
527 F.3d 54 (2008)
UNITED STATES of America
v.
Donald R. MILLER Jr., Appellant.
No. 06-5187.
United States Court of Appeals, Third Circuit.
Argued February 1, 2008.
Filed: June 2, 2008.
*57 Ronald A. Krauss, Esquire [ARGUED] Office of Federal Public Defender, Harrisburg, PA, for Appellant, Donald R. Miller Jr.
Christian A. Fisanick, Esquire [ARGUED] Office of United States Attorney, *58 Scranton, PA, Theodore B. Smith, III, Esq., Office of United States Attorney, Harrisburg, PA, for Appellee, United States of America.
Before: RENDELL and CHAGARES, Circuit Judges, and POLLAK,[*] District Judge.

OPINION OF THE COURT
POLLAK, District Judge:
Pursuant to a jury trial in the District Court for the Middle District of Pennsylvania, Donald R. Miller was found guilty of (1) receiving child pornography, in violation of 18 U.S.C. § 2252A(a)(2), (2) possessing the same images of child pornography, in violation of 18 U.S.C. § 2252A(a)(5)(B), and (3) marijuana possession, in violation of 21 U.S.C. § 844(a). Miller was sentenced to concurrent terms of 46 months' imprisonment on the two child pornography counts and a concurrent term of 12 months' imprisonment on the marijuana count. In calculating the applicable sentencing range under the Sentencing Guidelines, the District Court found that Miller, in the course of his testimony at trial, had committed perjury, and accordingly applied a two-level sentencing enhancement for obstruction of justice, pursuant to U.S.S.G. § 3C 1.1 (2003). On appeal, Miller argues (1) that there was not sufficient evidence to support his conviction for receiving child pornography, (2) the Constitution's double jeopardy clause barred entry of separate convictions for receiving and possessing the same images of child pornography, and (3) the record does not support the District Court's finding that Miller committed perjury.
We conclude that Miller's conviction for receiving child pornography was supported by substantial evidence. However, we further hold that (a) the double jeopardy clause barred convictions for both receiving and possessing the same images of child pornography, and (b) the entry of guilty verdicts on both of these counts was plain error. We also hold that Miller's testimony regarding his collection of adult pornography was neither willfully false nor material, as those terms are to be understood in the context of perjury, and thus did not support a sentencing enhancement. Accordingly, we will vacate the District Court's judgment and remand this case for re-sentencing consistent with this opinion.

I.
In January 2004, the FBI searched Miller's home while investigating the uploading of child pornography onto a website hosted by Prime Media, a company in Utah. In the basement of the house, the agents found a zip disk containing 1200-1400 images,[1] twenty of which, according to the government, depicted child pornography. (The District Court later found, for the purpose of calculating Miller's sentence, that eleven of these twenty images constituted child pornography). The agents also found 55.5 grams of marijuana in a jewelry box in Miller's wife's bedroom.
In the month of the search, January 2004, a grand jury charged Miller with two counts of child pornography relating to the images uploaded onto the Prime Media website. In November 2004, a five-count superseding indictment charged Miller *59 with: (count one) receiving child pornography, in violation of 18 U.S.C. § 2252A(a)(2), based on the images found on the zip disk; (count two) transporting and shipping child pornography, in violation of 18 U.S.C. § 2252A(a)(1); (count three) receiving and distributing child pornography, also in violation of 18 U.S.C. § 2252A(a)(2); (count four) possessing child pornography, in violation of 18 U.S.C. § 2252A(a)(5)(B), based on the images found on the zip disk; and (count five) marijuana possession, in violation of 21 U.S.C. § 844(a).
At trial, the jury found Miller guilty both of receiving child pornography stored on the zip disk, count one, and of possessing the same images of child pornography, count four. The jury also found Miller guilty of marijuana possession, count five. However, the jury acquitted Miller of counts two and three. Miller timely filed a Rule 29(c) motion for judgment of acquittal, which the District Court denied.
Miller's presentence investigation report ("PSR"), prepared by the Probation Office, recommended that the District Court apply three two-level enhancements to Miller's base offense level under the Guidelines. Miller objected to these enhancements, and the District Court held an evidentiary hearing to address his objections. The District Court determined that one of the recommended enhancements was inapplicable,[2] but accepted the other two. The first of the two enhancements was for possession of ten or more images of child pornography, pursuant to U.S.S.G. § 2G2.2(b), based on the District Court's finding, by a preponderance of the evidence, that Miller possessed eleven images of child pornography (including two images that were duplicates of one another).
The second enhancement was for obstruction of justice, pursuant to U.S.S.G. § 3C1.1 (2003).[3] The asserted obstruction took place when, at trial, Miller was asked, in the course of cross-examination regarding his collection of adult pornography: "Did you have sadomasochistic pictures." Appendix ("A.") 311. Miller replied: "Not that I'm aware of, no." Id. Contending that Miller's answer was a deliberate falsehood, the government, at the evidentiary hearing prior to the imposition of sentence, presented five images depicting adults that were found on the zip disk containing child pornography. The District Court, on viewing the five images, concluded that they "could fairly be described as sadomasochistic pornography." A. 21. Accordingly, the District Court ruled that Miller's answer at trial constituted perjury and, therefore, was an obstruction of justice.
The District Court entered separate judgments of conviction for counts one (receiving child pornography), four (possessing child pornography), and five (marijuana possession). The District Court imposed concurrent sentences of 46 months for each of the child pornography counts and a concurrent sentence of 12 months for the marijuana possession count.[4] Miller timely appealed.


*60 II.
We exercise plenary review over Miller's sufficiency-of-the-evidence claim. "In exercising that review, we must interpret the evidence in the light most favorable to the government as the verdict winner," United States v. Taftsiou, 144 F.3d 287, 290 (3d Cir.1998), and "do not weigh evidence or determine the credibility of witnesses in making [our] determination." United States v. Gambone, 314 F.3d 163, 170 (3d Cir.2003) (internal quotation omitted).
We review Miller's double jeopardy claim for plain error since he did not raise the issue before the District Court. See United States v. Jackson, 443 F.3d 293, 301 (3d Cir.2006).
With respect to the District Court's finding, for the purpose of applying the Guidelines, that Miller committed perjury, this court exercises plenary review over the District Court's interpretation of the Guidelines. See United States v. Grier, 475 F.3d 556, 561 (3d Cir.2007) (en banc) ("Under an advisory Guidelines scheme, district courts should continue to make factual findings by a preponderance of the evidence and courts of appeals should continue to review those findings for clear error.").[5] "When the application of the Guidelines presents a mixed question of law and fact, `our standard and scope of review takes on greater scrutiny, approaching de novo as the issue moves from one of strictly fact to one of strictly law.'" United States v. Felton, 55 F.3d 861, 864 (3d Cir.1995) (quoting United States v. Belletiere, 971 F.2d 961, 964 (3d Cir.1992) (internal quotation omitted)).

III.
Miller argues that there is not substantial evidence proving that he received child pornography. In addressing this claim, we must uphold a jury's verdict "if there is substantial evidence from which a rational trier of fact could find guilt beyond a reasonable doubt." United States v. Brown, 3 F.3d 673, 680 (3d Cir.1993). Before evaluating the merits of this claim and reciting the evidence relating to Miller's conviction, we must consider the government's threshold contention that the claim has been waived.

A.
Miller first raised his sufficiency-of-the-evidence claim before the District Court in a timely post-trial motion for acquittal pursuant to Fed.R.Crim.P. 29(c). The government contends that, though the motion was a proper vehicle for presenting the claim to the District Court, the motion failed to preserve the claim for appeal. To preserve a sufficiency-of-the-evidence claim for appeal, the government argues, a defendant must raise the issue at trial via a Rule 29(a) motion "[a]fter the government *61 closes its evidence or after the close of all the evidence." Fed.R.Crim. 29(a).
The government's argument finds no support in the language of Rule 29(c). The rule provides that "[a] defendant may move for a judgment of acquittal, or renew such a motion, within 7 days after a guilty verdict or after the court discharges the jury, whichever is later." Fed.R.Crim.P. 29(c)(1). The rule goes on to clarify that "[a] defendant is not required to move for a judgment of acquittal before the court submits the case to the jury as a prerequisite for making such a motion after jury discharge." Fed.R.Crim.P. 29(c)(3). These terms would seem to authorize a court of appeals to exercise plenary review over a claim raised in a Rule 29(c) motion without regard to whether the claim was earlier raised in a Rule 29(a) motion. It appears that each circuit court addressing this precise question has so held. See United States v. Holland, 381 F.3d 80, 86 n. 7 (2d Cir.2004); United States v. South, 28 F.3d 619, 626 n. 3 (7th Cir.1994); United States v. Castro-Lara, 970 F.2d 976, 980 (1st Cir.1992),[6]abrogated on other grounds by Bailey v. United States, 516 U.S. 137, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995); United States v. Allison, 616 F.2d 779, 783-84 (5th Cir.1980).[7]
This court, without confronting the question directly, appears to have treated a Rule 29(c) motion as preserving a sufficiency-of-the evidence claim irrespective of whether the claim was earlier raised at trial. In United States v. Thayer, 201 F.3d 214, 218-19 (3d Cir.1999), without specifying whether the defendant had filed a Rule 29(a) motion, we stated that the defendant had raised a sufficiency-of-the-evidence claim in a Rule 29(c) motion. On appeal, the defendant reasserted the sufficiency-of-the-evidence claim, and also put forth other claims that he did not raise before the district court. In articulating the applicable standard of the review, we stated that:

