Defendant Joel Miller, a former small-town doctor, was charged with numerous counts of health-care fraud, money laundering, and distributing a controlled substance outside the usual course of professional treatment, as well as one count of making a false statement in an application he submitted to the Drug Enforcement Administration. The jury acquitted him on all of the financial charges as well as several of the drug-distribution charges, but found him guilty on seven counts of distributing a controlled substance in violation of 21 U.S.C. § 841 (a) and one count of making a false statement to the DEA in violation of 21 U.S.C. § 843 (1)(4)(A). The district court granted Defendant's post-judgment motion for acquittal on one of the controlled-substances counts based on an error in the indictment. The court then sentenced him to forty-one months of imprisonment on the six remaining distribution counts, plus a consecutive sentence of nineteen months on the false-statement count, for a total sentence of sixty months of imprisonment. Defendant appeals his convictions and sentence.

On appeal, Defendant argues that (1) the government medical expert's testimony was not the product of reliable principles reliably applied to the facts of this case and accordingly should have been excluded under Rule 702; (2) the indictment was duplicitous on four of the six controlled-substances counts because each of these four counts included at least two different controlled substances that were prescribed on the same date to the same patient; (3) the trial evidence, jury instructions, and prosecutor's closing argument constructively amended the indictment on the false-statement count; (4) the false-statement count should not have been submitted to the jury because the statement at issue was not false as a matter of law; and (5) the sentence was procedurally unreasonable.

Before addressing the merits of any of these arguments, we first pause to explain the legal backdrop behind Defendant's controlled-substance convictions. Under § 841(a)(1), it is "unlawful for any person knowingly or intentionally" to dispense a controlled substance "[e]xcept as authorized by this subchapter." Medical practitioners are authorized to dispense *1226 non-schedule I drugs pursuant to 21 U.S.C. § 829 (a) and (b). However, in order for a medical practitioners's prescription of controlled substances to be considered a lawful prescription under § 829, it "must be issued for a legitimate medical purpose by an individual practitioner acting in the usual course of his professional practice." 21 C.F.R. § 1306.04 (a). "When this limited statutory authority is exceeded, the criminal sanctions of § 841 apply." United States v. Fellman , 549 F.2d 181 , 182 (10th Cir. 1977). Thus, a medical practitioner who prescribes controlled substances may be convicted of illegal distribution or dispensing under § 841"if he acts without a legitimate medical purpose or outside the usual course of professional practice." United States v. Nelson , 383 F.3d 1227 , 1233 (10th Cir. 2004).

To help the jury decide whether this standard for criminal liability has been met, "[e]xpert testimony from medical practitioners is of course admissible." United States v. Bartee , 479 F.2d 484 , 488 (10th Cir. 1973). "However, the jury is not bound by such expert testimony and may of course consider all of the facts and circumstances surrounding the prescribing as related by lay witnesses." Id. The jury is "free to sort out all the competing proof: the question [of] what constitutes usual medical practice remain[s], at all times, within its province." United States v. Lovern , 590 F.3d 1095 , 1100 (10th Cir. 2009). 1

With this legal backdrop in mind, we first consider Defendant's challenge to the admission of testimony from the government's medical expert. "The admission of expert testimony is within the discretion of the trial court and will be overturned on appeal only when a clear abuse of discretion has occurred." United States v. Varma , 691 F.2d 460 , 463 (10th Cir. 1982). "The district court abuses its discretion if the court's decision is arbitrary, capricious, whimsical or manifestly unreasonable, or when we are convinced that the district court made a clear error of judgment or exceeded the bounds of permissible choice in the circumstances." United States v. Chapman , 839 F.3d 1232 , 1237 (10th Cir. 2016) (internal quotation marks omitted).

The government's medical expert, Dr. Theodore Parran, was indisputably qualified to testify as an expert. Dr. Parran's training and experience included not only practicing medicine for many years, but also teaching residency programs relating to pain and pain management, directing an addiction-medicine training program, directing a doctoring course for first- and second-year medical students at a medical school in Cleveland, directing a continuing medical education program, and conducting clinical work at an outpatient methadone clinic and various other facilities. Defendant does not dispute Dr. Parran's qualifications; he only disputes the substance of his testimony.

Dr. Parran testified that he had reviewed several of Defendant's medical files and concluded, based on his training and experience, that Defendant's drug prescriptions relating to each of the counts of the indictment were outside the scope of usual professional practice and not for a legitimate medical purpose. Dr. Parran testified, for instance, that Defendant would "not uncommonly" increase dosages of narcotics for patients whose condition was described as "stable," with no indication in the records as to why the dosage *1227 was being increased, contrary to the typical medical practice. (R. Vol. IX at 1144.) Dr. Parran testified that Defendant failed to document the types of basic physical exams, medical histories, and requests for patients' past medical records that even medical students would know to do "as part of the routine course ... of medical practice." ( Id. at 1146.) With respect to one patient, he testified: "Anyone who knows anything about opiate pharmacology and about how to evaluate a patient for the presence or absence of tolerance to the life-threatening effects of opiates knows that before seeing a patient, that [there are certain] things that have to be done, and ... they were not done here." ( Id. at 1372.) Moreover, Defendant continued prescribing narcotics to patients despite the presence of clear red flags of drug abuse, such as regular requests for early refills and concerned phone calls from family members or from pharmacists who refused to fill any more narcotic prescriptions for a particular patient because the patient was so clearly overmedicated. He prescribed controlled substances when there were contraindications against use, such as pregnancy or respiratory ailments, and he prescribed multiple drugs that were dangerous in combination. He "relentlessly continued" prescribing controlled substances to a patient who had been admitted to the hospital with an overdose. ( Id. at 1250.) Dr. Parran testified that, based on these and similar deficiencies in Defendant's approach to and treatment of his drug-seeking patients, it was his expert opinion that Defendant's conduct was outside the course of usual medical practice and not for a legitimate medical purpose.

