’Brien, 14 F.3d 703, 706 (1st Cir.1994).
In the case at hand, the government had to prove that the defendant knowingly distributed a visual depiction of a minor engaging in sexually explicit conduct and that this visual depiction had either traveled in interstate commerce or been produced using materials that had traveled in interstate commerce. See 18 U.S.C. § 2252(a)(2). The government’s proof of the jurisdictional element is rock solid: the illicit files traveled via the Internet and, thus, traveled in interstate commerce. See United States v. Lewis, 554 F.3d 208, 215 (1st Cir.2009). The defendant does not contest — nor could he rewardingly do so — that the transmitted material satisfied the subject matter element of the statute. It constituted child pornography.
Our inquiry reduces, therefore, to whether there was enough evidence to prove that the defendant knowingly distributed the files. The defendant protests that there was not. He claims that he did not take any affirmative action in order to send the files to Agent Cecchini and that he may not even have been at his computer when the files were downloaded. Absent some positive act on his part, his thesis runs, evidence showing that he put files in a particular folder is insufficient to support a conviction for distribution.
Although it appears that this issue has not been addressed in this circuit, we believe that the defendant’s actions constituted distribution within the meaning of the statute. The word “distribution” is not defined in the statute itself, but the plain meaning of distribution is “[t]he act or process of apportioning or giving out.” Black’s Law Dictionary 543 (9th ed.2009). *282When an individual consciously makes files available for others to take and those files are in fact taken, distribution has occurred.
The fact that the defendant did not actively elect to transmit those files is irrelevant. In United States v. Shaffer, 472 F.3d 1219 (10th Cir.2007), the Tenth Circuit analogized passive distribution over a peer-to-peer network to a self-serve gas station: “Just because the operation is self-serve, or ... passive, we do not doubt for a moment that the gas station owner is in the business of ‘distributing’ ... gasoline; the raison d’etre of owning a gas station is to do just that.” So it is here. A rational jury could conclude, as this jury did, that the defendant intentionally made his files available for the taking and that Agent Cecchini simply took him up on his offer.6
The evidence unquestionably supports a finding that the defendant downloaded LimeWire and chose to make his files available for sharing. The evidence likewise supports a finding that the defendant set up LimeWire to share the contents of a specific folder called “limewire piesvids” with the entire LimeWire network. Hence, the defendant affirmatively acted to make the files in that particular folder available to other users because, by default, LimeWire shares only the files in a specially created “Shared” folder.
Other evidence buttresses these findings. The jury could have found that the defendant was computer-sawy. After all, he set up his home network and installed software to erase his web browsing history. Tellingly, however, he never availed himself of the LimeWire feature that allows users to turn off sharing, nor did he lift a finger to move the pornographic files out of the designated folder in order to prevent them from being shared with others. On these facts, the jury could rationally have concluded beyond any reasonable doubt that the defendant had the required scienter.
In upholding the district court’s denial of the defendant’s motion for judgment of acquittal, we reject the defendant’s argument that the proof showed no more than that he possessed files with the intent to distribute them. The evidence was sufficient to support a finding that the defendant transmitted child pornography to Agent Cecchini. The fact that distribution was effected to an undercover law enforcement officer does not mitigate the fact that distribution occurred.
F. Sentencing.
The defendant mounts a very narrow attack on his sentence. The target of this attack is the two-level enhancement for distribution other than to a minor or in exchange for a thing of value. USSG § 2G2.2(b)(3)(F). He accuses the sentencing court of double counting when it relied on the fact that he distributed pornographic images both to give him a higher base offense level and to support the challenged enhancement. Inasmuch as this argument centers on the district court’s legal interpretation of the guidelines, our review is de novo. United States v. Paneto, 661 F.3d 709, 715 (1st Cir.2011).