*62 Where the issues raised on appeal are preserved at trial, or through a timely motion for acquittal under Fed. R.Crim.P. 29(c), we will overturn a jury verdict only when the record contains no evidence, regardless of how it is weighted, from which the jury could find guilt beyond a reasonable doubt.... But issues on appeal which were not raised before the District Court, we will review for plain error.
201 F.3d at 218-19 (internal quotation omitted). We then proceeded to exercise plenary review over the defendant's sufficiency-of-the-evidence claim. See id. at 221.
The government argues that we are compelled to depart from Thayer's statement that we exercise plenary review over claims "preserved at trial, or through a timely motion for acquittal under Fed. R.Crim.P. 29(c)." Its argument is grounded in our statement, in a case more recent than Thayer, that a sufficiency-of-the-evidence claim is waived where it is not preserved "by making a timely motion for judgment of acquittal at the close of the evidence." United States v. Mornan, 413 F.3d 372, 381 (3d Cir.2005) (citing United States v. Wolfe, 245 F.3d 257, 260-61 (3d Cir.2001), and United States v. Gaydos, 108 F.3d 505, 509 (3d Cir.1997)). But we did not clarify in Mornan, or in Wolfe, whether the defendants in those cases had filed post-trial Rule 29(c) motions, or simply had failed to raise their claims before the district court. In Gaydos, however, we expressly held that the appellant failed to preserve her claim because her Rule 29(c) motion before the district court was untimely. We do not think, therefore, that our statement in Mornan, which was not in terms geared to the question whether a Rule 29(c) motion is sufficient to preserve a claim for review, requires us to reject our Thayer language and, in doing so, to adopt a strained interpretation of Rule 29 that has not commended itself to sister circuits. Accordingly, we now clarify that a timely motion for acquittal under Rule 29(c) will preserve a sufficiency-of-the-evidence claim for review, irrespective of whether the defendant raised the claim at trial.

B.
We turn, then, to whether Miller has raised a colorable sufficiency-of-the-evidence claim. Miller does not challenge the jury's determination that he committed the offense of possessing child pornography in violation of § 2252A(a)(5)(B). But, while conceding that there may be substantial evidence proving his guilt of possession, Miller contends that this evidence is not sufficient to prove his guilt of receipt under § 2252A(a)(2). To conclude otherwise, Miller argues, is to "extinguish the distinction between the offense of knowing receipt and the offense of knowing possession." Appellant's Brief at 28.
The proposition underlying this argument  namely, the proposition that a conviction for receiving child pornography must be supported by a greater quantum of evidence than that minimally required to prove guilt of possessing child pornography  is correct. We appreciate that, in reviewing a sufficiency-of-the-evidence claim, we must "examine the totality of the evidence, both direct and circumstantial," Gambone, 314 F.3d at 170, and doubtless there will be considerable overlap, in most instances, between the evidence relevant to the offenses of possession and receipt. However, receipt and possession of child pornography are punished by separate provisions of § 2252A, and we cannot conflate the provisions without running afoul of "the doctrine that legislative enactments should not be construed to render their provisions mere surplusage." Dunn v. *63 Commodity Futures Trading Commission, 519 U.S. 465, 472, 117 S.Ct. 913, 137 L.Ed.2d 93 (1997).
The government's distinct evidentiary burden with respect to § 2252A(a)(2), vis-à-vis § 2252A(a)(5)(B), traces to the intent-elements of the offenses. Sections 2252A(a)(2) and 2252A(a)(5)(B) punish only those who "knowingly" receive, or "knowingly" possess, child pornography. In evaluating whether there is sufficient evidence to support a conviction under one of these provisions, we must review "`whether the Government has adduced sufficient evidence respecting each element of the offense charged to permit jury consideration.'" United States v. Goldblatt, 813 F.2d 619, 621 (3d Cir.1987) (emphasis added) (quoting United States v. Giampa, 758 F.2d 928, 934 (3d Cir.1985)). A person's possession of a tangible object, such as a firearm, may constitute strong circumstantial evidence that defendant knowingly received the object. See, e.g., United States v. Ladd, 877 F.2d 1083, 1088 (1st Cir.1989) (noting that, in firearm cases, "[c]onstructive receipt can be shown circumstantially by proof of possession, either actual or constructive"). However, as portions of the expert testimony in this case illustrate, a person may come to knowingly possess a computer file without ever knowingly receiving it. This could happen, according to the parties' experts,[8] if the person's computer is infected with a virus or "spyware" software that surreptitiously installs advertising images.[9] Thus, when a defendant is charged with downloading a computer file, the court must rigorously scrutinize whether there is sufficient evidence to establish the intent-element of the crime. See, e.g., United States v. Kuchinski, 469 F.3d 853, 861-63 (9th Cir.2006) (reversing sentence based on knowingly receiving child pornography that was stored in cache files of defendant's computer, where defendant lacked knowledge of or access to the files); cf. United States v. Romm, 455 F.3d 990, 997-1001 (9th Cir.2006) (upholding conviction for knowingly receiving pornography stored in cache files that defendant knew he could access).
The evidence required to establish the intent-element of § 2252A(a)(2) may be greater than that required to establish the intent-element of § 2252A(a)(5)(B) because, while a person who "knowingly receives" child pornography will necessarily "knowingly possess" child pornography, the obverse is not the case. Cf. United States v. Myers, 355 F.3d 1040, 1042 (7th Cir.2004) (upholding sentencing calculation for defendant who received videos and computer-generated image files depicting *64 minors engaged in sexually explicit conduct, in violation of § 2252).[10] In Myers, the court observed that "a person who seeks out only adult pornography, but without his knowledge is sent a mix of adult and child pornography," could not be found guilty of knowingly receiving child pornography. Id. "That same person, however, could be in violation of the possession provision of § 2252(a)(4)(B) if he or she decides to retain that material, thereby knowingly possessing it." Id. It follows that the quantum of evidence required to prove knowing receipt of a downloaded file may, in some situations, be greater than that minimally required to prove knowing possession of the file.

C.
Because Miller raised a colorable sufficiency-of-the-evidence claim with respect to count one, receiving child pornography, we must recite the evidence adduced at trial pertaining to this count. The evidence was as follows:
In September 2003, someone created and uploaded child pornography onto a website that was hosted by Prime Media, the company in Utah. Prime Media identified the unique internet protocol ("IP") address of the computer that was used to upload the images. The company turned the information over to the FBI, which concluded that the IP address was that of a computer in Donald Miller's home.
The FBI searched Miller's house in January 2004. The agents seized one computer from the basement and one from the living room. These computers were not state-of-the-art, and had small hard drives relative to other computers on the market. Though the computers had dial-up network capability, which enables users to access the internet through an ordinary telephone connection, they did not have the capacity to connect at the faster speeds of broadband. The computer in the basement, which was the focus of the government's case, was equipped with an external zip drive, and the agents seized twenty-two zip disks that were also stored in the basement. The agents also seized 55.5 grams of marijuana from the bedroom of Miller's wife.
One of the zip disks contained 1200-1400 images, according to the government's expert witness (the defendant's expert counted 1373 image files). The majority of the images depicted adult pornography, but, the government contended, twenty of the images depicted child pornography. The twenty images characterized by the government as child pornography were not among the ones that had been uploaded onto the website hosted by Prime Media.
At trial, there was testimony that, during the search of Miller's home, the FBI's supervising investigator, Agent James A. Kyle, questioned Miller. Agent Kyle and Miller, both of whom testified at trial, gave differing accounts of the interview. They agreed that the tenor of the discussion was cooperative, and that Miller volunteered the location of the marijuana. They also agreed that Miller (a) claimed he was unaware *65 of why the FBI would investigate him, and (b) denied having any interest in or experience with viewing child pornography. According to Agent Kyle, during the interview, Miller denied having pornography of any kind. Miller testified, however, that he acknowledged possessing adult pornography, but not child pornography.
The day after the search, Miller contacted Agent Kyle with further information. Miller told Agent Kyle that his computer had been infected with a virus the previous year, which might account for the uploaded images having been traced to his computer. Miller also informed Agent Kyle that he stored adult pornography on one of the twenty-two zip disks that were seized, and gave Agent Kyle the password to access that zip disk. At trial, the government presented evidence pertaining to the twenty images on the zip disk that, the government contended, depicted child pornography. The government's evidence included testimony by Agent Kyle and two FBI forensic experts, Agents James P. McDonald and Donald J. Price. According to this testimony, four of the twenty images were embedded with the addresses of websites, which were visible when viewing the images and which may have connoted an association with child pornography. On cross-examination, Agent Kyle testified that these address listings likely advertised websites other than those from which the images were obtained, and Miller's expert witness, John R. Smith, stressed this point. Some of the image files bore sexually suggestive file names, but none of these file names suggested that they contained child pornography.
Agents McDonald and Price also testified as to when the images were copied onto the zip disk, and whether they had been viewed once copied onto the zip disk. The agents testified that, for each image file, there is a record of a "date created," a "date written," and a "date accessed." The "date created" records the date and time a file was copied onto the storage medium, and thus would indicate when the file was copied onto the zip disk. The "date written" records the date and time a file was last opened and altered in some way; this date will change, for example, if an image is cropped or resized by a user. The "date accessed" records when a file was accessed, either by a viewer or by some sort of program such as a scheduled virus check. According to Agent Price's testimony on cross-examination, "[y]ou can't tell," from a file's "date accessed," whether a file was opened automatically or by a user. A. 293.
Agent Price testified that seventeen of the twenty images presented by the government had a "date written" that was the same as its "date created."[11] Three of the images bore a "date created" of October 13, 2002, and a subsequent "date written" of May 31, 2003. Each of the images had a "date accessed" of December 26, 2003. When asked whether he checked the "dates accessed" for the other 1200-1400 image files on the disk, Price replied: "No. I mean, I have that recorded, but I didn't necessarily note it." A. 292.
Miller testified at trial that he had not previously seen any of these images and "did not knowingly and willingly put" the images in question on the zip disk. A. 323. Miller admitted that he stored images, including adult pornography, on zip disks, and that he looked at adult pornography on the internet. However, he testified that he had never seen the twenty images in question, and that he only looked at images of adults that he understood to be *66 legal, which he obtained from websites containing legal disclaimers. Miller also testified that, at the time of the alleged child pornography offenses, he was the victim of a billing fraud wherein he was charged by a foreign company for a subscription to a pornography website of which he had never heard. In support of this claim, Miller submitted a credit card statement for October 15-November 14, 2002, which indicated that the credit card company corrected a charge from a company in Tel Aviv called "web sitebilling.com." Miller speculated that, because of this fraud, someone may have gotten access to his "log ons" and credit card numbers. A. 321.
Miller's expert witness, John R. Smith, testified in support of Miller's claim that he was unaware of the images on the zip disk. According to Smith's testimony, the thirteen images presented by the government that were copied onto the zip disk on October 13, 2002, were among 586 image files copied to the disk over a seven-hour period, at periodic intervals suggesting that the images were copied automatically, perhaps as the result of a virus. Smith then presented a demonstration of how four image files may be inadvertently downloaded into a subdirectory of a computer's hard drive by a user who believes that he is downloading only a single image. If the user then saves the web page onto a zip disk or hard drive, according to Smith, the user will save all four of the images.
Prior to Smith's testimony, Agent Price testified that he was unaware of any virus that downloads child pornography. In his rebuttal to Smith's testimony, Agent Price testified that there were no web pages recovered from the zip disk, so the images found on the zip disk had been "extracted;" that is, they were not, as Agent Price characterized it, "embedded files." A. 423. Agent Price also testified that it was "highly unlikely," albeit possible, that someone would hack into another person's dial-up internet connection and transmit data that would be attributed to the IP address of that person's computer. A. 279.

