
612 F.3d 450 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Andrew SIEMASZKO, Defendant-Appellant.
No. 09-3167.
United States Court of Appeals, Sixth Circuit.
Argued: January 19, 2010.
Decided and Filed: July 15, 2010.
*452 ARGUED: Billie Pirner Garde, Clifford & Garde, LLP, Washington, D.C., for Appellant. John L. Smeltzer, United States Department of Justice, Washington, D.C., for Appellee. ON BRIEF: Billie Pirner Garde, Clifford & Garde, LLP, Washington, D.C., Charles M. Boss, Boss & Vitou Co., LPA, Maumee, Ohio, for Appellant. John L. Smeltzer, United States Department of Justice, Washington, D.C., for Appellee.
Before: MERRITT, GIBBONS, and ROGERS, Circuit Judges.

OPINION
JULIA SMITH GIBBONS, Circuit Judge.
Defendant-appellant Andrew Siemaszko appeals his conviction on three counts of concealing material facts and making false statements to the Nuclear Regulatory Commission ("NRC") in violation of 18 U.S.C. §§ 1001 and 2. On appeal, Siemaszko argues that there was insufficient evidence to support his convictions and that the government's presentation of evidence and an improper jury instruction constructively amended the indictment. For the following reasons, we find that there was sufficient evidence to support each of Siemaszko's convictions and that Siemaszko failed to establish that a constructive *453 amendment of the indictment occurred. Therefore, we affirm.

I. Factual and Procedural Background
This case arises out of an incident that occurred in 2001 at the Davis-Besse Nuclear Power Station ("Davis-Besse" or "the plant"), which is located on the shores of Lake Erie near Toledo, Ohio, and is owned and operated by FirstEnergy Nuclear Operating Company ("FENOC"). Siemaszko began work at the plant in 1999 as the systems engineer in charge of reactor coolant systems. After a safety incident at a similar plant prompted the NRC to require inspections at all like plants by the end of 2001, FENOC successfully petitioned the NRC to permit Davis-Besse to operate without interruption and thus delay inspection until a scheduled refueling shutdown in spring 2002. Siemaszko's involvement in preparing the documents that Davis-Besse submitted to the NRC in furtherance of the delayed inspection gave rise to his indictment on and subsequent conviction of three counts of concealing a material fact and making false statements to a United States agency. During the delayed inspection, Davis-Besse found five cracked nozzle heads and a football-sized cavity caused by boric acid erosion in the head of the reactor. The finding prompted NRC investigations into previous plant inspections and, eventually, the prosecution of Siemaszko.

A. Davis-Besse Nuclear Power Station
Davis-Besse is a two-loop, pressurized water reactor that is composed of a large cylindrical chamber filled with coolant water ("the Reactor Pressure Vessel" or "RPV"). Uranium rods at the core of the vessel fuel the nuclear reaction that heats the coolant water. The nuclear reaction is controlled by introducing boric acid and/or control rods into the reactor vessel. The control rods are inserted through sixty-nine penetration nozzles (tubes that are approximately four inches in diameter) that penetrate through the head of the reactor (approximately ten feet in diameter) into the reactor chamber. There is a gap between the RPV head and reflective metal insulation that encloses closure flanges and studs. The gap is narrowest at the top of the head, where it is only two inches wide. Control rod drive mechanisms ("CRDMs") allow the operators to lower the control rods into the reactor to control the rate of the nuclear reaction, and, thus, the energy output. The nozzles are welded onto the vessel head using a J-groove on the underside of the steel head, which is 6.5 inches thick.
The internal walls of the RPV and the underside of the RPV head are covered in non-corrodible stainless steel, but the RPV and the external components are made of carbon steel, which is corrodible by the boric acid in the coolant water if it escapes the RPV. This can happen when the coolant water leaks through the flanges that connect the CRDMs to the nozzles above the RPV head. Davis-Besse had a history of flange leakage and developed the Boric Acid Corrosion Control Procedure ("BACCP"), which it implements during inspections, to address this problem.
Davis-Besse operates in two-year fuel cycles and, therefore, shuts down the reactor only during the biennial refueling outages ("RFOs"). Davis-Besse was scheduled to conduct RFO13 (the thirteenth RFO conducted at Davis-Besse) in April 2002. In addition to permitting refueling, the RFOs are the primary opportunity for inspections and maintenance that cannot occur while the reactor is in operation. The RFOs at issue in this case are RFO 10 (1996), RFO 11 (1998), and RFO 12 (2000). During an RFO, in order to visually inspect the nozzles and the RPV head, operators *454 must insert a camera through a series of eighteen "weep holes" that are five by seven inches in size and that line the bottom of the RPV head above the head flange connecting the RPV head to the RPV. Because of the limited accessibility of the camera, it is impossible to visually inspect the very top of the RPV head and the nozzles located there. Siemaszko was in charge of inspecting and cleaning the RPV head during RFO12 in 2000, but was not present during the RFOs in 1996 and 1998. Prasoon Goyal, another engineer at Davis-Besse, oversaw this task during RFO10 in 1996 and reviewed the inspection reports following RFO11 and RFO 12. Another engineer, Peter Mainhardt, supervised inspection and cleaning during RFO11 in 1998. As of 2001, Goyal continued to work at Davis-Besse as an engineer, and Mainhardt worked for FENOC as an independent contractor preparing for RFO 13.
The 1996 RPV head inspection lasted only one hour due to limitations on the technicians' exposure to radiation. During that inspection, Goyal directed two technicians who were moving a camera on a pole across the vessel head. He watched on a monitor and narrated the camera location based on the "stud hole" numbers (the numbers on the studs between the weep holes). The nozzles are not numbered, so this is the only way to determine and document the condition of each nozzle based on the camera visual. Ed Chimahusky, a systems engineer in charge of coolant systems from 1991 to 1997, testified at Siemaszko's trial that by using a camera through the weep holes, "[i]f you did the best you could, you could probably look at ... 70 percent of [the RPV head]." Goyal, in testimony and in a Potential Condition Adverse to Quality report ("PCAQ") submitted to superiors after RFO 10, estimated that he was able to inspect fifty or sixty percent of the head area in 1996 and noted that it was difficult to estimate the amount of boron deposits on the head because of the limited visual inspection. In his PCAQ, Goyal attributed the boron deposits to flange leaks. The PCAQ also noted several deposits ranging in color from white to brown to rust. In both the PCAQ and in testimony, Goyal noted that the boron deposits and limited visual access prevented full implementation of the BACCP. Consequently, in the PCAQ, Goyal suggested modifications to the RPV head that would permit better access, such as installing access doors. The modifications were never made.
Mainhardt conducted a similar inspection with the help of technicians during RFO 11 in 1998. He testified that he found "[l]ots of flakes [of boric acid], ... also some fist-sized clumps ... which would be particles all stuck together," "one area that kind of was pasty looking, ... maybe like a paste that hardened there," and "some streaks on the control ride drive tubes [and around cracks in the insulation at the top of the head] that looked like milk." Goyal reviewed Mainhardt's PCAQ report and again faulted flange leaks with causing the boron deposits. The RFO11 PCAQ, signed by Goyal, stated that "most of the head area was covered with an uneven layer of boric acid along with some large lumps of boric acid." That PCAQ referred back to the RFO 10 PCAQ and the need for corrective action. The 1998 PCAQ also stated that "[t]he reactor vessel head was cleaned as best as we can" and noted that the cleaning was video recorded.