Defendant argues that this testimony should not have been admitted because it was not "the product of reliable principles and methods ... reliably applied ... to the facts of this case." (Appellant's Opening Br. at 28 (quoting Fed. R. Evid. 702 ).) Specifically, Defendant contends that Dr. Parran's testimony was unreliable because, unlike the defense medical expert, he did not clearly delineate where he would draw the line between bad conduct that only amounts to civil malpractice and bad conduct that violates the criminal standard, but merely opined that the criminal standard is much more stringent. In the defense expert's opinion, so long as a doctor prescribes a medication that could address a legitimate medical need for a patient with whom the doctor has a legitimate professional relationship, then the doctor has acted within the usual course of medical practice, and any deficits in treatment within that legitimate professional relationship must be redressed civilly, not criminally. Defendant argues that this testimony hews more closely to the Supreme Court's explanation in United States v. Moore , 423 U.S. 122 , 143, 96 S.Ct. 335 , 46 L.Ed.2d 333 (1975), that a doctor may be found to have exceeded the bounds of professional practice where, "[i]n practical effect, he acted as a large-scale 'pusher.' " Defendant contends that Dr. Parran's interpretation of the criminal standard improperly leaves a large gray area in which a doctor may be found criminally liable for prescriptions made within the bounds of a legitimate doctor-patient relationship. He argues that, because Dr. Parran failed to properly comprehend and describe the difference between criminal conduct and bad medical practice, "his testimony permitted conviction in a case that deviates sharply from those in which this Court has affirmed physicians' convictions." (Appellant's Reply Br. at 10.) He thus argues that Dr. Parran's testimony should have been excluded under Rule 702 as inherently unreliable.

We are not persuaded that the district court abused its discretion by admitting Dr. Parran's testimony. Although "the standard for criminal liability under *1228 § 841(a) requires more than proof of a doctor's intentional failure to adhere to the standard of care," United States v. Feingold , 454 F.3d 1001 , 1011 (9th Cir. 2006), this does not mean that an expert at a criminal trial must also propound on the similarities and differences between the criminal standard and inapplicable civil standards in order to provide reliable testimony on the relevant criminal standard. Defendant has not cited, nor have we found, a single case which even suggests, much less holds, that an expert witness must testify about the civil standard and establish a clear-cut delineation between civil malpractice and a doctor's violation of the Controlled Substances Act in order for his testimony on the criminal standard to be reliable. To the contrary, all of the pertinent cases indicate-sensibly enough-that expert testimony in a criminal case should be based on the criminal standard. Cf. United States v. Tran Trong Cuong , 18 F.3d 1132 , 1138-41 (4th Cir. 1994) (noting that district court erroneously told medical expert "to use a negligence or malpractice standard," but holding that expert's testimony "that he found almost every chart contained evidence of bad and harmful medical practice" was sufficient, along with evidence from patients and undercover agents, to establish a violation of the criminal standard).

Although Defendant relies on Moore , Moore does not support his position. No doubt the doctor in Moore violated civil standards of care as well as the criminal standard by prescribing large quantities of methadone to his patients in a way that was "inconsistent with all accepted methods of treating addicts," 423 U.S. at 126 , 96 S.Ct. 335 , but the Supreme Court felt no need to discuss malpractice or draw any distinctions between the civil and criminal standards in order to hold that the doctor could be prosecuted under § 841 for his conduct. Thus, nothing about Moore suggests that an expert witness must discuss the civil standard of care in order to reliably testify as to the criminal standard. Moreover, the fact that Moore involved more egregious behavior than the conduct at issue in this case does not prove that the only acceptable expert testimony in this case must be in Defendant's favor. "Although the record in this case does not indicate that the defendant was as nonchalant about controlled substances as the defendant doctors in [other cases], there was ample evidence to support the jury verdict." Varma , 691 F.2d at 464 ; see also United States v. MacKay , 715 F.3d 807 , 823 (10th Cir. 2013) ("Neither the Supreme Court in Moore , nor the Ninth Circuit in Feingold stated that a specific set of facts had to be present in order to find that a physician stepped outside of his role and issued prescriptions without a legitimate medical purpose.").

Contrary to Defendant's arguments, we have sustained convictions in other cases involving similarly ambiguous and disputed facts. In Varma , for instance, we noted that "the jury might have concluded that the defendant doctor had only made a few bad judgments when prescribing drugs." 691 F.2d at 464 . Although we acknowledged that there were "numerous other recently reported cases where the acts of doctors convicted of improperly prescribing controlled substances seem more egregious than those of Dr. Varma," we held that there was "ample evidence" to support the jury verdict based on evidence that (1) his staff took incomplete medical histories; (2) the physical examination he performed on each of the undercover agents "was patently too short and inadequate"; (3) Dr. Varma "told his staff that he was troubled by his suspicion that some patients were taking advantage of him by requesting prescriptions for controlled substances for nonmedical reasons"; (4) at his staff's suggestion, he put up a sign in the lobby stating that he would no longer *1229 prescribe certain drugs and told his staff "the patients probably would not return"; (5) while the sign was posted, Dr. Varma's case load "dropped from 80 patients per day to 20 per day"; and (6) when Dr. Varma removed the sign, "his patient load increased to at least its former level." Id. Likewise, in MacKay , we affirmed a doctor's § 841(a) conviction-even though "all of the prescriptions at issue were in the context of a regular doctor visit" and "his patients legitimately experienced pain"-based on evidence that the doctor's examinations "lack[ed] depth," he prescribed narcotics in too high of dosages, he failed to check controlled-substance database reports, he "often did not question his patients' excuses for early refills because he trusted them," and he "did not conduct follow-up examinations before writing prescriptions for refills." 715 F.3d at 822-25 . As in MacKay , Defendant "fails to see his conduct is similar" to defendants in other § 841(a) cases. Id. at 823 . While Defendant's conduct was less egregious than the conduct of many doctors who have been convicted under § 841(a), his conviction is not the "sharp deviation" from precedent that he claims.