D.
Having recited the evidence, we now assess whether it is sufficient to prove each element of the charged offense.

1.
We first conclude that there is substantial, circumstantial evidence supporting the inference that Miller downloaded child pornography, thus satisfying the act-element of receiving child pornography in violation of § 2252A(a)(2), the count one charge. The jury found Miller guilty of possessing a zip disk containing child pornography, which was among the twenty-two zip disks stored in the basement with Miller's computer. Miller volunteered the password to this zip disk to Agent Kyle, informing him that there was adult pornography on the disk. At trial, Miller testified that he stored digital images on his zip disk, and that he looked at adult pornography on internet websites. Some of the images of child pornography on the disk advertised the names of websites, suggesting that they were initially downloaded from the internet. Cf. United States v. Henriques, 234 F.3d 263, 267 (5th Cir.2000) (concluding that website address embedded on image establishes link to internet for jurisdictional purposes). This evidence supports the inference that Miller received the child pornography on the zip disk by downloading it from the internet. However, because we must review the evidence "respecting each element of the offense charged," Goldblatt, 813 F.2d at 621, our inquiry is not concluded.


*67 2.
More difficult is the question whether Miller received the images knowingly. Other courts, confronting this question, have deemed at least four factors relevant to this inquiry: (1) whether images were found on the defendant's computer, see United States v. Irving, 452 F.3d 110, 122 (2d Cir.2006); (2) the number of images of child pornography that were found, see id. (finding defendant's possession of 76 images relevant); (3) whether the content of the images "was evident from their file names," United States v. Payne, 341 F.3d 393, 403 (5th Cir.2003) (finding "number of images in [defendant's] possession, taken together with the suggestive titles of the photographs" established knowing receipt); and (4) defendant's knowledge of and ability to access the storage area for the images, see Romm, 455 F.3d at 997-1001 (addressing defendant's ability to access cache files in hidden subdirectory); cf. Kuchinski, 469 F.3d at 861-63 (same). We summarize the evidence bearing on these four factors:
(1) The government adduced no direct, forensic evidence that the images were downloaded onto Miller's computer. Agent Kyle testified that it was his "educated guess" that Miller downloaded the images onto the zip disk via the internet, perhaps by trading them in a chat room or by searching for them on a website. A. 195. However, Agent Kyle went on to testify, the government had no proof from Miller's hard drive that supported this hypothesis. Agent Price, on cross-examination, acknowledged that, despite the FBI's use of forensic software designed to recover deleted material from hard drives, the FBI had discovered no evidence that Miller's computer had been used to upload or download child pornography.[12] Agent Price further testified that there was no evidence that Miller ever used search engines to locate child pornography websites, or that such websites had ever been visited from Miller's computer (the FBI's investigation did reveal, however, that two websites containing adult pornography had been visited from the computer). Agent Price also acknowledged that there was no evidence that Miller ever participated in email exchanges or online chat rooms that pertained to child pornography. Finally, Price acknowledged that there was no evidence that Miller used a "wiping" or "eliminator" program to clear his hard drive of evidence that files had been downloaded. A. 296-97.
(2) The second factor, the number of images of child pornography found, likewise does not weigh in the government's favor in light of the overwhelming number of adult images that were found. The government presented evidence pertaining to only twenty of the 1200-1400 images *68 found on the zip disk, and the District Court subsequently determined, in the process of sentencing Miller, that only eleven of these images constituted child pornography. Miller contended that he was unaware of the existence of these images and, significantly, Miller volunteered the password of the zip disk to Agent Kyle, cautioning him that the disk contained pornography. Miller also presented evidence that 586 of the images were copied onto the disk at periodic intervals over a seven-hour period, suggesting that they were not individually viewed when they were being copied. Agent Price's rebuttal to this suggestion was that Miller may have first downloaded the images onto his hard drive, or that of another computer, before copying them onto the disk. This possibility puts sharp light, however, on the facts that no forensic evidence of child pornography was found on Miller's hard drive, and that there was no evidence adduced that another computer may have been used to download the images.
(3) Nor does the third factor, whether the content of the images "was evident from their file names," weigh in the government's favor. Several of the images were embedded with the names of websites that possibly advertised child pornography, but  according to Agent Kyle's and Smith's testimony  this does not suggest that the images were obtained from those websites. Moreover, these website names would not be seen unless a person opened and viewed the files. While there is strong evidence that Miller eventually came to view some of the images of child pornography that were on the disk,[13] and thus to knowingly possess the images, this evidence does not lend much support to the inference that Miller knowingly downloaded the images.
(4) Turning to the fourth factor, whether the defendant had knowledge of and an ability to access the storage space for the images, it is clear that Miller had access to the images on the zip disk. Indeed, Miller admitted to storing image files, including adult pornography, on the disk. In this respect, the facts of this case are more akin to the facts of Romm, 455 F.3d at 997-1001, where the court found that the defendant's knowledge that he could access cache files supported the inference that he knowingly possessed the files, than to the facts of Kuchinski, 469 F.3d 853, 861-63, where the court rejected this inference because the defendant was unaware of, "and concomitantly lack[ed] access to and control over the existence of the files." In contrast to the facts before us, however, the defendant in Romm had stored images of child pornography on the hard drive of his computer, albeit in a subdirectory that was difficult for a typical computer user to access. The Romm court acknowledged that "[n]o doubt, images could be saved to the cache when a defendant accidentally views the images, as through the occurrence of a `pop-up,' for instance." 455 F.3d at 1000. However, the court concluded that this "[wa]s not the case" in Romm's circumstance: "By his own admission..., Romm repeatedly sought out child pornography over the internet. When he found images he "liked," he would "view them, save them to his computer, look at them for about five minutes [] and then delete them." Id. By contrast, Miller has consistently denied that he knowingly viewed or had any interest in viewing child pornography.
*69 Beyond the facts relevant to these four factors, however, the evidence presents a fifth factor that may support the jury's determination: the number of occasions that the images were copied onto the zip disk. Smith testified that the images copied onto the zip disk on October 13, 2002, were likely transferred automatically. However, images of child pornography were also copied onto the disk on subsequent dates. Specifically, according to their dates created, the eleven images that the District Court determined to actually be child pornography were copied to the zip disk on October 13, October 29, December 17, and December 20, 2002. A reasonable juror might have concluded, from this evidence, that Miller copied the images on more than one occasion.
In light of this evidence, and considering all of the evidence in its totality, we cannot say that "no reasonable juror could accept the evidence as sufficient to support the conclusion of [Miller's] guilt beyond a reasonable doubt." United States v. Lacy, 446 F.3d 448, 451 (3d Cir.2006) (quoting United States v. Coleman, 811 F.2d 804, 807 (3d Cir.1987) (internal quotation omitted)). While there certainly is evidence supporting the conclusion that Miller did not receive the images knowingly, a reasonable juror could look to contrary evidence and conclude otherwise. Therefore, mindful that we may not "weigh evidence or determine the credibility of witnesses in making [our] determination," Gambone, 314 F.3d at 170, we will uphold the jury's verdict that Miller knowingly received child pornography.