Siemaszko conducted RFO 12's RPV head cleaning after attending a training session on BACCP. Mainhardt, who inspected the outside of the RPV head personally, stated that there were "heavy streams of red/brown boric acid ... stream[ing] out of the [weep] holes" and *455 submitted photographs ("the red photographs") and a PCAQ to his supervisors and, he alleges, to the NRC's resident inspector (who did not recall receiving it). The deposits prevented insertion of the camera into five of the weep holes and visually impaired inspection through other weep holes. The deposits also required more elaborate cleaning maneuvers than previous inspections, which had used a vacuum cleaner to remove boron deposits. In 2000, Siemaszko directed the technicians to spray hot, distilled water onto the RPV head to loosen the deposits and to use bars to knock off chunks of deposits and to flush them out through the weep holes. One of the members of the cleaning crew testified that they "[g]ot what [they] could get removed" but that deposits remained on the RPV head. Greg Gibbs, a consultant brought to Davis-Besse to prepare for RFO13, reviewed the cleaning tapes of RFO12 and testified that, although "the areas on the curvature of the hemispherical head were essentially cleaned, ... as you got up near the top, there were large significant accumulations of boric acid near the top center of the head." Gibbs noted that, in parts, there were crystals that "were almost solid and almost touching the mirror insulation, so you had ... areas there at the top of the head that were just entirely covered with boric acid." Despite the incomplete cleaning during RFO12, an industry magazine congratulated Siemaszko on removing the deposits. However, Siemaszko later admitted to Goyal that the cleaning had been incomplete at the top of the head. The RFO 12 PCAQ again attributed the increased boron accumulation to flange leakage.
In a 2000 PCAQ, Siemaszko noted that the RPV head should be "free of boron deposits" to adequately inspect the nozzles in accordance with an NRC letter requiring plants to inspect the CRDMs adequately. Siemaszko put the RPV head on a restraint that required action before the plant was put back into operation. His supervisor, David Geisen, removed the restraint, however, stating that the RPV head would be cleaned of all boron deposits before it was put online. It was not.

B. NRC Bulletin 2001-01
In 2001, small "popcorn" deposits of boric acid were found at the nozzle penetrations of the reactor at the Oconee Nuclear Station in South Carolina, a nuclear plant of similar design to Davis-Besse. Earlier cracks had been lengthwise, but the 2001 cracks were circumferential (around the nozzle), and above the J-groove weld and within the "pressure boundary." This posed a risk that the nozzle would blow out of the vessel head and cause significant loss of coolant and structural threats, including possible plant safety failure. In the early 1990s, the NRC determined that nozzles were susceptible to "stress corrosion cracking" on the nozzles and on the welding but determined that the cracks did not pose an imminent safety threat because the NRC presumed that any leakage would be readily apparent before threatening the structural integrity of the reactor or catastrophic failure. The leakages occur when coolant escapes the containment vessel within the reactor and either exits the reactor or comes into contact with the hot vessel head. The result is that the coolant flashes to steam and the boric acid within the coolant fluid is left as a deposit on the reactor head near the leak. In 1997, the NRC advised licensees of this type of reactor to develop programs to periodically inspect the vessel head penetrations and look for cracks, but, because it was not yet aware of the problem, did not warn about the link between popcorn deposits and circumferential cracking.
*456 In light of the Oconee incident and similar experiences in the French nuclear industry, on August 3, 2001, the NRC issued NRC Bulletin 2001-01 ("NRC 2001-01" or "the Bulletin"), entitled "Circumferential Cracking of Reactor Pressure Vessel Head Penetration Nozzles." The Bulletin outlined which plants had a "high susceptibility" to nozzle stress cracking, and the NRC's criteria indicated that Davis-Besse was among them. The Bulletin also requested information from affected nuclear power stations such as Davis-Besse. The Bulletin stated that such plants "need to use a qualified visual examination of 100% of the ... nozzles," that the inspection "should be able to reliably detect and accurately characterize leakage from cracking," and that "the effectiveness of the ... examination should not be compromised by the presence of insulation, existing deposits on the RPV head, or other factors that could interfere with the detection of leakage." Due to the risks, the NRC wanted all high-risk plants such as Davis-Besse to shut down and conduct a complete inspection for nozzle cracks by December 31, 2001. Because of the costs involved in an early and unscheduled shutdown, Davis-Besse wanted to continue operation until its scheduled RFO13 in April 2002.
The Bulletin required plants to provide detailed information about susceptibility to cracking and previous inspections within thirty days. As part of that information, the NRC directed high-risk plants that, "[i]f [the plant's] future inspection plans do not include performing inspections before December 31, 2001, [the plant must] provide [the] basis for concluding that the regulatory requirements discussed in the Applicable Regulatory Requirements section will continue to be met until the inspections are performed." Section 1.d. required all such plants to provide:
[A] description of the [vessel head penetration] nozzle and RPV head inspections (type, scope, qualification requirements, and acceptance criteria) that have been performed at your plant(s) in the past 4 years, and the findings. Include a description of any limitations (insulation or other impediments) to accessibility of the bare metal of the RPV head for visual examinations.

C. Davis-Besse's Submissions to the NRC
In accordance with federal regulations governing the nuclear industry, Davis-Besse was obligated to respond to the NRC Bulletin with "written statements, signed under oath or affirmation." 10 C.F.R. § 50.54(f); see also 42 U.S.C. § 2011 et seq. Federal regulations also require that all information provided to the NRC "be complete and accurate in all material respects." 10 C.F.R. § 50.9(a). Davis-Besse hired Rodney Cook to coordinate the response to NRC 2001-01. Between September 4 and November 30, 2001, FENOC submitted a series of serial letters ("SLs") containing the information requested in the Bulletin. Various conference calls and meetings between FENOC employees and the NRC also took place between September 4 and December 4, 2001, when the NRC finally permitted Davis-Besse to continue operation until an accelerated shutdown for RFO13 in February 2002. The five letters at issue in this case and charged to contain false statements in the indictment against Siemaszko, Geisen, and Cook are: SL 2731, September 4, 2001 (count 1); SL 2735, October 17, 2001 (count 2); SL 2741, October 30, 2001 (count 3); SL 2744, October 30, 2001 (count 4); and SL 2745, November 1, 2001 (count 5). Count 1 also included allegations of concealment of material facts in several of the serial letters and meetings between FENOC and the NRC. Siemaszko *457 was convicted of the first, second, and fifth counts of the indictment.