At its heart, Defendant's argument boils down to the contention that his expert's interpretation of the criminal standard is the only correct one, and thus only his expert's testimony should have been admitted at trial. However, Dr. Parran's testimony was consistent with expert testimony we have considered in similar cases, see, e.g. , MacKay , 715 F.3d at 822-23 , and Defendant has not shown that the district court committed a clear error of judgment or otherwise abused its discretion by allowing this testimony to be presented. In a § 841(a) case, "[t]here are no specific guidelines concerning what is required to support a conclusion that an accused acted outside the usual course of professional practice." United States v. August , 984 F.2d 705 , 713 (6th Cir. 1992). Instead, this is a fact-intensive inquiry in which the district court should avoid "unduly cabining the jury's ability to consider a broad swath of evidence in determining whether [the medical practitioner's] conduct had no legitimate medical purpose." United States v. Volkman , 797 F.3d 377 , 388 (6th Cir. 2015). The district court appropriately followed our guidance in Lovern by allowing the jury to receive conflicting "witnesses and documentary proof at trial focused on the contemporary norms of the medical profession" so it could "sort out all the competing proof" to decide whether the conduct at issue in this case satisfied the criminal standard. 590 F.3d at 1100 ; see also MacKay , 715 F.3d at 828-29 ("When experts do not reach the same conclusion, the jury is responsible for making credibility determinations, not the court."). We see no abuse of discretion, and we therefore affirm the admission of Dr. Parran's expert testimony.

We turn next to Defendant's argument that his conviction on four of the six controlled-substance counts must be reversed because they were duplicitous, since they each included at least two different controlled substances that were prescribed by Defendant to a specific patient on a particular date. "Duplicity is defined as the joinder of two or more distinct and separate criminal offenses in the same count of an indictment." United States v. Schneider , 594 F.3d 1219 , 1228 n.8 (10th Cir. 2010). We review the question of duplicity de novo. United States v. Trammell , 133 F.3d 1343 , 1354 (10th Cir. 1998).

Defendant argues that the unit of prosecution under § 841(a) is a single controlled substance, and he contends that the indictment was duplicitous because it lumped different controlled substances-prescribed at the same time to the same patient-into a single count, rather than charging each substance as an individual *1230 offense. For support, he relies on United States v. Richardson , 86 F.3d 1537 , 1552-53 (10th Cir. 1996), in which we held that "the simultaneous possession of different controlled substances constitute[s] separate offenses under section 841(a)" because "[t]he plain language of section 841 confirms that Congress intended to treat different controlled substances as separate offenses." Defendant contends that the same reasoning applies to his distribution of controlled substances: just as the statute "prohibits possession of 'a controlled substance,' not of 'a controlled substance or group of controlled substances,' " id. at 1553 (internal quotation marks omitted), so too the statute prohibits distribution of "a controlled substance," not distribution of "a controlled substance or group of controlled substances."

In response, the government contends that Defendant's prescription of a combination of controlled substances to a specific patient during a particular medical visit constitutes a single completed transaction that was appropriately charged as a single count of the indictment. As this court has previously noted, "we know of no rule that renders an indictment duplicitous because it charges as one joint offense a single completed transaction instead of charging in separate counts as many offenses as the evidence at trial might conceivably sustain." United States v. McKneely , 69 F.3d 1067 , 1072 (10th Cir. 1995) (quoting Korholz v. United States , 269 F.2d 897 , 901 (10th Cir. 1959) ) (brackets omitted). The government argues that there is no reason for the indictment in this case to be viewed as duplicitous where each count charges a single transaction, albeit one involving multiple drugs, conducted at the same time and place.

We need not resolve this dispute, however, because any possible error in the indictment was cured by the district court's instructions to the jury that it must not only unanimously agree "that the same act or acts or state of mind or states of mind have been proven beyond a reasonable doubt" (R. Vol. I at 875), but that it must also unanimously agree "on which controlled substance or substances, if any, the government has proven beyond a reasonable doubt the defendant dispensed, distributed, or caused to be dispensed or distributed" ( id. at 876). As we held in Trammell , 133 F.3d at 1354-55 , "[o]ne cure for an otherwise duplicitous indictment is to give an augmented instruction requiring unanimity on one or the other of the acts charged within a count that otherwise appear to constitute separate offenses." The district court appropriately gave such instructions here and thus counteracted any problems that may have been created by the possibly duplicitous indictment. Id. at 1355 .