The defendant’s claim of sentencing error is unavailing. We have said before, and today reaffirm, that “[d]ouble counting in the sentencing context ‘is a phenomenon that is less sinister than the name im*283plies.’ ” United States v. Lilly, 13 F.3d 15, 19 (1st Cir.1994) (quoting United States v. Zapata, 1 F.3d 46, 47 (1st Cir.1993)). The Sentencing Commission has shown itself fully capable of expressly forbidding double counting under the guidelines when appropriate. See, e.g., USSG § 3A1.1, comment, (n.l). We regard it as settled that when “neither an explicit prohibition against double counting nor a compelling basis for implying such a prohibition exists,” courts should be reluctant to read in a prohibition where there is none. Lilly, 13 F.3d at 19-20; see United States v. Vizcarra, 668 F.3d 516, 525-27 (7th Cir.2012) (collecting cases requiring a textual basis for prohibiting double counting).
In this instance, the commentary to section 2G2.2 provides no such directive. Instead, the structure of the ‘guideline strongly suggests the opposite. The sentencing guidelines set the base offense level for child pornography offenses at either 18 or 22, depending on the particular statute of conviction. See USSG § 2G2.2(a). Section 2G2.2(b) further stratifies the offenses: for example, a greater enhancement is warranted if the offender was compensated for transferring child pornography or gave it to a minor; more lenient treatment is warranted if the defendant only engaged in distribution simpliciter. Id. § 2G2.2(b)(3).
The variations are nearly infinite. On the one hand, there are offenses, such as solicitation, 18 U.S.C. § 2252A(a)(3)(B), for which the higher base offense level of 22 but none of the section 2G2.2(b)(3) enhancements may apply. See USSG § 2G2.2(a), (b)(1) & comment, (n.l) (adjusting downward two levels if offense is simple solicitation and clarifying that solicitation is not distribution). On the other hand, there are offenses, like the one at issue here, under which one or more of the distribution-related section 2G2.2(b)' enhancements almost always will apply. See USSG § 2G2.2, comment. (n.l). Viewed against this chiaroscuro backdrop, it is apparent that the sentencing guidelines broadly cover all child pornography offenses and use the offense level spread and subsequent adjustments to reach appropriate benchmarks for different permutations of possession, solicitation, and distribution.
To sum up, there is absolutely no basis for an inference that the Sentencing Commission intended to preclude double counting under these circumstances. Thus, the district court did not err in dialing up the challenged enhancement.
G. Restitution.
We end our odyssey with the district court’s grant of restitution. We review restitution orders for abuse of discretion, examining the court’s subsidiary factual findings for clear error and its answers to abstract legal questions de novo. See United States v. Hensley, 91 F.3d 274, 277 (1st Cir.1996).
After learning of the pendency of this prosecution, two of the children depicted in images collected by the defendant — whom we shall call “LS” and “Vicky” — requested restitution. Each victim proffered psychological reports and other documentation in support of her claim for restitution. The claimed losses were rion-pecuniary and, therefore, difficult to quantify. LS calculated her losses due to the online trading of her image to be close to $2,000,000, whereas Vicky sought slightly more than half that amount. The district court awarded restitution in the amount of $10,000 to each claimant.
The restitution scheme associated with child pornography offenses is limned in 18 U.S.C. § 2259. It provides that the issuance of a restitution order is mandato*284ry if certain criteria are met, regardless of either the defendant’s ability to pay or the victim’s receipt of some compensation from another source. See id. § 2259(b)(4). We have interpreted this statute to require district courts to find, as a predicate to an award of restitution, (i) that the individual is a “victim” within the meaning of the law and (ii) that the defendant’s actions proximately caused the victim’s losses. See United States v. Kearney, 672 F.3d 81, 94-100 (1st Cir.2012). If these requirements are satisfied, the court must proceed to make a “reasonable determination of appropriate restitution.” Id. at 100 (quoting United States v. Innarelli, 524 F.3d 286, 294 (1st Cir.2008)) (internal quotation marks omitted).
The defendant does not dispute that both LS and Vicky are victims: they have suffered and continue to suffer as a result of the ongoing trade and publication of their images online. Nor does the defendant dispute the reasonableness of the dollar amounts awarded. Instead, he takes aim at whether the government made an adequate showing that his actions caused the victims’ losses.
Under Kearney, the applicable causation standard is one of proximate cause. The evidence must show that the defendant’s conduct created a reasonably foreseeable risk of harm to the victim, notwithstanding that others may also have contributed to that harm.7 Id. at 96, 98.