In approving Davis-Besse's continued operation until RFO13, the NRC relied on all of the serial letters:
Based on the information provided in your responses [dated September 4, 2001, as supplemented by letters dated October 17, October 30, November 1, and November 30, 2001] and the information available to the staff regarding the industry experience with VHP nozzle cracking, the staff finds that you have provided sufficient information to justify operation until February 16, 2002, at which time you will shut down the [plant] ... and perform VHP nozzle inspections as discussed in your letter dated November 30, 2001. The commitments contained in your letter dated November 30, 2001, were integral to the staff's finding.
The serial letter submitted on November 30, 2001, SL 2747, was not readily discoverable in the record.
FENOC's first submission to the NRC in response to NRC 2001-01 was SL 2731 on September 4, 2001. Siemaszko was tasked with reviewing the inspection tapes from previous RFOs and providing information for NRC 2001-01's section 1.d. inquiry, Cook was in charge of putting together the information, and Goyal was to review the submission. Siemaszko sent a draft of the section to Goyal, who returned comments on August 9, 2001. In that draft, Siemaszko prefaced his response with: "The response is limited in scope to discuss the issues associate [sic] with the type, scope, qualification requirements, and acceptance criteria for the Reactor Pressure Vessel Head Inspections within the last 4 years." The draft stated, inter alia, that a guidance procedure other than BACCP was used in RFO 11 and RFO12, that "[t]he head cleaning was limited by the opening size of the weep holes," and that, during RFO12, "[n]o evidence of nozzle leakage was detected. 95% of the nozzles were inspected." Goyal questioned the ninety-five-percent assertion given the amount of boron visible on the top of the RPV head during RFO12, and Siemaszko subsequently sent another draft asserting that "[n]o visible evidence of nozzle leakage was detected[, m]ajority of nozzles were inspected," and stating that the procedure used was the BACCP. Later, after Cook questioned the meaning of "majority," Siemaszko stated that ninety percent of the nozzles had been inspected. Drafts circulated to Siemaszko on August 22 and 23, 2001, contained a ninety-percent visual inspection assertion. Goyal expressed concern regarding the ninety-percent claim in emails to Cook and Siemaszko, leading Cook to delete the ninety-percent statement. In emails copied or sent to Siemaszko, Goyal also questioned the assertion in the draft that all of the CRDMs were inspected given the amount of boric acid deposits obstructing the view and also cautioned that a notation should be included stating that the weep holes and the two-inch gap at the top of the RPV head impeded a 100-percent visual examination.
The final letter included a statement that "a gap exists between the RPV head and insulation, the minimum ... is approximately 2 inches, and does not impede visual inspection." The letter also asserted that Davis-Besse's BACCP procedure had been utilized in both inspections and that "[t]he scope of the visual inspection was to inspect the bare metal RPV head area that was accessible through the weep holes to identify any boric acid leaks/deposits." Siemaszko's limiting preface was not included in the later drafts, which also incorporated information added by others editing the document, nor was the limiting preface included in the final letter to the *458 NRC. SL 2731 also described the boron deposits discovered during the 1998 inspection as an "uneven layer of boric acid deposits scattered over the head ... [and] some lumps of boron, with the color varying from brown to white." Of the 2000 inspections, SL 2731 noted that "[s]ome boric acid crystals had accumulated on the RPV head insulation beneath the leaking flanges. These deposits were cleaned (vacuumed)," that "[i]nspection of the RPV head/nozzles area indicated some accumulation of boric acid deposits," and that the RPV head area was cleaned with demineralized water to the greatest extent possible. Referencing the review of the videotaped 1998 and 2000 inspections conducted in May 2001, following Oconee, SL 2731 also noted that "indications such as those that would result from RPV head penetration leakage [like at Oconee] were not evident." SL 2731 also asserted that a full inspection, unimpeded by boric deposits, would take place during RFO13.
The "green sheet"the cover document listing contributors and allowing space for each to initial and date when he or she received and approved the document to be sent to the NRCfor SL 2731 listed Siemaszko as "responsible engineerplant engineering," but "see attached" was noted in place of initials. The FENOC secretary in charge of maintaining the green sheets testified at trial that attachment sheets often were used for signatures but she could not recall whether that had happened in this instance. Goyal was listed as "responsible engineermechanical design" and testified that he refused to sign the green sheet until Cook and Siemaszko assured him in person that there was "no problem" and that Siemaszko could "see the whole head."
On October 17, 2001, FENOC sent SL 2735 to the NRC after the NRC notified the plant that SL 2731 was not entirely responsive to NRC 2001-01 and was insufficient to guarantee safe operation until RFO13. Siemaszko, as "plant engineeringsystems engineer," initialed and dated the green sheet for SL 2735. He maintains, however, that he signed the green sheet before the submission was finalized and never saw the final version sent to the NRC. SL 2735 contained a table detailing the status of each nozzle at each inspection ("nozzle inspection table"). The table indicated whether each nozzle had been recorded and whether leaks were apparent on each nozzle. After the NRC's request for more information, Geisen had asked Siemaszko to review the inspection videos and to prepare the table. In an interview with investigators in 2002, Siemaszko stated that he spent "weeks" preparing the table.
According to Siemaszko, after submitting a draft table including only the 1998 and 2000 inspections, he was told to include the 1996 inspection. Because he had never seen the head in 1996, he relied on information from others to complete the table. He included a note addressing the scope of the 1996 inspection:
100% of nozzles were inspected by visual examination. Since the video was void of head orientation narration, each specific nozzle view could not be correlated by nozzle number. Nozzles 1, 2, 3, and 4 which do not have sufficient interference gap were excluded. The remaining 65 nozzles did not show any evidence of leakage.
For the 1998 and 2000 inspections, each nozzle had one of the following notations: (1) "no leak observed," indicating that a visual inspection was sufficient and no video record was needed; (2) "no leak recorded," indicating that the nozzle inspection was recorded on the video; or (3) "flange leak evident," indicating that the nozzles were not visible due to boric acid deposits.
*459 Siemaszko sent the table to Goyal and Cook on October 17, 2001. In a deposition after he was fired, Siemaszko stated that before he emailed the table to Goyal and Cook, he took the table to Geisen and Dale Miller, a compliance supervisor, on a diskette and that the three completed the table together. Siemaszko maintained that Miller and Geisen dictated the additional footnotes. Evidence revealed that Siemaszko did send the document to himself from a borrowed work station before sending it to Goyal and Cook, but, at trial, Miller could not remember being involved in drafting the footnotes and Geisen did not testify. Miller did recall editing out the last two sentences of the footnote at a later date. Goyal also testified that he notified Siemaszko that he had not seen 100 percent of the nozzles in 1996 as indicated in the table.
The version of SL 2735 submitted to the NRC contained the nozzle inspection table as Attachment 2, with the footnote as to the 1996 inspections stating that "the entire RPV head was inspected. Since the video was void of head orientation narration, each specific nozzle view could not be correlated." The sentences lined out by Miller included the caveat about four of the nozzles being obscured. The letter also stated that "50 of 69 nozzles" were "viewed" in 1998, "45 of 69" were "viewed" in 2000, and the reason some nozzles were not viewed in 2000 was because they were "obscured by boric acid crystal deposits" that were "clearly attributable to leaking... flanges from the center CRDMs." The letter noted that the visual inspections in 1996, at which time sixty-five of the sixty-nine nozzles were inspected, and in 1998 and 2000 "consisted of a whole head visual inspection" as required by the BACCP. The document also asserted that none of the videos indicated "boric acid chrystal deposits that would have been attributed to leakage from the CRDM nozzle penetrations."