Defendant argues that the unanimity instructions in this case failed to cure the duplicity problem because the instructions permitted the jury to find Defendant guilty if the jurors unanimously agreed beyond a reasonable doubt that Defendant should be found guilty based on more than one controlled substance that was prescribed during a particular medical visit. In other words, to take just one example, the jury might have unanimously agreed that Defendant was guilty of Count Twenty of the indictment based on both the hydrocodone and the zolpidem he prescribed to patient L.D. on March 3, 2009, rather than finding him guilty based on just one of these drugs. However, the fact that the jurors might have unanimously agreed that more than one specific drug had been improperly prescribed during the course of a medical visit does nothing to undermine the unanimity of its finding that Defendant violated the Controlled Substances Act in the course of that visit. If anything, this just indicates that Defendant *1231 could possibly have been convicted of more offenses than he was. "[T]he effect of joining several violations as one redounds to the benefit of defendant." Korholz , 269 F.2d at 901 .

Defendant contends that the combination of multiple drugs into a single count of the indictment prejudiced his case because it allowed the jury to consider the propriety of prescribing these drugs in combination. According to Defendant, each controlled substance must stand or fall on its own grounds. Thus, Defendant argues, the government was required to prove that each controlled substance was improperly prescribed in and of itself, without regard to the other prescriptions issued at the same time. Defendant cites no authority to support this argument, and we find it to be unpersuasive. By Defendant's reasoning, the prescription of large quantities of several different powerful narcotics at the same time would not violate § 841(a) so long as the patient had a problem with pain that each individual narcotic could help alleviate in isolation, even if the prescription of all of them together would be contrary to any legitimate medical practice. We see no reason for adopting such a rule. Defendant has provided no persuasive reason why a jury may not consider whether the prescription of multiple controlled substances, in combination, took a doctor's actions outside the usual course of medical practice and into the realm of criminal activity. We thus reject his argument that the unanimity instruction failed to cure the potential problem created by charging multiple controlled substances in the same count based on an individual medical visit.

We must "presume that the jurors conscientiously observed the instructions and admonitions of the Court." United States v. Morris , 623 F.2d 145 , 148 (10th Cir. 1980). The jury was appropriately instructed on unanimity in this case, and we presume that the jury conscientiously followed this instruction and did not convict Defendant of any of the controlled substances counts unless it unanimously agreed on which controlled substance or substances were inappropriately prescribed to Defendant's patients. We therefore affirm Defendant's convictions on the controlled-substance counts.

We turn then to Defendant's first challenge to the false-statement conviction. Defendant argues that the trial evidence, the jury instructions, and the prosecutor's closing arguments constructively amended the indictment on this count, allowing him to be convicted on a basis not alleged in the indictment. Defendant did not raise this objection below, so we review only for plain error. See United States v. Brown , 400 F.3d 1242 , 1253 & n.6 (10th Cir. 2005). "We find plain error only when there is (1) error, (2) that is plain, (3) which affects substantial rights, and (4) which seriously affects the fairness, integrity, or public reputation of judicial proceedings." United States v. Romero , 491 F.3d 1173 , 1178 (10th Cir. 2007). "However, we apply this rule less rigidly when reviewing a potential constitutional error." United States v. James , 257 F.3d 1173 , 1182 (10th Cir. 2001).

Even under plain error review, we will "find that a constructive amendment occurred when the evidence presented at trial, together with the jury instructions, raises the possibility that the defendant was convicted of an offense other than that charged in the indictment." United States v. Wonschik , 353 F.3d 1192 , 1197 (10th Cir. 2004) (internal quotation marks omitted) (emphasis added); see also, e.g. , Hunter v. State of New Mexico , 916 F.2d 595 , 599-600 (10th Cir. 1990) (holding that constructive amendment constitutes plain error and requires reversal). "In assessing a claim of an impermissible *1232 constructive amendment, our ultimate inquiry is whether the crime for which the defendant was convicted at trial was charged in the indictment; to decide that question, we therefore compare the indictment with the district court proceedings to discern if those proceedings broadened the possible bases for conviction beyond those found in the operative charging document." United States v. Farr , 536 F.3d 1174 , 1180 (10th Cir. 2008). The jury instructions are of particular importance in this analysis:

[W]hen conduct necessary to satisfy an element of the offense is charged in the indictment and the government's proof at trial includes uncharged conduct that would satisfy the same element, we need some way of assuring that the jury convicted the defendant based solely on the conduct actually charged in the indictment. Typically, that assurance will be provided by jury instructions requiring the jury to find the conduct charged in the indictment before it may convict. If the jury instructions do not impose that limitation, however, the defendant's conviction could be based on conduct not charged in the indictment. That possibility results in a constructive amendment of the indictment, requiring reversal, because it "destroys the defendant's substantial right to be tried only on charges presented in an indictment."

United States v. Ward , 747 F.3d 1184 , 1192 (9th Cir. 2014) (quoting Stirone v. United States , 361 U.S. 212 , 217, 80 S.Ct. 270 , 4 L.Ed.2d 252 (1960) ) (internal brackets omitted). "Measuring against this standard, we are persuaded that the trial proceedings in this case effected a constructive amendment." Farr , 536 F.3d at 1180 .

The indictment charged Defendant with violating § 843(a)(4)(A) and (d) based on a specific false statement:

2. Specifically, in an application filed with the Drug Enforcement Administration ("DEA"), for registration pursuant to 21 U.S.C. Section 823, required for eligibility to dispense controlled substances, the defendant answered in the negative ("N") to the question, "Has the applicant ever surrendered (for cause) or had a state professional license or controlled substance registration revoked, suspended, denied, restricted, or placed on probation, or is any such action pending?" when in truth and fact the defendant's professional license to practice medicine had been previously suspended by the State of Colorado.