E.
Miller makes two additional, time-related arguments in support of his sufficiency-of-the-evidence claim. Miller argues that there was not substantial evidence proving that he received child pornography within the five-year statute-of-limitations for § 2252A(a)(2). Nor, Miller argues, is there substantial evidence proving that he received child pornography "on or about" the period between October 13, 2002 and December 20, 2002, as charged in the superseding indictment.
Miller waived his statute-of-limitations argument by failing to raise it at trial. See United States v. Oliva, 46 F.3d 320, 324-25 (3d Cir.1995). Since we cannot consider whether his conviction was time-barred on this ground, we are able to reverse the verdict on time-related grounds only if there is a "material variance" between the evidence adduced at trial and the dates charged in the superseding indictment. United States v. Schurr, 775 F.2d 549, 553 (3d Cir.1985). This would require that we find both that "(1) there was at trial a variance between the indictment and the proof and (2) the variance prejudices a substantial right of the defendant." Id.; see also United States v. Akande, 200 F.3d 136, 141 (3d Cir.1999). This rule, as Judge Becker observed in Schurr, "protects the defendant's right to an indictment sufficiently inform[ing][him] of the charges against him so that he may prepare his defense and not be misled or surprised at trial."[14] 775 F.2d at 553 (internal quotation omitted). Thus, in evaluating whether such prejudice *70 occurred, we consider whether the defendant was disadvantaged by lack of notice as to the nature of the government's trial evidence. See id. at 559 (evaluating defendant's opportunity to prepare defense); see also United States v. Somers, 496 F.2d 723, 743-46 (3d Cir.1974) (considering whether variance created risk that defendant was "so surprised by the proof adduced that he was unable to prepare his defense adequately").
The government did not present direct evidence that the images on the disk were downloaded, and thus were received, "on or about October 13, 2002, through December 20, 2002," the period alleged in the superseding indictment. Furthermore, the government's expert, Agent Price, suggested that the images may have been downloaded sometime before they were copied onto the zip disk in October and December 2002. However, Miller does not identify, and we do not find, any prejudice to his substantial rights that can be traced to a variance between the date charged in the superseding indictment and the evidence adduced at trial. Miller was aware that the images on the zip disk formed the basis of the government's case against him with respect to count one. He presented expert testimony attacking the government's forensic evidence pertaining to these images, and addressed the images in his own testimony. We therefore cannot reverse Miller's conviction on count one based on a variance that may exist between the government's proof at trial and the dates charged in count one of the superseding indictment.

F.
Accordingly, we reject Miller's sufficiency-of-the-evidence claim.

IV.
Miller next contends that the District Court's entry of separate convictions for count one, receiving child pornography in violation of 18 U.S.C. § 2252A(a)(2), and count four, possessing the same images of child pornography in violation of 18 U.S.C. § 2252A(a)(5)(B), violated the double jeopardy clause. Because Miller failed to raise this claim before the District Court, we review the entry of separate convictions for plain error; that is, we must determine whether the entry of separate convictions constitutes an "`(1) error, (2) that is plain, and (3) that affect[s] substantial rights. If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error seriously affect[s] the fairness, integrity, or public reputation of judicial proceedings.'" United States v. Vazquez, 271 F.3d 93, 99 (3d Cir.2001) (quoting Johnson v. United States, 520 U.S. 461, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997)). We address each of the factors of plain error review in turn.

A.
We first consider whether the District Court's entry of separate convictions for counts one and four of Miller's superseding indictment constituted an error. The double jeopardy clause bars courts from "prescrib[ing] greater punishment than the legislature intended" to impose for a single offense. Rutledge v. United States, 517 U.S. 292, 297, 116 S.Ct. 1241, 134 L.Ed.2d 419 (1996) (quoting Missouri v. Hunter, 459 U.S. 359, 366, 103 S.Ct. 673, 74 L.Ed.2d 535 (1983)). There is a rebuttable presumption that "where two statutory provisions proscribe the same offense, a legislature does not intend to impose two punishments for that offense." Id. (internal quotations omitted). Thus, if (a) two statutory provisions "proscribe *71 the same offense" and (b) it is not clear that the legislature intended multiple punishments for the offense, then the double jeopardy clause protects a defendant from being convicted under both of the provisions.

1.
Miller argues that possessing child pornography is a lesser-included offense of receiving child pornography, and thus that § 2252A(a)(2) (prohibiting receipt) and § 2252A(a)(5)(B) (prohibiting possession) "proscribe the same offense." For the purpose of double jeopardy analysis, two offenses are the same if one is a lesser-included offense of the other under the "same-elements" (or Blockburger) test. This test "inquires whether each offense contains an element not contained in the other; if not, they are the `same offence'...." United States v. Dixon, 509 U.S. 688, 696, 113 S.Ct. 2849, 125 L.Ed.2d 556 (opinion of the court) (internal quotation omitted); see also Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 76 L.Ed. 306 (1932) ("[W]here the same act or transaction constitutes a violation of two distinct statutory provisions, the test to be applied to determine whether there are two offenses or only one, is whether each provision requires proof of a fact which the other does not.").
This court has not considered whether § 2252A(a)(5)(B) punishes a lesser-included offense of that punished by § 2252A(a)(2). However, it is clear that, as a general matter, possession of a contraband item is a lesser-included offense of receipt of the item. See Ball v. United States, 470 U.S. 856, 105 S.Ct. 1668, 84 L.Ed.2d 740 (1985). In Ball, a felon convicted of possessing a firearm in violation of 18 U.S.C. § 922(h) (since revised) was also convicted of receiving that firearm in violation of 18 U.S.C.App. § 1202(a) (since repealed). Applying the same-elements test, the Supreme Court concluded, in Ball, that "[w]hen received, a firearm is necessarily possessed. In other words, Congress seems clearly to have recognized that a felon who receives a firearm must also possess it, and thus had no intention of subjecting that person to two convictions for the same criminal act." Id. at 862, 105 S.Ct. 1668 (internal quotation omitted).
Drawing on Ball, the Ninth Circuit, in United States v. Kuchinski, 469 F.3d 853, 859 (9th Cir.2006), in which the defendant was indicted both under § 2252A(a)(2) and under § 2252A(a)(5)(B), observed, in dicta, that "[i]f, as it seems, the counts were based on the same acts, entering judgment on both the offenses would be improper." See also United States v. Morgan, 435 F.3d 660, 662-63 (6th Cir.2005) (noting that a defendant charged under § 2252A(a)(2), who pled guilty to violating § 2252A(a)(5)(B), had pled to "a lesser-included offense of the charged violation"); United States v. Mohrbacher, 182 F.3d 1041, 1048-49 (9th Cir.1999) (consulting dictionary definitions of "receive" after concluding that "there is no indication that Congress intended a specific legal meaning for the term").[15] The observation of these courts that possession of child pornography is a lesser-included offense of receipt of child pornography, though offered in dicta, appears to be correct under Ball. See also United States v. Kamen, 491 F.Supp.2d 142 (D.Mass.2007) (holding that possessing videotapes depicting "a minor engaging in sexually explicit conduct," in violation of § 2252(a)(4)(B) is a lesser-included *72 offense of receiving the same videotapes in violation of § 2252(a)(2)).
The government argues, however, that, even if § 2252A(a)(2) contains all the elements of § 2252A(a)(5)(B), the provisions punish separate offenses because there is a defense available for violations of § 2252A(a)(5)(B) that is not available for violations of § 2252A(a)(2). 18 U.S.C. § 2252A(d) provides an affirmative defense to a defendant who "possessed less than three images of child pornography" and "promptly ... took reasonable steps to destroy each such image" or "reported the matter to a law enforcement agency and afforded that agency access to each such image." The government contends that this affirmative defense constitutes an additional "element" of § 2252A(a)(5)(B) for double jeopardy purposes because "it is more than theoretically possible for one to be guilty of receipt without being guilty of the purported lesser included offense of possession." Appellee's Brief at 47.
That possibility  whether or not more than theoretical  is immaterial to whether two offenses are the same under the same-elements test. Under Blockburger, as this court has explained, "[t]he elements of the offense are compared in the abstract, without looking to the facts of the particular case." Government of Virgin Islands v. Joseph, 765 F.2d 394, 396 (3d Cir.1985) (emphasis in original). Thus, under the same-elements test, affirmative defenses are not among the elements to be considered in comparing the charged offenses. Cf. Kamen, 491 F.Supp.2d at 150-52 (holding that affirmative defenses that do not "actually negate required elements of the crime" are not "elements" under Blockburger). The "elements" to be compared are rather those that must necessarily be proved to establish the commission of a charged offense. See United States v. Chorin, 322 F.3d 274, 281 (3d Cir.2003) ("Under the Blockburger test, a court looks to the statutory elements of the crime charged to determine if there is any overlap."). We therefore conclude that Ball controls our analysis, and that possession of child pornography in violation of § 2252A(a)(5)(B) is a lesser-included offense of receipt of child pornography in violation of § 2252A(a)(2).