Based on the assertion that all nozzles were leak-free during RFO 10 as demonstrated in the table, FENOC conducted a risk analysis that determined that the earliest a crack could develop was May 1996, after RFO10 concluded. In the worst-case scenario, that crack would take seven-and-one-half years to grow to beyond a safe size, and, therefore, Davis-Besse could safely operate until RFO13. This risk analysis formed the basis of Davis-Besse's representations to the NRC that a delayed inspection was safe.
On October 30, 2001, FENOC submitted two further serial letters to the NRC, both of which contained the nozzle inspection table. SL 2741 included a risk analysis and reiterated that the inspections in 1996, 1998, and 2000 constituted a "whole head visual inspection" of the "bare head" in accordance with BACCP procedure. SL 2744 contained still photographs from past inspection videos. Siemaszko provided the "representative" photographs, and Geisen wrote the captions. Siemaszko was not included on the green sheets for these letters.
On November 1, 2001, FENOC submitted SL 2745, which contained a "plant specific assessment" expanding on the risk assessment provided in SL 2741. Siemaszko was not listed on the green sheet. Kendall Byrd, who was a senior engineer in the safety analysis and probabilistic safety assessment group in 2001, prepared SL 2745 and testified that, in conducting the risk assessment, he credited all nozzles but four as being free from popcorn deposits at RFO10 in 1996 based on Siemaszko's nozzle inspection table, which stated that the "entire head" was inspected in 1996, and information provided in SL 2731, which stated that four nozzles were not visible in 1996. Byrd also spoke with Goyal, *460 but not in relation to preparing SL 2745, regarding Goyal's 1996 inspection and whether "he had any discomfort regarding where we were going with [the responses]." Byrd did not have any conversations with Siemaszko in preparation for SL 2745.
Siemaszko also met with the NRC on November 14, 2001, to discuss the inspections. Those present included Byrd and Dr. Alan Hiser, an NRC staff member. Byrd testified that Siemaszko "did state that he felt I believe it was secure in his heart regarding the condition of the head." Hiser "recall[ed], ... not verbatim, ... something along the lines of he would swear on the stack of bibles as to how good the inspection and the activities that they performed in 2000 were."

D. Procedural Background
During the resulting 2002 inspection, the plant discovered a large cavity in the head of the reactor created by boric acid eroding the steel. The erosion had penetrated through the carbon steel wall, leaving only the 0.24" to 0.38" stainless steel lining of the reactor head and was located near five cracked nozzles, four of which were at the very top of the reactor head (nozzles 1, 2, 3, and 5). The cavity was discovered only by chance when one of the cracked nozzles moved. As a result of the ensuing internal investigation, Davis-Besse fired Siemaszko and Goyal in September 2002 because of their roles in providing inaccurate and misleading information to the NRC in the serial letters.
In January 2006, a grand jury indicted Geisen, Siemaszko, and Cook on five counts of violating 18 U.S.C. §§ 1001 and 2.[1] Goyal and three other Davis-Besse employees signed a deferred prosecution agreement. The indictment charged that based on the statements made in the serial letters submitted to the NRC and two public meetings, the NRC permitted Davis-Besse to operate beyond December 31, 2001. Count 1 charged that the three "did knowingly and willfully conceal and cover up, and cause to be concealed and covered up, by tricks, schemes and devices, material facts in a matter within the jurisdiction of the executive branch of the government of the United States, to wit, the condition of Davis-Besse's reactor vessel head, and the nature and findings of previous inspections of the reactor vessel head." The detailed indictment regarding count 1 listed SL 2731, the other serial letters, and various meetings with NRC authorities between September and December 2001 in which the three defendants participated in various ways. Counts 2 through 5 alleged that Siemaszko "did knowingly and willfully make, use, and cause others to make and use a false writing," including: (count 2) SL 2735, containing five allegedly false statements; (count 3) SL 2741, containing five allegedly false statements; and (count 4) SL 2744, containing six allegedly false statements. Count 5 alleged that Siemaszko "did knowingly and willfully cause others to make and use a false writing."
Siemaszko's trial subsequently was severed from that of Geisen and Cook.[2] At the trial, which followed Geisen's and Cook's, the key issue was whether Siemaszko had the requisite intent to be criminally liable under § 1001. Mainhardt testified that during the NRC's investigation and Davis-Besse's internal investigation, he spoke to Siemaszko regarding his representations *461 that the head had been completely cleaned in 2000. Mainhardt asked Siemaszko why he had said that, and Siemaszko replied "I just told you that so you wouldn't bother me anymore." Mainhardt also testified that Siemaszko was worried that the NRC would count all of the nozzles after it was given a diskette of the video inspections "because all the nozzles aren't there." Goyal testified that in a phone conversation with Siemaszko in October 2002, after both had been fired, Goyal expressed concern about the "100 percent inspection of the head" assertions. Goyal testified that Siemaszko replied, "We will say you inspected 60 percent; I inspected 40 percent. Licensing wanted 100 percent."
During investigations into the Davis-Besse incident in 2002, the NRC interviewed Siemaszko in the presence of counsel. Interviews with Siemaszko were also conducted by Eric Calhoun of the United States Office of Special Counsel regarding a whistle-blower complaint that Siemaszko had filed against FENOC. In his testimony at Siemaszko's trial, Calhoun stated that "FirstEnergy had alleged that he provided inaccurate and/or misleading information to the NRC. And I asked him about that as well. He said that that was true." Calhoun continued, "I asked him why, and he said that he was a hero in the eyes of the company and that he had received a $1,000 bonus" and indicated that others had a greater role than he did. Calhoun testified that he was surprised that Siemaszko would say this because it defeated his whistle-blower complaint and suggested criminal liability. Calhoun testified that Siemaszko's attorney never addressed or attempted to retract the admission.
To demonstrate the falsity of the statements included in the serial letters, the government introduced the inspection videos and summaries of the prior cleanings into evidence through the expert testimony of Melvin Holmberg. Holmberg, who conducted an audit of the inspections and created a "map" of the RPV head identifying each nozzle by number, walked the jury through the various videos. He identified which nozzles were visible during each inspection and to what extent the view of each nozzle in each inspection was sufficient to enable the "qualified visual examination" ("QVE") required by NRC 2001-01. In the diagrams he produced, he also identified which of those nozzles were designated by FENOC as "no leak observed," i.e., "visual inspection satisfactory, no video record required," and which were designated as affected by flange leakages. Summarizing Holmberg's results, the government included in its brief before this court the following table illustrating how many of the nozzles were visible for inspection:


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                                 Nozzles Visible    Nozzles Subject to QVE
                    Inspector   (total out of 69)   (total out of 69)
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  RFO10 (1996)      Goyal        51                 28
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  RFO11 (1998)      Mainhardt    43                 18
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  RFO12 (2000)      Siemaszko    23                 5
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This is inconsistent with the assertions made in SL 2735 that "50 of 69 nozzles" were visibly inspected in 1998 and "45 of 69" were visibly inspected in 2000, although the serial letter did not differentiate between the QVE required by NRC 2001-01 and "viewed."