(R. Vol. I at 457-58.) At trial, however, the government's witnesses testified that Defendant had also made a second false statement in his DEA application by answering "no" to a similar question about the surrender or suspension of a federal controlled-substance registration; the witness asserted it was dishonest for him to "mark[ ] both of those 'No' " when "he had, in fact, lost his state license and surrendered his DEA registration." (R. Vol. IX at 717; see also id. at 784.) The government also introduced into trial an unredacted copy of Defendant's responses to all of the questions on the DEA application, with no indication that Defendant's response to Question 3 was the only statement at issue in this case.

This evidence of a different, unindicted false statement was not corrected by the jury instructions, which failed to narrow the basis for the false-statement count back down to the specific false statement charged in the indictment. Rather, the jury was simply instructed that it should find Defendant guilty of making a false statement if it concluded that the government had proven five facts beyond a reasonable doubt: (1) Defendant applied for a DEA registration on or about September 19, 2012; (2) "[i]n that application, Dr. Miller knowingly and intentionally furnished false or fraudulent information"; (3) this information *1233 was material to the DEA determination; (4) Defendant knew the information was false or fraudulent; and (5) Defendant acted knowingly and intentionally. (R. Vol. I at 724.) The jury was never instructed that the charged false statement was Defendant's response to Question 3 of the application, nor was it instructed that it could only find Defendant guilty if it found that his answer to this question was false specifically because "in truth and fact the defendant's professional license to practice medicine had been previously suspended by the State of Colorado." ( Id. at 457-58.)

The prosecutor's closing arguments likewise indicated that the jury could find Defendant guilty based on a false statement other than the indicted false statement regarding Defendant's suspended Colorado professional license. Specifically, the prosecutor argued:

Let's look at a question he answered himself and see if there's any additional evidence that he lied. In fact, it's kind of a double-barreled question. That's usually because most applicants say "no" to both.

But, in fact, Dr. Miller should have said "yes" to both parts of the question. With regard to state professional license, it was suspended. With regard to his controlled substance registration, he had surrendered it for cause. His answer "no" to both of these things, which are both falsehoods, is evidence he was working to get that registration back, no matter what he had to do.

(R. Vol. IX at 3227-28.) The government argues on appeal that the prosecutor's arguments did not cause or contribute to a constructive amendment of the indictment because the prosecutor's argument was still premised on Question 3, which was the question mentioned in the indictment. In other words, although the prosecutor's argument that Defendant lied on the second half of this "double-barreled question" was erroneous-either as an argument that Defendant lied about a state controlled-substance registration, which was not supported by the evidence, or as an argument that Question 3 was asking about federal controlled-substance registrations, which is not a reasonable interpretation of the application's plain language-the government argues that this error did not amount to a constructive amendment of the indictment because it was still tied to Question 3. However, this argument misses the point. The indictment did not simply charge Defendant with providing a false statement as to Question 3; rather, the indictment specifically alleged that Defendant made a false statement in his response to this question because "in truth and fact the defendant's professional license to practice medicine had been previously suspended by the State of Colorado." The indictment thus directly tied the false-statement charge to Defendant's suspended Colorado license, and the prosecutor's argument that the jury could convict him based instead on the surrender of his federal controlled-substance registration reveals the very real possibility that Defendant was convicted on a different set of facts than those alleged in the indictment. See Hunter , 916 F.2d at 599 .

The Fifth Circuit considered a similar situation in United States v. Adams , 778 F.2d 1117 (5th Cir. 1985). The defendant in that case was charged with violating 18 U.S.C. §§ 922 (a)(6) and 924(a), which prohibit the use of false statements or false identification in connection with firearm or ammunition sales. The indictment specifically alleged that the defendant "did knowingly furnish and exhibit a false, fictitious and misrepresented identification, that is, a Mississippi Driver's License Number XXX-XX-XXXX, to the firearms dealer, which identification was likely to deceive the firearms dealer ... in that Ernest Adams represented that he was Ernest *1234 Cole, whereas, in truth and fact, as he then well knew, he was Ernest Adams." Id. at 1118-19 . At trial, however, the government's theory of the case was "that the driver's license was false because it bore the name Ernest Cole, which was not Adams' true name, and also because it bore a Meridian, Mississippi address, while the defendant was in fact not a Mississippi resident, but instead resided in Detroit, Michigan." Id. at 1120 (emphasis omitted). "Consistent with this theory the government introduced evidence on the falsity of the name Ernest Cole and on the falsity of the Meridian, Mississippi, address." Id. The jury instructions also failed to limit the jury to consideration of the false name, but simply instructed the jury it should consider whether the defendant's purpose in "furnishing and exhibiting a Mississippi driver's license, indicating the identity and address thereon," was to deceive the dealer. Id. at 1122 .

Based on the evidence and instructions presented to the jury in that case, the Fifth Circuit held that the applicable legal standards, and particularly the Supreme Court's decision in Stirone , 361 U.S. 212 , 80 S.Ct. 270 , compelled the "inescapable conclusion" that a constructive amendment had occurred because the defendant's conviction might have been impermissibly based on the false address, not the false name. Adams , 778 F.2d at 1124 . "The manner in which the driver's license was false bears on an essential element of the crime charged." Id. While the grand jury could have chosen to draw up an indictment alleging falsity as to both name and residence, it chose instead to indict him only as to the false name, and thus the introduction of evidence concerning the defendant's residence permitted conviction upon a set of facts different than those alleged in the indictment. "[W]hen only one particular kind of falsity is charged to have been made in furnishing a license, a conviction must rest on that charge and not another, even though a conviction might have rested on a more general indictment that omitted the reference to Ernest Cole." Id. at 1125 (citing Stirone , 361 U.S. at 217-18 , 80 S.Ct. 270 ). By going "beyond the grand jury's charge," the government and trial court "constructively and impermissibly amended the indictment, thereby denying Adams a substantial right under the fifth amendment." Id.