2.
Having concluded that §§ 2252A(a)(2) and 2252A(a)(5)(B) punish the same offense, triggering the presumption that "a legislature did not intend to impose two punishments for that offense," Rutledge, 517 U.S. at 297, 116 S.Ct. 1241, we next consider whether this presumption "must ... yield to a plainly expressed contrary view on the part of Congress." Garrett v. United States, 471 U.S. 773, 779, 105 S.Ct. 2407, 85 L.Ed.2d 764 (1985). No such view is discernible, in this case, from the language of § 2252A or the general descriptions of the statute's purpose contained in the Congressional reports. See, e.g., H.R.Rep. No. 104-863, at 28-34 (Conf. Rep.) (1996); see also H.R.Rep. No. 95-811, at 5-7, as reprinted in 1978 U.S.C.C.A.N. 69, 69-71 (Conf.Rep.) (1977) (addressing parallel provisions of § 2252A); S. Rep. 95-438, at 1-34, as reprinted in 1978 U.S.C.C.A.N. 40, 40-69 (1977) (same). Without evidence of such intent, we conclude that these provisions, which are part of a single statute, are "directed to similar, rather than separate, evils," Rutledge, 517 U.S. at 304 n. 14, 116 S.Ct. 1241 (discussing Ball). We therefore hold that the entry of separate convictions for the same offense under both § 2252A(a)(2) and § 2252A(a)(5)(B) contravenes the double jeopardy clause, and thus constitutes an error for the purpose of plain error review.


*73 B.
Having concluded (1) that the entry of separate convictions for counts one and four transgressed the double jeopardy clause, and thus constitutes an error, we turn to whether (2) that error is plain. In making this determination, we follow this court's analysis in United States v. Jackson, 443 F.3d 293 (3d Cir.2006). In Jackson, we held, as a matter of first impression for this circuit, that possession with intent to distribute cocaine base, in violation of 21 U.S.C. § 841(a)(1), is a lesser-included offense of possession with intent to distribute cocaine base within 1,000 feet of a school, in violation of 21 U.S.C. § 860(a). Reviewing the district court's entry of separate convictions for these offenses under the plain error rubric, we determined that, notwithstanding that the double jeopardy question had not previously been addressed by this court, the district court's error was plain. See 443 F.3d at 301.
We find that the error in this case is likewise plain. As addressed above, we hold that possessing child pornography is a lesser-included offense of receiving child pornography, and thus that §§ 2252A(a)(2) and 2252A(a)(5)(B) punish the same offense. Though we reach this conclusion as a matter of first impression, we do so on the basis of the Supreme Court's holding in Ball, which is well entrenched in our law and clear in its implications with respect to the double jeopardy question in this case. We therefore find that the error in entering separate convictions for counts one and four of Miller's superseding indictment is, indeed, plain.

C.
Having determined that (1) the entry of convictions under both statutes was error and (2) the error is plain, we now consider (3) whether that plain error "affected substantial rights." In Jackson, we held that the district court's entry of separate convictions for the same offense affected the defendant's substantial rights because "[t]he Fifth Amendment right to be free from duplicative prosecutions and punishment is a hallmark of American jurisprudence." 443 F.3d at 301. The Jackson court's observation is no less true with respect to the double jeopardy error in this case, and we therefore hold that Miller's substantial rights have been affected by the entry of separate convictions for counts one and four.

D.
Having considered three factors of plain error review, we now turn to the fourth factor  namely, whether the District Court's error "seriously affected the fairness, integrity, or public reputation of judicial proceedings." In Jackson, the court determined that, although the district court imposed concurrent sentences for the separate convictions, its entry of the convictions seriously affected the fairness of the sentencing proceeding because the defendant received two special assessments of $100 instead of one. See id. These monetary penalties are not the sole costs resulting from the entry of separate convictions, however. In Rutledge, the Supreme Court observed that, in considering whether the entry of separate convictions imposes multiple punishments, "`the potential adverse collateral consequences'" that inhere in each separate conviction "`may not be ignored.'" 517 U.S. at 302, 116 S.Ct. 1241 (quoting Ball, 470 U.S. at 865, 105 S.Ct. 1668).
The entry of separate convictions for violation of §§ 2252A(a)(2) and § 2252A(a)(5)(B) saddles the defendant with separate $100 special assessments and threatens him with "the potential adverse collateral consequences" of two convictions *74 on child pornography charges. We therefore hold that the entry of separate convictions for counts one and four of Miller's superseding indictment seriously affected the fairness of the District Court's proceedings. Accordingly, we conclude that, under the plain error standard, we may notice this double jeopardy error, and we turn to addressing the appropriate remedy.

E.
Where we conclude that a defendant was erroneously convicted for the same offense under two separate counts, but find the evidence sufficient to support either conviction, "the only remedy consistent with the congressional intent is for the District Court, where the sentencing responsibility resides, to exercise its discretion to vacate one of the underlying convictions." Ball, 470 U.S. at 864, 105 S.Ct. 1668. Accordingly, we will remand this case to the District Court for further appropriate proceedings.

V.
Miller also appeals the District Court's determination that he committed perjury in testifying to the nature of his adult pornography collection, which formed the basis of the District Court's addition of a two-level enhancement pursuant to U.S.S.G. § 3C1.1 (2003),[16] to his recommended Guidelines sentencing level. The District Court applied the enhancement based on the following colloquy, which took place during the government's cross-examination of Miller at trial:
Q. You do collect pornography, correct?
A. I had a small collection of adult pornography, yes. It was primarily Playboy images.
Q. What's that?
A. Primarily Playboy centerfolds.
Q. Primarily Playboy centerfolds?
A. Yes.
Q. Did you have sadomasochistic pictures?
A. Not that I'm aware of, no.
A. 311. The government then sought to introduce into evidence five images that were found on the zip disk containing child pornography. The images, which were of adults, were said by the government to be "sadomasochistic." The District Court excluded these images as unduly prejudicial under Fed.R.Evid. 403, and the government asked no further questions of Miller on this subject.[17] At a post-trial evidentiary hearing to address Miller's objections to the PSR, the government introduced the five images, and Agent Kyle provided detailed *75 descriptions of them. The District Court concluded from this evidence that the images "could fairly be described as sadomasochistic pornography," and that Miller's testimony that he was not aware of having any sadomasochistic images constituted perjury. A. 21.

A.
Section 3C1.1 of the 2003 version of the Guidelines provides for an enhancement if a defendant "willfully ... attempted to obstruct or impede, the administration of justice during the course of the ... prosecution" through conduct that is "related to (i) the defendant's offense of conviction and any relevant conduct; or (ii) a closely related offense...." U.S.S.G. § 3C1.1 (2003).[18] The commentary to § 3C1.1 instructs that it covers perjury. See U.S.S.G. § 3C1.1 cmt. n. 4 (2003). Writing for a unanimous Court in United States v. Dunnigan, 507 U.S. 87, 113 S.Ct. 1111, 122 L.Ed.2d 445 (1993), Justice Kennedy stated that: "In determining what constitutes perjury, we rely upon the definition that has gained general acceptance and common understanding under the federal criminal perjury statute, 18 U.S.C. § 1621." 507 U.S. at 94, 113 S.Ct. 1111. Accordingly, to trigger application of § 3C1.1 on perjury grounds, a defendant must give "false testimony concerning a material matter with the willful intent to provide false testimony...." Id.
Miller argues that his testimony as to his adult pornography collection was neither false nor material, and thus did not warrant a sentencing enhancement. We review the factual findings underlying the District Court's perjury determination for clear error, while exercising plenary review over the District Court's conclusions of law. See Grier, 475 F.3d at 561. In undertaking the review, we are guided by the precept, stated in the commentary to § 3C1.1, that the section "is not intended to punish a defendant for the exercise of constitutional right," and accordingly we are "cognizant that inaccurate testimony or statements sometimes may result from confusion, mistake, or faulty memory and, thus, not all inaccurate testimony or statements necessarily reflect a willful attempt to obstruct justice." U.S.S.G. § 3C1.1 cmt. n. 2 (2003).
Addressing this obligation, Dunnigan instructs that "if a defendant objects to a sentence enhancement resulting from her trial testimony, a district court must review the evidence and make independent findings necessary to establish a willful impediment or obstruction of justice, or an attempt to do the same, under the perjury definition we have set out." 507 U.S. at 95, 113 S.Ct. 1111. In doing so, "it is preferable for a district court to address each element of the alleged perjury in a separate and clear finding." Id.; cf. United States v. Boggi, 74 F.3d 470, 479 (3d Cir.1996) (upholding perjury determination that necessarily encompassed "all of the elements of perjury  falsity, materiality, and willfulness").
*76 Consistent with Dunnigan's instruction, the District Court made express findings as to each element of perjury. The District Court concluded that Miller possessed "images that could fairly be described as sadomasochistic pornography," and that Miller testified falsely in claiming that he was not aware of possessing "sadomasochistic pictures." The District Court further found that this testimony concerned a "material matter." A. 32. We separately address each finding.

B.
Miller does not directly challenge the District Court's factual determination that the zip disk containing child pornography also contained five images depicting adults "that could fairly be described as sadomasochistic pornography." We cannot conclude, based on the testimony in the record as to the content of the images, that this finding is clearly erroneous. However, Miller's testimony will support a sentencing enhancement for perjury only if he also gave willfully false testimony as to his understanding of the images. Thus, notwithstanding whether the images "could fairly be described as sadomasochistic pornography," the court must consider (a) whether Miller was both aware that he possessed the assertedly "sadomasochistic" images, and (b) whether Miller himself considered those images to be "sadomasochistic."