*462 The jury found Siemaszko guilty of counts 1, 2, and 5. The district court denied Siemaszko's motion for acquittal and for a new trial, citing the testimony of Goyal and Calhoun as particularly "damning." The district court sentenced him to three years of probation for each count, to run concurrently, assessed him a $4,500 fine, and prohibited him from working in the nuclear industry during his probation without the approval of his probation officer.

II. Sufficiency of the Evidence Claims
We review a district court's refusal to grant a motion for judgment of acquittal and a defendant's claim of insufficiency of the evidence de novo. See United States v. Gunter, 551 F.3d 472, 482 (6th Cir.2009) (sufficiency of the evidence claims); United States v. Kone, 307 F.3d 430, 433 (6th Cir.2002) (motions of acquittal). "[T]he relevant question is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original); see also United States v. Dedman, 527 F.3d 577, 592 (6th Cir.2008).
All conflicts in the testimony are resolved in favor of the government, and every reasonable inference is drawn in its favor. United States v. Bashaw, 982 F.2d 168, 171 (6th Cir.1992). In considering the claim, "we do not weigh the evidence presented, consider the credibility of witnesses, or substitute our judgment for that of the jury." United States v. M/G Transp. Servs., Inc., 173 F.3d 584, 588-89 (6th Cir.1999) (citing United States v. Hilliard, 11 F.3d 618, 620 (6th Cir.1993)). This standard applies even if the evidence is purely circumstantial. See Kone, 307 F.3d at 434. Consequently, in raising a sufficiency of the evidence claim, a defendant "bears a very heavy burden." United States v. Spearman, 186 F.3d 743, 746 (6th Cir.1999).
In order to convict a defendant for making false statements to a federal agency in violation of 18 U.S.C. § 1001, the government must prove: "(1) the defendant made a statement; (2) the statement is false or fraudulent; (3) the statement is material; (4) the defendant made the statement knowingly and willfully; and (5) the statement pertained to an activity within the jurisdiction of a federal agency." Dedman, 527 F.3d at 598 (quoting United States v. Lutz, 154 F.3d 581, 587 (6th Cir.1998)). Only the last element is not disputed. When, as in the instant case, the indictment alleges multiple fraudulent statements for each count, this court must "uphold a conviction where there was sufficient evidence for at least one of the alleged false statements" for each count. Id. (emphasis added). After reviewing the extensive record in this case, we find that the government presented sufficient evidence to sustain Siemaszko's convictions on all three counts.

A. Count 1  Concealing Material Facts
Count 1 of the indictment charged Siemaszko with "knowingly and willfully conceal[ing] and cover[ing] up, and caus[ing] to be concealed and covered up, by tricks, schemes and devices, material facts in a matter within the jurisdiction of the [NRC], to wit, the condition of Davis-Besse's [RPV] head, and the nature and findings of previous inspections of the [RPV] head" in violation of §§ 1001 and 2. The "tricks, schemes and devices" that the indictment charges to Siemaszko were: (1) drafting parts of SL 2731 that (a) "deliberately omitted critical facts concerning the inspections and limitations on accessibility" *463 and (b) "falsely stated that the inspections complied with ... Davis Besse's [BACCP]"; and (2) compiling the nozzle inspection table, included in SLs 2735, 2741, and 2744, which falsely reported that (a) the entire RPV head was inspected in 1996, (b) that the 1996 inspection video was "void of head orientation narration," and (c) that in 1998, "satisfactory" inspection results were obtained for the ten nozzles for which "no video record was required." We must uphold the conviction on this count unless we find that there was insufficient evidence for a jury to convict on any one of these six assertions. See id. at 598.
Siemaszko argues that the limited information he provided for SL 2731 as a draft response to section 1.d. of NRC 2001-01 was accurate and merely responded to Goyal's request. He argues that any false information was the result of an "iterative process" by those who subsequently edited and altered the text without his final review. However, the government entered sufficient evidence for a rational trier of fact to find that the original drafts forwarded by Siemaszko to Goyal were already misleading and inaccurate, that Siemaszko did not act to correct material omissions in future drafts that were forwarded to him for review, and that Siemaszko acted knowingly and willfully. Additionally, §§ 1001 and 2 prohibit willfully causing the concealment of material facts, and a rational juror could conclude that Siemaszko knew that others were relying on his drafts and representations of the prior inspectionswhich turned out to be false, misleading, and incomplete in some material respectsin editing and submitting the serial letters.
In section 1.d. of NRC 2001-01, the NRC required full disclosure of the scope of prior inspections and any impedimentswhether insulation or depositsto a full "bare metal" visual inspection. Siemaszko's first draft of SL 2731 stated that ninety-five percent of the nozzles were inspected in 2000, and his second draftin response to Goyal's unease with that representationstated that the "majority" of the nozzles were inspected. It is undisputed that Siemaszko oversaw the 2000 inspection and had seen the videos of the inspections that revealed significant visual impediments. The jury also saw the inspection videos, including the visibility impediments, and reviewed Holmberg's audit report that estimated that only twenty-three of the sixty-nine nozzles were visible in 2000. The government also presented evidence that the earlier drafts did not include information that the NRC considered critical, such as descriptions or photographs of the large boron deposits found in 2000, including the "red photographs" taken during RFO12. Siemaszko argues that he could not have "concealed" the "red photographs" because they already had been submitted to the NRC resident inspector in 2000, but a juror could reasonably consider their omission as concealing the status of the RPV head in SL 2731 when taken in conjunction with other understatements that the government pointed out at trial. For example, Siemaszko's draft reported "some accumulation of boric acid" in 2000, while Siemaszko had seen the "lava-like" flows of boric acid on the RPV head in 2000. Siemaszko also stated that the "[RPV] head was cleaned with the demineralized water as best as it could be," but did not state that bars were used to knock off chunks of deposits and that significant deposits remained at the top of the RPV head after cleaning.
Siemaszko also argues that there is no evidence that he was asked to review the final draft of SL 2731 or to sign the green sheet and so did not make any statements directly to the NRC in that letter. Whether Siemaszko signed the green sheet via *464 attachment remains unclear, as the secretary in charge of circulating it testified that "see attached" could indicate initialing on a separate sheet but could not recall if Siemaszko had done so in this case. However, there is sufficient evidence that Siemaszko was involved in the final submission of the letter and that material language from his original draft remained in the submitted SL 2731. Goyal testified that after he expressed doubts about signing the green sheet, because of his concerns regarding the lack of any description of impediments to a complete, 100-percent inspection of the RPV head, Siemaszko and Cook came to his cubicle to urge him to sign. Goyal testified that he eventually signed the green sheet only after Siemaszko personally assured him that he had seen the entire head in his review of the video. A rational juror could infer from this evidence that the relevant portions of SL 2731 constituted a statement by Siemaszko himself and that, in any case, Siemaszko caused Goyal to sign the green sheet and thereby make the relevant statements to the NRC.