Here, the able district court correctly anticipated Kearney and found that the harms suffered by the victims were the “proximate result” of the defendant’s actions. It concluded that although the defendant was “further down the food chain” than the victims’ initial abusers, his viewing and distribution of the images damaged the victims and caused them ongoing shame, humiliation, and feelings of helplessness. Since the record adequately supports these findings, see id. at 97-100 (upholding finding of proximate cause in analogous circumstances), we uphold the restitutionary awards.
III. CONCLUSION
The only remaining question is how to redress the double jeopardy violation that we have identified. See supra Part 11(A). We conclude that the most salubrious course is for us to remand to the lower court for the purpose of redressing the constitutional violation. The court, after hearing from the parties, should either merge the two possession counts or vacate the conviction and sentence on one of them. The conviction on the distribution count may stand. The district court may, if it deems it appropriate to do so, resentence the defendant on the two surviving counts. Cf. United States v. García-Ortiz, 657 F.3d 25, 31 (1st Cir.2011) (observing that when a conviction on one of several counts is vacated, “the proper course often is to remand for resentencing on the other (non-vacated) counts”); United States v. Pimienta-Redondo, 874 F.2d 9, 14-16 (1st Cir.1989) (en banc) (holding that a district court may review and redetermine the appropriate sentence on remand from a partially successful appeal). In the alternative, it may allow the sentences on those counts to remain intact.
We need go no further. All of the defendant’s claims of error, save for his claim *285of multiplicity, see supra Part 11(A), are rejected.
Affirmed in part and remanded for further proceedings consistent with this opinion.
. For ease in exposition, we follow traditional grammar rules and spell out single-digit numbers (even where Arabic numerals have been used in the statutory text).
. In endorsing this reasoning, we join the Second Circuit in rejecting the view of those district courts that have suggested that the statutory changes evince Congress’s intent to change the unit of prosecution. See United States v. Polouizzi, 564 F.3d 142, 156 (2d Cir.2009) (rejecting logic of United States v. Hamilton, Civil No. 07-50054, 2007 WL 2903018, at *2-3 (W.D.Ark. Oct. 1, 2007), and United States v. Flyer, No. CR 05-1049, 2006 WL 2590459, at *4-6 (D.Ariz. Sept. 7, 2006)).
. We recognize that our holding may be in tension with dictum in United States v. Schales, 546 F.3d 965, 979 (9th Cir.2008), which suggests that "where a defendant has stored sexually explicit images in separate mediums, the government may constitutionally charge that defendant with separate counts [under section 2252] for each.” The Schales court relied on Planck, 493 F.3d at 504, in support of this statement, apparently without realizing that Planck was a section 2252A case. This imprecision undercuts the statement because, as we have explained, these statutes are differently worded, and each of them needs to be interpreted on its own terms.
. In the court below, the defendant also attempted to invoke Federal Rule of Criminal Procedure 16(a)(1)(F), which requires the government to turn over certain reports of scientific examinations, and Federal Rule of Criminal Procedure 16(a)(1)(G), which requires the government to turn over written summaries of proposed expert testimony. These remonstrances are patently meritless, and we reject them out of hand.
. In passing, the defendant alludes to the hampering of his ability to cross-examine witnesses effectively. See U.S. Const, amend. VI. But he has offered no developed argumentation on this ground, and it is a "settled appellate rule that issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.” United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990).
. The defendant attempts to distinguish this case from Shaffer by noting that he did not receive anything of value for sharing his files. See 472 F.3d at 1222. We think that this is a distinction without a difference. The statute of conviction does not provide any justification for insisting upon such a limitation.
. Vicky has filed an amicus brief urging us to find that there is no proximate cause requirement under 18 U.S.C. § 2259 and that Kearney's contrary suggestion is dictum. Neither the government nor the defendant has espoused this theory. Consequently, we adhere to the established principle that an amicus may not "interject into a case issues which the litigants, whatever their reasons might be, have chosen to ignore.” Lane v. First Nat’l Bank of Bos., 871 F.2d 166, 175 (1st Cir.1989).