This circuit has likewise held that a constructive amendment occurs when the indictment alleges a violation of the law based on a specific set of facts, but the evidence and instructions then suggest that the jury may find the defendant guilty based on a different, even if related, set of facts. For instance, in United States v. Bishop , 469 F.3d 896 , 901-03 (10th Cir. 2006), overruled in part on other grounds by Gall v. United States , 552 U.S. 38 , 128 S.Ct. 586 , 169 L.Ed.2d 445 (2007), we held that a constructive amendment had occurred where the indictment charged the defendant with unlawfully possessing "any ammunition and firearm which has been shipped or transported in interstate commerce, that is a Hi-Point 9mm pistol, serial number P117787," but the government introduced evidence and a jury instruction referring to a .38 caliber bullet as well as the Hi-Point pistol. "Even though the indictment in question used the language 'any ammunition and firearm which has been shipped or transported in interstate commerce,' it explicitly modified that terminology with the phrase 'that is, a Hi-Point 9mm pistol.' " Id. at 903. We noted that, as in the Seventh Circuit case of United States v. Leichtnam , 948 F.2d 370 , 379 (7th Cir. 1991), "the government could have left the indictment language broad, but here [chose] to limit the bases for possible conviction to a specific firearm." Bishop , 469 F.3d at 903 (internal quotation marks omitted). Thus, "the admission of the .38 caliber bullet and the jury instructions *1235 constructively amended the indictment against Mr. Bishop." Id. In that case, we found the constructive amendment to be harmless because the jury filled out a special verdict form specifically stating that it had unanimously found the defendant guilty of possessing both the pistol and the bullet, and this specific finding allowed us to "definitively conclude that the jury would have convicted Mr. Bishop on the same count merely due to his possession of the pistol." Id. at 904 . There was no such special verdict form to save the constructive amendment in this case. Cf. Farr , 536 F.3d at 1185 n.7 ("We acknowledge that in some constructive amendment cases we have loosely invoked the term 'harmless error.' In reality, however, we declined to reverse convictions in these cases only because the alleged variation from the indictment at trial did not raise the possibility that the defendant was convicted of a crime different from that charged in the indictment-that is, there simply was no conviction under an improperly added charge." (citations omitted) ).

Likewise, in Farr , a constructive amendment occurred where "the government opted to include in its indictment particulars about the nature of the tax at issue," rather than simply charging the defendant with tax evasion, and "the evidence and jury instructions at trial introduced to the jury an alternative way in which the crime could have occurred," through "a different tax evaded." 536 F.3d at 1181-84 . And in Brown , we held that a constructive amendment had occurred where the defendant was indicted for carrying a gun in relation to a drug-trafficking offense, but the jury instructions suggested that he could be convicted "for some activity other than carrying the gun, such as having the gun readily available, displaying it, or brandishing it." 400 F.3d at 1252-53 .

In short, "[i]t is settled law in this circuit, as elsewhere, that the language employed by the government in its indictments becomes an essential and delimiting part of the charge itself, such that if an indictment charges particulars, the jury instructions and evidence introduced at trial must comport with those particulars." Farr , 536 F.3d at 1181 (internal quotation marks omitted); see also, e.g. , Ward , 747 F.3d at 1192 (constructive amendment occurred where defendant was indicted for aggravated identity theft as to two named victims, but trial evidence and prosecutor's arguments referred to other individual victims, and juror instructions did not specify that conviction must be based on victims named in the indictment); United States v. Randall , 171 F.3d 195 , 203-10 (4th Cir. 1999) (constructive amendment occurred where indictment charged defendants with carrying firearm "during and in relation to a drug trafficking crime, ... specifically, distribution of a narcotic controlled substance," but "the government, through its presentation of evidence and its closing argument, and the district court, through its jury instructions, constructively amended Count Six of the indictment by allowing proof of an alternative § 924(c) predicate offense not charged in the indictment-possession with intent to distribute drugs" (emphasis omitted) ); United States v. Weissman , 899 F.2d 1111 , 1112-14 (11th Cir. 1990) (constructive amendment occurred when indictment alleged that defendant committed a RICO violation "while employed by or associated with an enterprise, to wit, a group ... known as the DeCavalcante Family of La Cosa Nostra," but district court instructed jury that "it isn't necessary for [the government] to prove that the enterprise was the DeCavalcante Family if there was an enterprise proved that meets the definitions of the term"); United States v. Willoughby , 27 F.3d 263 , 266 (7th Cir. 1994) (constructive amendment occurred where indictment charged defendant with using firearm *1236 "during and in relation to a drug trafficking crime, to wit, the distribution of cocaine," but trial evidence showed that firearm was used while possessing drugs with intent to distribute, not while actually distributing). When the evidence and jury instructions do not "comport with those particulars," Farr , 536 F.3d at 1181 , the indictment has been constructively amended, and "[s]uch a constructive amendment must be corrected on appeal, even [when the defendants] failed to preserve the issue by objection," Randall , 171 F.3d at 210 .