Furthermore, the government provided evidence to suggest that Siemaszko had knowledge of the final content of SL 2731. The government presented evidence suggesting that Siemaszko reviewed the results of the editing after he submitted the revised draft to Goyal on August 9, 2001, but before it was sent to the NRC on September 4, 2001. The record indicates that Cook and Goyal had discussedover email and in personthe section 1.d. response and the entire draft with Siemaszko, including whether the two-inch gap at the top of the RPV head impeded inspections (Siemaszko's draft and SL 2731 falsely stated that it did not) and whether the claim of ninety-percent inspection in 2000 was accurate. Drafts of SL 2731 were circulated to Siemaszko on August 22 and 23, 2001. On August 27, 2001, Cook sent Siemaszko and others a draft that is in all material and relevant parts identical to that submitted to the NRC. In the email accompanying the draft, Cook stated that the time for their review was "of the essence," requested comments, and noted an added caveat to the first paragraph of section 1.d.: "`The scope of the visual inspection was to inspect the bare metal RPV head area that was accessible through the weep holes to identify any boric acid leaks/deposits.' This is to ensure that we state that not all of the head was accessible or inspected for inspection for whatever reason." The government also presented evidence that Siemaszko was involved in changes to commitments in SL 2731 regarding the intended scope of RFO13 up until August 30, 2001.
A rational juror, therefore, could infer that Siemaszko willfully and knowingly concealed or caused to be concealed material facts in SL 2731 regarding the prior impediments to complete inspections, that he reviewed the final document sent to the NRC after editing, was aware of the changes made, and did not object to them. Therefore, the evidence presented at trial sustains Siemaszko's conviction for count 1 based on the first allegation in the indictment.
Although we need not inquire into the sufficiency of the evidence with respect to the remaining allegations contained in count 1 in order to affirm Siemaszko's conviction, a discussion of Siemaszko's participation in the creation of the misleading nozzle inspection chart bolsters our conclusion that the government presented sufficient evidence to convict Siemaszko and demonstrates the degree of his involvement in concealing the limited nature of prior inspections and the extent of the boron buildup discovered in those inspections.
*465 Because there was no full "bare metal" visualization of the entire RPV headand all sixty-nine nozzlesin 1998 or 2000, Davis-Besse needed to demonstrate to the NRC that the 1996 inspection was complete and revealed no leakage or deposits that could progress to significant circumferential cracking before the planned shutdown in April 2002. The government argues that the underlying message of Davis-Besse's second letter to the NRC, SL 2735, was "that if there was stress cracking at Davis-Besse, the cracking had not progressed sufficiently to allow leakage in 1996 and, thereforebased on crack-growth modelingany cracking would not progress to a point of significant concern before [RFO13]." The government further argues that the nozzle inspection table, with its footnote stating that "[i]n 1996 during 10 RFO, the entire RPV head was inspected," and a statement in the body of the letter that no leakage had been identified in 1996, were the key elements of FENOC's representation and misrepresentationto the NRC in SL 2735. Siemaszko, however, argues that there is no evidence that he was the "origin" of the 1996 footnote; that the footnote was edited and altered by Miller in the licensing department; and that there was no evidence that Siemaszko ever reviewed the final SL 2735. While a rational jury could agree with Siemaszko, there is sufficient evidence that he participated and acquiesced in the drafting of the additional footnote, that he knew that the nozzle inspection table, which he prepared in draft form, concealed the incomplete nature of the prior inspections and the extent of boron accumulation, and that he did review the final document.
Siemaszko told the NRC's special agent conducting the investigation that he had spent "weeks" preparing the table and reviewing the inspection tapes and that he had relied on others for information on the 1996 inspection. He also stated in an interview with NRC special agents that he sat down with Geisen and Miller to complete the table and that Miller and Geisen had dictated the footnotes. Siemaszko, therefore, was aware of and did not object to the 100-percent inspection assertion and, the government argued at trial, after reviewing the video of the inspection he would have been aware that at least eighteen nozzles were not visible in the video. Goyal testified that, after he saw a draft of the table, he reminded Siemaszko that he had not seen 100 percent of the RPV head, the language was subsequently changed to "the entire RPV head." While evidence supports Siemaszko's assertion that it was Miller who removed the last two lines of the original footnote that stated that four nozzles were not included in the 1996 inspection, the original footnotewhich Siemaszko credited to Geisen and Miller did state falsely that "100% of nozzles were inspected by visual examination." The jury could have found that Geisen and Miller relied on Siemaszko's representations regarding the inspection in crafting the footnote, and Siemaszko did not object to their mischaracterization of the inspection's scope. Furthermore, the information regarding the four nozzles was included in the body of SL 2735. Moreover, Siemaszko signed the green sheet for SL 2735, implying that he had reviewed its final content.
The government also argued at trial that Siemaszko's statement in the SL 2735 footnote that "[s]ince the video was void of head orientation narration, each specific nozzle view could not be correlated" was an attempt to conceal the fact that the entire RPV head had not been inspected in 1996. If Siemaszko had followed the method of documenting each nozzle by looking at videos of the inspection, he could not have completed the table for *466 1996. A blanket assertion as to the absence of head orientation narration, therefore, meant that he need not reveal the impediments to a full visualization even in 1996. Siemaszko counters that he did not have the knowledge or expertise to interpret the orientation on the video because he did not know which nozzle he was looking at in correlation with the numbers. Circumstantial evidence, however, suggests otherwise.
The 1996 video, including narration, was played for the jury. Holmberg testified that in performing his audit of the 1996 inspection video, he had used the stud hole numbers and other clues to compile a map of the nozzles by number and demonstrated the method to the jury. Goyal, who supervised the 1996 video inspection, testified that the video contained head orientation narration because the technicians had called out the stud numbers when inserting the camera into the weep holes. Goyal also testified that Siemaszko had called him to ask about the stud numbers recited on the video, although Goyal could not recall their meaning at that time. However, the government entered into evidence a map of the RPV head that Siemaszko had used to plot the inspections that indicated the stud hole numbers, demonstrating that he was aware of the numbers' meaning and that there was an adequate method of charting each nozzle from the 1996 video. These inconsistencies could lead a rational jury to conclude that Siemaszko knew that the 1996 video was not "void of head orientation narration" and that he knew this at the time that he drafted the nozzle inspection table submitted to the NRC.
Siemaszko next argues that any inaccuracies in his draft submissions were caused by the lack of skills and guidance necessary to complete the table and not because of improper intent. He rightly asserts that incompetence or negligence are not sufficient to convict under § 1001 and that statements made innocently or inadvertently are not false statements under § 1001. See United States v. Brown, 151 F.3d 476, 486 (6th Cir.1998). However, the government submitted evidence to the jury that Siemaszko was aware of the inaccuracies and had a motive to portray prior inspections as complete in order to keep the plant running until RFO13.