B.
Miller argues that the District Court had no valid basis for concluding that he gave willfully false testimony by saying  in response to the question "[d]id you have sadomasochistic pictures?"  "[n]ot that I'm aware of, no." The District Court found this testimony to be willfully false for the following reason: "The jury found Miller guilty of knowingly possessing child pornography. Since the zip disk containing the sadomasochistic pornography was knowingly in his possession, we are of the view that he knowingly possessed the images themselves." A. 31 (emphasis in original).
This recital is not, of itself, sufficient to support a finding that Miller gave willfully false testimony. "[I]n order to warrant the two point enhancement for obstruction of justice, the perjury of the defendant must ... be clearly established, and supported by evidence other than the jury's having disbelieved him ...." United States v. McLaughlin, 126 F.3d 130, 140 (3d Cir.1997) (emphasis in original) (quoting United States v. Colletti 984 F.2d 1339, 1348 (3d Cir.1992), abrogated on other grounds by United States v. Fiorelli, 133 F.3d 218, 222-23 (3d Cir.1998)).[19] Moreover, the jury's determination that Miller knowingly possessed child pornography does not, in light of the evidence, compel the inference that Miller knowingly *77 possessed each of the 1200-1400 images on the zip disk, as the government adduced no forensic testimony regarding images on the disk that depicted adults. We are thus bound to reject the District Court's inference, and consider whether the record can nevertheless support the District Court's "view that [Miller] knowingly possessed" sadomasochistic pictures.

1.
The District Court's finding that Miller gave willfully false testimony was predicated on Miller's answer to a single question at trial:
Q. Did you have sadomasochistic pictures?
A. Not that I'm aware of, no.
In evaluating whether this testimony can sustain a finding of perjury, we must consider whether, in the context of the defendant's testimony, the government's question is open to multiple interpretations.
"Precise questioning is imperative as a predicate for the offense of perjury." Bronston v. United States, 409 U.S. 352, 362, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973) (holding that a defendant's true, if misleading, testimony cannot support a conviction under the federal perjury statute). The Bronston Court stressed that it is incumbent on the government to examine a witness with the precision and thoroughness necessary to establish the elements of perjury:
[W]e perceive no reason why Congress would intend the drastic sanction of a perjury prosecution to cure a testimonial mishap that could readily have been reached with a single additional question by counsel alert  as every examiner ought to be  to the incongruity of petitioner's unresponsive answer. Under the pressures and tensions of interrogation, it is not uncommon for the most earnest witnesses to give answers that are not entirely responsive. Sometimes the witness does not understand the question, or may in an excess of caution or apprehension read too much or too little into it.... It is the responsibility of the lawyer to probe; testimonial interrogation, and cross-examination in particular, is a probing, prying, pressing form of inquiry. If a witness evades, it is the lawyer's responsibility to recognize the evasion and to bring the witness back to the mark, to flush out the whole truth with the tools of adversary examination.
409 U.S. at 358-59, 93 S.Ct. 595. In United States v. Serafini, 167 F.3d 812 (3d Cir.1999), we heeded this guidance and held that a perjury conviction under 18 U.S.C. § 1623 cannot be predicated on a response to a "fundamentally ambiguous" question. 167 F.3d at 820; see id. at 824 ("[L]ack of specificity [i]s a form of imprecision whose `consequences must be laid at the table of the questioner, not the questioned.'" (ellipses omitted) (quoting United States v. Sainz, 772 F.2d 559, 563 (9th Cir.1985))).
While our opinion in Serafini speaks to whether a question is so "fundamentally ambiguous" that it cannot be submitted to the jury as the basis for a finding of perjury, it compels us to consider whether, in the context of § 3C1.1, a question is sufficiently precise to support the factual findings made by the District Court. As the Tenth Circuit has stated: "The purpose of the rule of fundamental ambiguity is three-fold, namely, to (1) preclude convictions grounded on surmise or conjecture; (2) prevent witnesses from unfairly bearing the risks of inadequate examination; and (3) encourage witnesses to testify (or at least not discourage them from doing so)." United States v. Farmer, 137 F.3d 1265, 1269 (10th Cir.1998). This threefold purpose echoes the precepts that *78 guide our application of a sentencing enhancement for perjury: namely, that § 3C1.1 "is not intended to punish a defendant for the exercise of constitutional right," and that we must be "cognizant that inaccurate testimony or statements sometimes may result from confusion, mistake, or faulty memory and, thus, not all inaccurate testimony or statements necessarily reflect a willful attempt to obstruct justice." U.S.S.G. § 3C1.1 cmt. n. 2 (2003). Just as these concerns require district courts, in addressing a defendant's objections to a sentencing enhancement for perjury, to "make independent findings necessary to establish a willful impediment or obstruction of justice, or an attempt to do the same," Dunnigan, 507 U.S. at 95, 113 S.Ct. 1111, they oblige us to consider the clarity of the questioning that underlies the District Court's findings.

2.
In two respects, the question put to Miller, the answer to which the District Court found willfully false, lacked the precision adequate to support the District Court's finding. First, the government did not lay a suitable foundation for the question: "Did you have sadomasochistic pictures?" It is apparent that, in asking this question of Miller during cross-examination, the government sought to elicit testimony concerning five specific image files, depicting adults, that were found on a zip disk containing 1200-1400 image files. It does not appear that the government provided Miller with notice that it was these five images to which it was referring. The government proffered no testimony describing the image files, and was precluded from admitting the images themselves into evidence. Furthermore, the government made no effort to refresh Miller's recollection by showing him copies of the images (without introducing them into evidence). Without such a foundation, there is no basis for concluding that Miller was aware of which assertedly "sadomasochistic pictures" the prosecutor might have had in mind.
Second, even if Miller had been aware that he possessed the five image files to which the government was alluding, the government's questioning did not establish that he gave a willfully false answer by denying that he possessed "sadomasochistic pictures." The meaning of the term "sadomasochistic" is both contested and context-dependent. See, e.g., United States v. Turchen, 187 F.3d 735, 739 (7th Cir.1999) (endorsing district court approach of surveying the "ordinary and more clinically precise" meanings of "sadistic and masochistic conduct" before finding that material fit this description). The government made no attempt to probe Miller's understanding of the term. This omission is particularly significant in view of the government's failure to present Miller with copies of the five images that it subsequently contended to be "sadomasochistic." While we defer to the District Court's factual determination at the sentencing hearing that the images "could fairly be described as sadomasochistic pornography," this finding is not by itself controlling with respect to whether Miller gave willfully false testimony. The salient considerations, with respect to this inquiry, are whether, in undertaking to give a truthful answer to the question posed at trial, Miller (1) would necessarily have called to mind those five images, stored on a zip disk containing no fewer than 1200 images, that would have particularly engaged the government's attention as "sadomasochistic," and (2) would necessarily have acknowledged not merely that the images "could," as the District Court was later to say, "fairly be described as sadomasochistic," but that he, Miller, would, if *79 being truthful, acknowledge that the images were indeed "sadomasochistic."[20]
Because the government did not clarify what Miller understood the term "sadomasochistic" to mean, we have no basis for concluding whether Miller thought that he possessed "pictures" that would fit that description. Accordingly, we conclude that the government failed to engage in the "[p]recise questioning that Bronston holds to be "imperative as a predicate for the offense of perjury." 409 U.S. at 362, 93 S.Ct. 595. Miller's response to the government's questioning cannot, therefore, support the District Court's determination that Miller gave willfully false testimony as to whether he was aware that he possessed "sadomasochistic pictures."