In this case, the government chose to indict Defendant on the specific charge that he made a false statement by answering no to a question about past problems with a state professional license when in fact his state Colorado license had previously been suspended. The government then introduced evidence that Defendant had made a different false statement by answering no to a question about past problems with a controlled-substance registration when in fact his DEA registration had previously been surrendered. The government further argued to the jury that both of these statements were falsehoods sufficient to sustain a conviction. And the jury instructions did not specify that the jury could only convict Defendant if it found that he had provided a false statement relating to his previously suspended Colorado license. Thus, we have no "assur[ance] that the jury convicted the defendant based solely on the conduct actually charged in the indictment." Ward , 747 F.3d at 1191 . Rather, the government's trial evidence and arguments, combined with the non-specific jury instructions, raise a real possibility that the jury based its finding of guilt on a different false statement than the false statement that was specified in the indictment, thus "broadening the possible bases for conviction from that which appeared in the indictment," United States v. Miller , 471 U.S. 130 , 138, 105 S.Ct. 1811 , 85 L.Ed.2d 99 (1985) (emphasis omitted). We, like the Fifth Circuit in Adams , are compelled to the "inescapable conclusion" that a constructive amendment occurred in this case, 778 F.2d at 1124 . And because this constructive amendment was contrary to the "settled law" of this circuit, Farr , 536 F.3d at 1181 , this error was clear and obvious, thus satisfying both the first and the second prongs of plain error review.

As for the third and fourth prongs of plain error review, the government argues that Defendant cannot satisfy either of these prongs because "[t]he evidence is overwhelming that Dr. Miller made a false statement when he answered no in his DEA application," since "[t]here is no dispute that ... his medical license had been suspended by the state." (Appellee's Br. at 33.) This argument is based on a flawed premise. True, the district court ruled before trial that his statement was false as a matter of law, thus preventing Defendant from contesting this particular element of the offense. However, the district court's ruling left open the question-hotly disputed at trial-as to whether his false statement was knowingly or intentionally made. Defendant testified at length that his negative answer to this question was based on his honest belief-based in part on conversations with his attorney-that he did not need to answer "yes" to this question because his prior suspension had been voided and effectively erased from existence when the Colorado medical board issued an order that "vacated" the suspension. Perhaps the jury credited this testimony; perhaps it did not. We cannot tell whether the jury based its verdict on a finding that Defendant knew of the falsity of his statement regarding his Colorado professional license, or whether it instead based its verdict on the unindicted-and mostly uncontested-false statement regarding the surrendered DEA registration. We will not "presume the jury's *1237 thinking." Hunter , 916 F.2d at 600 . But this testimony certainly makes the evidence of Defendant's "guilt on the charged crime " far from " 'overwhelming' and 'essentially uncontroverted.' " Brown , 400 F.3d at 1254 .

Our review of the record persuades us that there is a "reasonable probability that, but for the error claimed, the result of the proceeding would have been different." United States v. Kaufman , 546 F.3d 1242 , 1252 (10th Cir. 2008) ; see also United States v. Hill , 749 F.3d 1250 , 1263-64 (10th Cir. 2014) ("A reasonable probability is a probability sufficient to undermine confidence in the outcome," and "should not be confused with[ ] a requirement that a defendant prove by a preponderance of the evidence that but for error things would have been different." (internal quotation marks omitted) ). Based on the evidence, the government's arguments, and the non-specific jury instructions, the jury might very well have based its verdict on the largely undisputed statement regarding the DEA registration, rather than the hotly contested statement charged in the indictment. Defendant has thus satisfied the third prong of plain error review.

We are also persuaded that Defendant has satisfied the fourth prong of plain error review, which requires a defendant to show that the error "seriously affects the fairness, integrity, or public reputation of judicial proceedings." Brown , 400 F.3d at 1253 . This case does not present the type of "overwhelming and essentially uncontroverted" evidence we relied on to uphold a conviction under the fourth prong of plain error review in Brown . Id. at 1254 . Rather, as discussed above, Defendant's testimony, if credited by the jury, would defeat an essential element of this crime-the mens rea requirement. Cf. United States v. Laughlin , 26 F.3d 1523 , 1528 (10th Cir. 1994) (holding, in case involving inadequate jury instructions, that "it would be grossly unfair" to affirm a conviction for medicaid fraud where "we cannot confidently know whether the jury" found that defendant knew his claims were false).

As we noted in United States v. Gonzalez-Huerta , 403 F.3d 727 , 745 (10th Cir. 2005), where a constitutional error has affected the defendant's substantial rights, thus satisfying the third prong of the plain error test, "it is ordinarily natural to conclude that the fourth prong is also satisfied and reversal is necessary in the interest of fairness, integrity, and the public reputation of judicial proceedings. Not to reverse to correct the error is to ignore the injury the defendant suffered from the violation of his or her constitutional rights." The constructive amendment of an indictment violates two separate constitutional rights, depriving the defendant of both his Fifth Amendment right to be indicted by a grand jury on the charges against him and his Sixth Amendment right to receive notice of those charges. Farr , 536 F.3d at 1179 . Thus, "it is a fundamental precept of the federal constitutional law that a 'court cannot permit a defendant to be tried on charges that are not made in the indictment.' " Hunter , 916 F.2d at 598 (quoting Stirone , 361 U.S. at 217 , 80 S.Ct. 270 ). As Defendant argues, "[t]o countenance the constructive amendment here would be to contravene this long-standing and fundamental foundation of a fair trial." (Appellant's Opening Br. at 45.) "Given our relaxed standard in the plain error analysis when reviewing a potential constitutional error," United States v. Saucedo , 950 F.2d 1508 , 1517 (10th Cir. 1991), abrogated on other grounds by Stinson v. United States , 508 U.S. 36 , 113 S.Ct. 1913 , 123 L.Ed.2d 598 (1993), we are convinced that the circumstances of this case warrant an exercise of our discretion to vacate Defendant's unconstitutional conviction on this *1238 count. Cf. United States v. Hauk , 412 F.3d 1179 , 1197 (10th Cir. 2005) ("To leave an erroneous sentence intact after acknowledging that it was calculated through constitutionally suspect means could reflect poorly on the public reputation of the judiciary.").