Siemaszko reported in the draft of the tableand it was included in the final SL 2735that ten nozzles were not visible on the video of the inspection in 1998 (RFO11), but the table listed those nozzles as having "satisfactory" visual inspection with no leaks observed and that "no video record [was] required." Mainhardt, who conducted the RPV head inspection in 1998, could not remember conducting any of the inspection without recording it and also testified that Siemaszko never consulted him when compiling the table, even though he was working for FENOC at the time. The government also argued that Siemaszko knew that there were no unrecorded parts of the inspection because he had seen the videos, which depicted complete inspections. The government argues, therefore, that the status of "no video record required" was fabricated by Siemaszko to conceal the lack of documentation of inspections of certain nozzles in the table.
The government also provided evidence that Siemaszko was worried about the NRC investigation that resulted from RFO13 in 2002 and argued that his concern was evidence that he knew that his representations were false, incomplete, and misleading. For example, Mainhardt testified that Siemaszko had been worried in 2002 that the NRC would count the nozzles on the videos "because all the nozzles aren't there." Also, Goyal testified that after he and Siemaszko were fired, *467 Siemaszko spoke to him about what they would say to the NRC regarding certain assertions in the serial letters. The jury also heard testimony that Siemaszko admitted to the whistle-blower investigator that he had provided misleading information to the NRC and that, because of that, "he was a hero in the eyes of the company and ... received a $1,000 bonus." At the very least, this evidence suggests that Siemaszko knew that the statements were false, and a rational juror could infer that he presented a more favorable representation of the inspections in the nozzle inspection table in order to help keep Davis-Besse operating until RFO13.
Because there was ample circumstantial evidence of Siemaszko's direct and indirect participation in drafting the serial letter submissions, including the false statements and material omissions alleged in count 1 of the indictment, there was sufficient evidence for a rational juror to find him guilty of that count. We, therefore, affirm his conviction on count 1.

B. Count 2  Making False Statements in SL 2735
Count 2 of the indictment charged Siemaszko with "knowingly and willfully mak[ing], us[ing], and caus[ing] others to make and use a false writing, that is, [SL 2735], knowing that it contained ... material statements, which were fraudulent," to the NRC in violation of §§ 1001 and 2. The allegedly false material statements related almost exclusively to the nozzle inspection table:
1. "[d]uring 10RFO, 65 of 69 nozzles were viewed," whereas, as the defendants then well knew, significantly fewer than 65 nozzles were viewed;
2. "[i]n 1996, during 10 RFO, the entire RPV head was inspected," whereas, as the defendants then well knew, the entire head had not been inspected ...;
3. "[s]ince the [RFO10] video was void of head orientation narration, each specific nozzle view could not be correlated," whereas, as the defendants then well knew, the [RFO10] inspection video included head orientation;
4. "[t]he inspections performed during the 10th, 11th, and 12th Refueling Outage... consisted of a whole head visual inspection of the RPV head in accordance with [BACCP]," whereas, as the defendants then well knew, areas covered by boric acid had not been inspected, nor had other required steps in the [BACCP] been taken; and
5. "[f]ollowing 12RFO, the RPV head was cleaned with demineralized water to the extent possible to provide a clean head for evaluating future inspection results," whereas, as the defendants then well knew, a substantial layer of boric acid remained, which would impede future inspections.
We must uphold the conviction on this count if there was sufficient evidence for a jury to convict based on any one of these five allegations. See Dedman, 527 F.3d at 598.
The nozzle inspection table was an integral element of Davis-Besse's submissions to the NRC. Not only was it included as an attachment to SLs 2735, 2741, and 2745, but it formed the basis of Davis-Besse's risk analysis. Again, Siemaszko argues that he lacked the requisite intent to commit a violation of § 1001 because his original work was edited and altered by others and that he did not view the final version of the letter that was submitted. Siemaszko also relies heavily on his allegation that he signed the green sheet after submitting his draft but before the final draft was completedwithout seeing the final version. A rational juror could find that, although it is unclear when Siemaszko signed the green sheet, he did so after *468 reviewing a draft including the false statements. Indeed, because some of the false statements in SL 2735 originated in the first draft written by Siemaszkofor example, the statement that some of the nozzles were "satisfactor[ily]" inspected and did not require recordinghe signed the green sheet at a time when a rational juror could find that he knew and intended to submit false statements to the NRC.
Thus our discussion of the evidence presented with respect to the allegations in count 1 of the indictment reviewed the sufficiency of the evidence to support several of the allegations of false statements made in count 2. As a result, we have already determined that the government presented sufficient evidence for a rational juror to find that Siemaszko knowingly and falsely stated or caused to be stated that RFO10 included an inspection of the "entire head" and that the RFO10 video did not contain head orientation narration.
Furthermore, a rational juror could attribute the admittedly false statement that there was a "whole head visual inspection" in compliance with BACCP in 1996, 1998, and 2000 to Siemaszko. Siemaszko admits that those three inspections were not in compliance with BACCP but argues that he did not make the false statement regarding BACCP in SL 2735 because it merely was copied from SL 2731. This argument is unavailing because Siemaszko was the origin of that language in SL 2731 and, therefore, a jury could determine that he caused it to be included in SL 2735.
Goyal testified that boron deposits and limited access to the RPV head prevented an inspection in compliance with BACCP in 1996. The inspections in 1998 and 2000 were less complete than that in 1996, demonstrating that the BACCP procedure could not be fully utilized in either of those inspections. Siemaszko's first draft of SL 2731 stated that "the general guidance of [another procedure] was used for these inspections." After Goyal noted that the draft referenced the incorrect procedure, Siemaszko switched the procedural reference number to indicate the BACCP had been used. Furthermore, even if Siemaszko had not himself made this alteration, he was asked to review later drafts of the letter that included the "in accordance with" language. A rational juror, therefore, could infer that he approved that language while knowing that the boric acid deposits prevented inspection in compliance with BACCP in 1996, 1998, and 2000.
Siemaszko also argues that the "whole head visual inspection" language was not his. However, a draft co-authored by Siemaszko that was submitted to aid others in drafting the text of SL 2735 made the assertion that the whole head had been visualized during the three inspections because it stated that all of the nozzles not visible during the 2000 inspection "were fully inspected during 1996." The nozzle inspection table also asserted that the entire RPV head was inspected in 1996. Therefore, a rational juror could conclude that Siemaszko made or caused to be made this false statement in violation of §§ 1001 and 2, and we may affirm on this ground without addressing the remaining allegations in count 2 of the indictment.

C. Count 5  Causing False Statements to Be Made in SL 2745
Count 5 of the indictment charged Siemaszko with "knowingly and willfully caus[ing] others to make and use a false writing, that is, [SL 2745], that contained... material statements, which were fraudulent," to the NRC in violation of §§ 1001 and 2. The allegedly false statement was that "`[d]uring 10RFO, in spring of 1996, the entire head was visible so 100% of the CRDM nozzles were inspected with the exception of four nozzles in the *469 center of the head,' whereas, as defendants then well knew, many more than the center four nozzles were not inspected." While the evidence supporting this count is more circumstantial than the evidence supporting counts 1 and 2, there was sufficient evidence presented to demonstrate that Siemaszko caused Davis-Besse to submit this false statement to the NRC.