D.
Miller also argues that the District Court erred in finding that his allegedly false testimony concerned a "material matter." We exercise plenary review over this determination, as it involves a mixed question of law and fact. See United States v. Gaudin, 515 U.S. 506, 511-22, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995);[21]United States v. Kiam, 432 F.3d 524, 527 (3d Cir.2006) ("Our review of legal rulings and mixed questions of law and fact is plenary."). The commentary to § 3C1.1 provides that a "material" statement, "as used in th[e] section," is a statement that, "if believed, would tend to influence or affect the issue under determination." This guidance meshes with the restriction that § 3C1.1 may be applied only to "obstructive conduct related to (i) the defendant's offense of conviction and any relevant conduct; or (ii) a closely related offense." U.S.S.G. § 3C1.1 (2003). Accordingly, in harmony with many of our sister circuits,[22] we apply the commentary's definition of "material" in determining whether the materiality element of perjury has been established for the purpose of a sentencing enhancement.
*80 The five assertedly "sadomasochistic" images that underlie the District Court's perjury determination feature adults. The District Court nevertheless concluded that the testimony was material to Miller's offense for the following reason:
There is a significant distinction to be drawn between a collection of Playboy images and a collection of pornography which includes images of women being raped and tortured. The images in a collection obviously reflect the collector's preferences and interests. A collection entirely comprised of Playboy centerfolds may be viewed as more acceptable or "mainstream." A collection which includes sadomasochistic pornography may well reflect interests in more deviant sexual practices, or at least in other images depicting such conduct.
A. 31. Therefore, the District Court concluded, Miller's testimony "constitutes false testimony on a material matter. His statement, if believed by the jury, would have influenced or affected their resolution of the offense charged in count 1 of the indictment...." A. 32.
Two appellate courts have confronted a similar question, in the context of determining the propriety of admitted evidence, and concluded that a defendant's interest in unusual adult pornography is irrelevant to whether he is guilty of a child pornography count. In United States v. Harvey, 991 F.2d 981 (2d Cir.1993), the court held that, because they were irrelevant, videos depicting adults "performing gross acts involving human waste, and people engaging in bestiality and sadomasochism," 991 F.2d at 996, were inadmissible as evidence that a defendant received child pornography:
The ... X-rated material, which did not involve either child pornography or simulated child pornography, did not bear on the disputed trial issues, and thus was not relevant. See Fed.R.Evid. 401 and 402[. (providing that "evidence which is not relevant is not admissible")].... The[ ] questions and the answers [regarding the videos] concerned material for which Harvey was not being prosecuted and that did not bear on the disputed trial issues. We have little difficulty in concluding that the likely effect of this evidence was to create disgust and antagonism toward Harvey, and resulted in overwhelming prejudice against him.
Id.
The Fifth Circuit drew upon this holding to conclude, in Ward v. Dretke, 420 F.3d 479 (5th Cir.2005),[23] that images depicting adults engaging in bestiality, which were stored on a defendant's computer along with child pornography, were irrelevant to a "sentencing jury's" assessment of a defendant's *81 culpability for possessing child pornography:
We can identify no objectively reasonable basis in this case for permitting the sentencing jury to view the images of adult bestiality. The images did not form part of the factual basis for the charges to which Ward plead guilty, and had no relevance to the jury's sentencing determination apart from demonstrating the depths of depravity to which Ward had sunk. Even if the evidence were relevant in some tangential way to the determination of Ward's sentence, we believe it highly probable that considerations of unfair prejudice would have sufficed to keep this evidence from the jury.
Id. at 494-95 (citing Harvey, 991 F.2d at 995-96).
We agree with the Harvey and Ward analyses, and find them relevant to whether testimony regarding a defendant's interest in adult pornography is "related to [] the defendant's offense" of child pornography "and any relevant conduct." U.S.S.G. § 3C1.1 (2003). As the District Court did not point to any empirical or theoretical grounds for its conclusion, and we cannot identify such grounds, we follow the reasoning of the Harvey and Ward courts and reject the proposition that a defendant's taste for an unusual genre of adult pornography is material to his interest in child pornography. We are therefore of the view that the District Court erred in finding that Miller gave false testimony on a material matter.

E.
In summary, we hold that the record does not support the District Court's determination that (a) Miller's testimony, with respect to the assertedly "sadomasochistic pictures," was willfully false, or (b) the testimony was material. Accordingly, we conclude that it was error to find that Miller committed perjury and, on that ground, to add to the Guideline calculation of Miller's sentence an enhancement for obstruction of justice.

VI.
For the foregoing reasons, we will VACATE the District Court's Judgment and Commitment Order, and will REMAND the case for further proceedings in accordance with this Opinion.
RENDELL, Circuit Judge, Concurring in Part and Dissenting in Part.
While the majority opinion goes to great lengths to point out the distinction between knowing receipt and knowing possession of child pornography, and that proof of the latter is not enough to satisfy the former, I suggest that the only proof adduced by the Government here is of the latter. There is simply no non-speculative evidence that would tend to show, let alone prove beyond a reasonable doubt, that Miller received the eleven images  out of the 1200-1400 total on the zip disk  knowing that they were child pornography. Perhaps there is enough from which the jury could infer his knowing possession  because the images were on a password-protected zip disk that he acknowledged was his. However, without any evidence whatsoever that would point to how he accessed or obtained the child pornography images, let alone any evidence tending to show that he was or should have been aware of what they were at the time he took possession of them, I suggest that a jury could not properly find knowing receipt.
Knowing receipt is a much more serious crime than knowing possession. Generally, it carries with it a five-year minimum sentence and a twenty-year maximum, while knowing possession has no statutory minimum and the maximum sentence is ten years. See 18 U.S.C. § 2252A(b). Inferring "knowing receipt" from (a) the *82 presence of the images on the zip disk, and (b) the differing "copied" dates requires too great a leap. When combined with the burden of proof beyond a reasonable doubt, it strains credulity.
There were at least 1200 images on the zip disk and the Government only characterized twenty-less than 2%  of them as child pornography.[1] Thirteen of the twenty images were created on October 13, 2002, one on October 29, 2002, five on December 17, 2002, and one on December 20, 2002. It should be noted that the thirteen copied on October 13 were among 586 image files copied to the zip disk over a seven-hour period, at intervals suggesting they were copied automatically. (The record before us does not indicate how many total images were copied on the three dates other than October 13.) Further, the District Court determined that only eleven of the twenty images put forth by the Government  less than 1% of all of the images on the zip disk  constituted child pornography.
Given the amazing capabilities of technology to trace and find, backtrack and connect, so as to prove the source and path of computer-generated and-transmitted data, the sheer inability of the Government to posit a non-speculative explanation as to how these images came to be on the zip disk, let alone prove they were "knowingly received" by Miller is, to me, striking.
I would REVERSE the jury verdict as to knowing receipt and REMAND for resentencing on the possession charge.[2]
NOTES
[*]  Honorable Louis H. Pollak, District Judge for the United States District Court of the Eastern District of Pennsylvania, sitting by designation.
[1]  A "zip disk" is a portable storage device that looks similar to a conventional 3.5-inch "floppy" disk, but has significantly greater storage capacity than a floppy disk. A zip disk may be used on a computer equipped with a "zip drive."
[2]  The PSR recommended an enhancement for possessing pornographic material depicting children who are prepubescent or under twelve years of age. The District Court determined that the government had failed to prove by a preponderance of the evidence that there was a factual basis for this enhancement.
[3]  The District Court applied the 2003 version of the Guidelines, which was effective at the time of the offenses charged in counts one and four of the superseding indictment, rather than the 2006 version of the Guidelines, which was effective at the time of Miller's sentencing.
[4]  The "PROTECT Act of 2003" amended § 2252A to impose a prison sentence of "not less than 5 years" for violations of § 2252A(a)(2), which previously carried no statutory minimum. See H.R.Rep. No. 108-66, at 50-51 (2003) (Conf.Rep.), as reprinted in 2003 U.S.C.C.A.N. 683, 685. The Act became effective after the dates charged in count one of Miller's superseding indictment, and it was therefore inapplicable to Miller's offense.
[5]  A number of years ago, this court held that a finding of perjury, for purposes of sentencing, must be supported by "clear and convincing" evidence. See United States v. Arnold, 106 F.3d 37, 43-44 (3d Cir.1997). But that holding was based on language in the commentary to U.S.S.G. § 3C1.1 that has since been revised. Arnold's holding has thus been abrogated and, as we recognized in United States v. Johnson in addressing a sentencing enhancement for perjury, "the facts underlying a sentencing enhancement need only be proven by a preponderance of the evidence." 302 F.3d 139, 154 (3d Cir.2002).
[6]  The Castro-Lara court stated its position as follows:

We feel confident that Rule 29(c) means precisely what it says. Consequently, even absent any motion for judgment of acquittal at trial, a defendant who files a timeous post-trial motion for acquittal stands on the same footing as a defendant who moves for acquittal at the close of all the evidence; and the former is, therefore, entitled to the benefit of the same standard of appellate review as the latter.
970 F.2d at 980
[7]  The government cites cases from two other circuits that, it contends, support its position. See United States v. Chance, 306 F.3d 356, 368-69 (6th Cir.2002); United States v. Ward, 914 F.2d 1340, 1346 (9th Cir.1990). The government is correct that these courts stated, respectively, that a sufficiency-of-the-evidence claim is waived "if the defendant failed to make a Rule 29 motion for judgment of acquittal at the end of the prosecution's case-in-chief and at the close of the evidence," Chance, 306 F.3d at 368, and that "[i]n order to preserve this issue on appeal, the defendant must move for a judgment of acquittal during the trial pursuant to Fed.R.Crim.P. 29(a)." Ward, 914 F.2d at 1346. However, neither of these courts clarified whether the defendant had filed a Rule 29(c) motion. The Sixth Circuit, in cases decided before Chance, had exercised plenary review over sufficiency-of-the-evidence claims preserved by a Rule 29(c) motion without stating whether the defendant had filed a Rule 29(a) motion. See United States v. Al-Zubaidy, 283 F.3d 804, 808 (6th Cir.2002); United States v. Wuliger, 981 F.2d 1497, 1509 (6th Cir.1992). The Sixth Circuit's practice following Chance appears to be unclear. See, e.g., United States v. Davis, 473 F.3d 680 (6th Cir.2007) (addressing commerce clause argument raised in Rule 29(c) motion without specifying the standard of review, but stating that it exercised plain error review over separate commerce clause argument that was not raised in Rule 29(c) motion). The Ninth Circuit, in a case following Ward, exercised plenary review over an argument raised in a Rule 29(c) motion without stating whether it had earlier been raised in a Rule 29(a) motion. See United States v. Garcia, 497 F.3d 964, 967 (9th Cir.2007).
[8]  Both the government's expert, Agent Donald J. Price, an FBI forensic analyst, and the defendant's expert, John R. Smith, owner of a business that configures and supports computer networks, acknowledged the possibility that child pornography could be unknowingly downloaded onto a hard drive as the result of a virus, or "spyware." They disagreed, however, as to whether it was likely that this possibility occurred in Miller's case. Agent Price testified that he was unaware of there ever being, in the prosecutor's words, "any reports of a child porn dropping virus." A. 286. Smith demonstrated how an image could be inadvertently downloaded onto a computer. Though Agent Price testified that he had not heard of a "virus program capable" of accounting for Miller's possession of the images, he went on to explain that such a virus would have to "take the zip diskette out of the case, put it into the computer ..., take the zip out, put it back in the case and delete the original images off the computer." A. 285-86, 382.
[9]  See also John Schwartz, Acquitted Man Says Virus Put Pornography on Computer, N.Y. Times, August 11, 2003 (quoting, Mark Rasch, former head of U.S. Department of Justice's computer crimes unit, as stating, with respect to defense in British case that virus downloaded child pornography, "[t]he scary thing is that the defense might be right").
[10]  The jurisprudence concerning the receipt and possession provisions of 18 U.S.C. § 2252 and the comparable provisions of 18 U.S.C. § 2252A often converges. Section 2252(a)(2) prohibits the receipt of material "transported [in interstate or foreign commerce] by any means including by computer" that depicts "a minor engaging in sexually explicit conduct," and § 2252(a)(4)(B) prohibits the possession of such material. These statutory provisions have been characterized as "materially identical" to § 2252A(a)(2) and § 2252A(5)(B), which, respectively, prohibit the receipt and possession of child pornography. United States v. Malik, 385 F.3d 758, 760 (7th Cir. 2004) (relying on Myers in holding that possession and receipt of child pornography in violation of § 2252A are distinct offenses).
[11]  These file dates were October 13, 2002 (ten images); October 29, 2002 (one image); December 17, 2002 (five images); and December 20, 2002 (one image).
[12]  Agent Price testified, however, that the images may have been downloaded directly onto the zip disk from the internet without first being stored on the computer's hard drive, or may simply have been downloaded off of the hard drive of some other computer. Moreover, Agent Price testified, even if the files had, at one point, been downloaded onto the hard drive of Miller's computer, they would not have been found by the FBI's forensic software if the computer's operating system, Microsoft Windows, had "overwritten" the files, after they were deleted, with newer files. A. 301. According to Agent Price, Microsoft Windows overwrites deleted files on a continual basis to avoid "fragmenting" the hard drive with gaps of free space that are clustered between other files, and thus unusable for storage.

Smith, the defendant's expert, spoke to this testimony. Smith testified that two-thirds of the hard drive on Miller's basement computer was unused, and consequently that the computer's operating system (Microsoft Windows) was unlikely to have overwritten any files. Agent Price does not appear to have addressed this evaluation in his rebuttal to Smith's testimony.
[13]  Specifically, the "dates written" of three of the images on the zip disk, all of which the District Court found to be child pornography, are subsequent to the date they were copied onto the disk (i.e. the images' "dates created").
[14]  Judge Becker also recognized two other core functions of the rule against variance: (1) it "protects the right of each defendant not to be tried en masse for the conglomeration of distinct and separate offenses committed by others" and (2) "helps to minimize the danger that the defendant may be prosecuted a second time for the same offense." Schurr, 775 F.2d at 553 (internal quotations omitted). While a double jeopardy concern is raised by Miller's conviction on separate counts of knowing and possessing child pornography, that issue is unrelated to Miller's variance claim.
[15]  The Oxford English Dictionary (2d ed.1989) defines "receive" as "[t]o take in one's hand, or into one's possession (something held out or offered by another); to take delivery of (a thing) from another, either for oneself or for a third party."
[16]  Miller's presentence investigation report also recommended the obstruction of justice enhancement on the basis that Miller gave perjured testimony regarding the marijuana he was found to have possessed. The District Court rejected this recommendation.
[17]  During Miller's cross-examination, the government made two requests to introduce the images. When its first request was denied, the government stated an intention to reintroduce the images in its rebuttal, and the District Court said it would consider the request at that time. When the government made its second request during Miller's cross-examination, shortly following its first request, Miller's counsel said that he would not object to the government's introduction of "non-prejudicial adult pornography" to impeach Miller's testimony, but that he objected to the admission of images of an extremely prejudicial nature that "are not indicative of the majority of the images" on the zip disk. A. 317. Despite this concession, the government did not seek to introduce any other images to impeach Miller's testimony. It did, however, elicit testimony from Smith, Miller's expert, that he found images on the disk that he considered to depict sadomasochistic pornography.
[18]  As noted above, the District Court applied the 2003 version of Guidelines, which was in effect at the time of Miller's offense. The 2003 version of § 3C1.1 states:

If (A) the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the course of the investigation, prosecution, or sentencing of the instant offense of conviction, and (B) the obstructive conduct related to (i) the defendant's offense of conviction and any relevant conduct; or (ii) a closely related offense, increase the offense level by 2 levels.
U.S.S.G. § 3C1.1 (2003). The provision was revised in 2006 to punish obstructing the administration of justice "with respect to," rather than "during the course of" the prosecution.
[19]  The above-quoted McLaughlin-sentence reads, in full:

[I]n order to warrant the two point enhancement for obstruction of justice, the perjury of the defendant must not only be clearly established, and supported by evidence other than the jury's having disbelieved him, but also must be sufficiently farreaching as to impose some incremental burdens upon the government, either in investigation or proof, which would not have been necessary but for the perjury. McLaughlin, 126 F.3d at 140 (emphasis and alteration in original) (quoting Colletti, 984 F.2d at 1348). In Fiorelli, the court affirmed that a jury's verdict cannot itself support a finding of perjury. However, it rejected, as dictum, the proposition that a false and material statement must impose an incremental burden on the government. See 133 F.3d at 222-23.
[20]  The government argues, without proffering a definition for the term "sadomasochistic," that the brutality of the images in question is so manifest that any truthful viewer would find the term to be descriptively correct. However, in concluding that the images "could fairly be described as sadomasochistic," the District Court did not find that any truthful viewer would necessarily describe them as such, an undertaking that would warrant consideration of popular understandings of the term "sadomasochism." See, e.g., Turchen, 187 F.3d at 739. We may not augment the District Court's findings.
[21]  Just over thirty years ago, in United States v. Crocker, 568 F.2d 1049, 1056 (3d Cir.1977), we ruled that "both under the perjury statute, 18 U.S.C. § 1621, and under the false declarations statute, 18 U.S.C. § 1623, materiality is an essential element of the offense and a question of law reserved for decision by the court." But Crocker has been overtaken by Gaudin, in which the Supreme Court held that, because materiality is an essential element of perjury, it must be decided by the trier of fact. See 515 U.S. at 511-22, 115 S.Ct. 2310. The elements of perjury for the purpose of § 3C1.1 are the same as those under the perjury statute, § 1621, see Dunnigan, 507 U.S. at 94, 113 S.Ct. 1111, and we consequently treat materiality as a mixed question of law and fact, which we continue to review de novo.
[22]  See United States v. Thundershield, 474 F.3d 503, 508 (8th Cir.2007), United States v. Salazar-Samaniega, 361 F.3d 1271, 1275 (10th Cir.2004); United States v. Quinn, 359 F.3d 666, 681 (4th Cir.2004); United States v. Owens, 308 F.3d 791, 795 (7th Cir.2002); United States v. Singh, 291 F.3d 756, 762-63 (11th Cir.2002); United States v. Ahmad, 202 F.3d 588, 593 (2d Cir.2000); United States v. Haas, 171 F.3d 259, 268 (5th Cir.1999); United States v. Jones, 159 F.3d 969, 980-81 (6th Cir.1998); Cf. United States v. Fox, 393 F.3d 52, 61 n. 9 (1st Cir.2004) (finding testimony material where it tended to undermine the credibility of law enforcement officer testifying against defendant), vacated on other grounds, 545 U.S. 1125, 125 S.Ct. 2949, 162 L.Ed.2d 864 (2005).
[23]  In Ward, a habeas petitioner, when he was a defendant in Texas state court, pled guilty to charges including possession of child pornography, and elected to have a jury determine his sentence. The jury sentenced the defendant-petitioner to 66 years' imprisonment. The district court found that the petitioner received ineffective assistance of counsel at the punishment trial. The Fifth Circuit reviewed this determination under AEDPA's constraint that a state court determination may be reversed only if it "involved an unreasonable application of[ ] clearly established Federal law...." 28 U.S.C. § 2254(d)(1). Bound by this constraint, the Fifth Circuit concluded that the state court did not unreasonably apply the second prong of the "performance and prejudice" test, as set forth in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), in concluding that the petitioner was not prejudiced by the failures of his counsel. The Fifth Circuit did find, however, that, with respect to the first prong of Strickland, the performance of petitioner's counsel was constitutionally deficient. This finding was based, in part, on counsel's failure to object to the admission, at the sentencing trial, of images depicting adults engaging in bestiality.
[1]  The Government's expert did not even know the total number of images on the zip disk, testifying that there were between 1200 and 1400. The defendant's expert testified that there were 1373.
[2]  I do agree with the majority that the perjury enhancement was improperly applied and that the knowing possession of child pornography is a lesser-included offense of the knowing receipt of child pornography.