Siemaszko argues that no evidence indicates that he had the requisite intent to deceive the government through this statement in SL 2745. He argues, and the record supports his assertion, that he had no direct role in preparing this document and that Byrd, who prepared the letter, did not contact him for information during the preparation. However, Byrd testified that in formulating his risk analysis, he based his assumption that all of the nozzles were free of stress cracks in 1996 on the information provided in Siemaszko's nozzle inspection table. Based on Byrd's testimony and the evidence presented with respect to Siemaszko's role in preparing the nozzle inspection table, a jury could convict Siemaszko on count 5. Indeed, that the jury convicted Siemaszko on counts involving SLs 2731, 2735, and 2745, but not on counts involving SLs 2741 and 2744, is consistent with this conclusion.
Siemaszko also argues that the panel must reverse his conviction on this count because it is multiplicitous. In support, he cites United States v. Olsowy, 836 F.2d 439, 443 (9th Cir.1987), which held that "where identical false statements, in either oral or written form, are made in response to identical questions, the declarant may be convicted only once." Siemaszko argues that the statement on which this conviction is based is the nozzle inspection table, which also formed the basis of his conviction on count 2. Although the information in the table formed the basis of Byrd's analysis in SL 2745, SL 2745 was not submitted "in response to identical questions." In fact, the Olsowy court distinguished cases like Siemaszko's by specifically stating that it "ha[d] previously upheld multiple counts under section 1001 for submitting separate documents at the same time and multiple convictions for submitting subsequent documents summarizing earlier documents." Id. at 443 n. 4 (citations omitted).
Thus, although Siemaszko's involvement in preparing SL 2745 was considerably less direct than his involvement in formulating the statements and documents made in counts 1 and 2, there is sufficient evidence for a reasonable jury to find him guilty of count 5 beyond a reasonable doubt. We therefore affirm his conviction on this count.

III. Constructive Amendment Claim
We review de novo the legal question of whether an indictment has been constructively amended. See United States v. Budd, 496 F.3d 517, 528 (6th Cir.2007). The defendant bears the burden of establishing that a constructive amendment has occurred. United States v. Chilingirian, 280 F.3d 704, 712 (6th Cir.2002). Constructive amendments are "per se prejudicial," and, when established, entitle a defendant to a reversal of his conviction. United States v. Hynes, 467 F.3d 951, 962 (6th Cir.2006) (citation omitted). "To determine whether a constructive amendment has occurred, therefore, we review the language of the indictment, the evidence presented at trial, the jury instructions and the verdict forms utilized by the jury." United States v. Kuehne, 547 F.3d 667, 683-84 (6th Cir.2008).
We explained in Kuehne that:
A constructive amendment "results when the terms of an indictment are in effect altered by the presentation of evidence and jury instructions which modify *470 essential elements of the offense charged such that there is a substantial likelihood that the defendant may have been convicted of an offense other than the one charged in the indictment."
Id. at 683 (quoting United States v. Martinez, 430 F.3d 317, 338 (6th Cir.2005)).
Count 1 of the indictment charged Siemaszko with "knowingly and willfully conceal[ing] and cover[ing] up, and caus[ing] to be concealed and covered up, by tricks, schemes and devices, material facts in a matter within the jurisdiction of the executive branch of the government of the United States" in violation of §§ 2 and 1001. Count 2 of the indictment charged him with "knowingly and willfully mak[ing], us[ing], and caus[ing] others to make and use a false writing, ... knowing that it contained ... material statements,... in a matter within the jurisdiction of the executive branch of the government of the United States" in violation of §§ 2 and 1001. Count 5 charged him with "knowingly and willfully caus[ing] others to make and use a false writing ... that contained... material statements." This language tracked the elements of the crime as laid out in § 1001(a).
According to Siemaszko, however, the jury instruction permitted the jury to convict based on a finding that the statements and facts could have been material rather than were material, as was alleged in the indictment. Siemaszko, however, fails to demonstrate that the jury instruction was improper. Moreover, a "statement is material for purposes of 18 U.S.C. § 1001 if it has the natural tendency to influence or is capable of influencing the [NRC]." Lutz, 154 F.3d at 588. Thus we have found that the government need not prove "that the statement actually influenced [the NRC]" to carry its burden of proof. Id. (emphasis added).
According to the jury instructions as read to the jury, the district court properly recited the elements of § 1001 with respect to all counts and instructed the jury that a necessary element to be found beyond a reasonable doubt was that "the fact was material" for count 1 and that "the statement was material" for counts 2 and 5. In each case, the district court also gave an additional definition for materiality: "A `material' fact or matter [or statement or entry] is one that has the tendency to influence or is capable of influencing a decision of the [NRC]." It is this additional definition that Siemaszko argues constitutes a constructive amendment. However, we have already found this precise materiality definition to be proper. The instruction on materiality given by the district court followed Lutz and this circuit's pattern jury instructions. See Pattern Criminal Jury Instructions for the Sixth Circuit § 13.01. Therefore, Siemaszko could not have been "convicted of an offense other than the one charged in the indictment." See Kuehne, 547 F.3d at 683 (citation omitted).
Siemaszko also suggests that the evidence presented by the government at trial constructively amended the indictment because it demonstrated that SL 2747, a serial letter not cited in the indictment, in fact prompted the NRC's decision not to shut down Davis-Besse. However, the NRC specifically cited the five letters referenced by the indictment when it granted Davis-Besse permission to delay the inspection required by NRC 2001-01 until February 2002:
You provided your response to the information requested in the Bulletin by letter dated September 4, 2001, as supplemented by letters dated October 17, October 30, November 1, and November 30, 2001. In addition, public meetings were held on October 24, and November 28, 2001, to discuss your responses.

*471 Based on the information provided in your responses and the information available to the staff regarding the industry experience with VHP nozzle cracking, the staff finds that you have provided sufficient information to justify operation until February 16, 2002, at which time you will shut down the [plant] ... and perform VHP nozzle inspections as discussed in your letter dated November 30, 2001. The commitments contained in your letter dated November 30, 2001, were integral to the staff's finding.
The argument that the letters were not material seems merely to be another attempt to rehash the insufficiency of the evidence claim.
Therefore, neither the jury instructions nor the evidence presented at trial constructively amended the indictment to lower the burden of proof necessary to convict Siemaszko. The government presented evidence of the NRC's reliance on all of Davis-Besse's submissions in permitting the plant to operate until RFO13, and the district court followed the guidance of our pattern jury instructions in preparing the jury to review the evidence before it. Siemaszko, therefore, was convicted of the offense charged in the indictment and not of another charge carrying a lesser burden of proof.

IV.
For the foregoing reasons, we affirm Siemaszko's conviction on counts 1, 2, and 5 of the indictment and deny his claim of constructive amendment of the indictment.
NOTES
[1]  Cook was indicted on all counts except count 4.
[2]  We decided Geisen's appeal this day in a separate opinion. See United States v. Geisen, No. 08-3655, 2010 WL 2774237, 612 F.3d 471 (6th Cir.2010).