We therefore vacate Defendant's false-statement conviction and sentence. As in Farr , "our ruling on the constructive amendment question does not speak to the question of evidentiary sufficiency, and thus does not implicate double jeopardy concerns." 536 F.3d at 1186 . The evidence, arguments, and jury instructions in this case "unconstitutionally broadened the basis for conviction, constructively amending the indictment." Id. at 1188 . "At the same time, however, the government's evidence at trial was legally sufficient to convict [Defendant] for [making a false statement] and thus no double jeopardy impediment exists to h[is] retrial," if the government so elects. Id. at 1188-89 . Unlike the situation in Farr , however, the government may not reframe the indictment to fit its alternative set of facts on remand: broadening or substantially amending the indictment would run afoul of the five-year statute of limitations. See United States v. Davis , 953 F.2d 1482 , 1491 (10th Cir. 1992) ; see also 18 U.S.C. § 3282 (a) (setting forth a general five-year statute of limitations for non-capital federal crimes). Thus, any retrial on this count must be based on the specific false statement charged in the indictment.

On appeal, Defendant also challenges his false-statement conviction on the grounds that his statement was not false as a matter of law, entitling him to acquittal by the court. This argument presents a question of pure law that will be at issue again in any retrial. It is accordingly appropriate for us to address this argument now.

As previously discussed, the indictment charged Defendant with providing false information on his DEA application by answering "no" to a question that asked if he had "ever surrendered (for cause) or had a state professional license or controlled substance registration revoked, suspended, denied, restricted, or placed on probation." (R. Supp. Vol. I at 12.) One month prior to answering "no" to this question, Defendant's state medical license had been suspended. Defendant contends, however, that his answer was not false as a matter of law because, in the interim, the state medical board had "ordered that the order of suspension ... be vacated" effective ten days after his license was suspended. ( Id. at 7.) Defendant argues that the term "vacate" is a legal term of art which means that the previous order has been nullified and made as if it never existed. Thus, he argues that his response on the DEA application was true as a matter of law based on the vacatur of his prior suspension.

Both parties agree that the district court was correct in treating this issue as a matter of law to be decided by the court, rather than a matter of fact to be left for the jury; Defendant simply contends that the issue should have been resolved as a matter of law in his favor, rather than the government's. Both parties also appear to agree that Colorado law governs this issue. For purposes of this appeal, we do not question these assumptions, but proceed on the basis of the parties' agreement to decide whether the vacatur of the order of suspension made Defendant's statement true or false as a matter of law under the substantive law of Colorado. "We consider this purely legal question de novo." Haynes v. Williams , 88 F.3d 898 , 899 (10th Cir. 1996).

Neither party has cited, nor have we found, any Colorado cases (nor cases from any other jurisdiction, for that matter) addressing the question of whether the vacatur of an order suspending a medical license *1239 renders the suspension as if it had never happened as a matter of law. Defendant relies instead on cases from dissimilar contexts. For instance, Defendant cites to First National Bank of Telluride v. Fleisher , 2 P.3d 706 , 716 (Colo. 2000), in which the Colorado Supreme Court considered whether a judgment lien was superior to a deed of trust where (1) in an action for breach of a promissory note, the court issued a default judgment, and the defendant filed a judgment lien against certain property; (2) the trial court vacated the default judgment because it had not given adequate notice to the defaulting party and thus default judgment was a violation of due process; (3) a third party obtained a deed of trust on the same property; and (4) the plaintiff ultimately succeeded in the contract case and obtained a second lien on the property. The Colorado Supreme Court held that, based on the specific facts of this case, the default judgment should have been vacated as "a legal nullity," rendering the first judgment lien "without legal effect," and thus causing the deed of trust to be superior to the subsequent second lien. Id. Defendant argues that this case establishes Colorado's position that vacatur always renders the vacated order "a legal nullity" that is essentially erased from history. We are not persuaded, however, that Fleisher or the other cases cited by Defendant are so broad as to cover the very dissimilar situation before us.

In deciding the legal effect of the vacatur order at issue in this case, there are a few important points that must be considered. First, it is important to note that the medical board did not "vacate" Defendant's order of suspension based on some defect in the order itself. The board did not conclude, for instance, that the suspension had been improper or that some procedural defect rendered it a legal nullity. Defendant's medical license was suspended because the Colorado Physician Health Program had reported "that [Defendant] was unable to practice medicine with reasonable skill and safety to patients until he underwent a substance abuse evaluation at an out-of-state facility." (R. Supp. Vol. I at 2.) Rather than undergoing the recommended evaluation, Defendant "notified CPHP that he declined to participate in an assessment." ( Id. at 3.) When Defendant still failed to schedule an evaluation, the medical board suspended Defendant's license based on his "fail[ure] to comply with CPHP's requirement for evaluation," with the suspension effective August 21, 2012. ( Id. ) The suspension order stated: "Such suspension shall remain in effect until such time as [Defendant] has met the recommendations made ... and until [Defendant] has received written notice from the Board that the suspension has been vacated. The suspension shall not be lifted until the Board has reviewed a final report issued by CPHP." ( Id. ) A few weeks later, after "[Defendant], through counsel, and CPHP, provided adequate confirmation to the board of [Defendant's] compliance with CPHP's recommendations," the board ordered that the suspension order "be vacated" effective August 31, 2012. ( Id. at 7.) Thus, whereas the default judgment at issue in Fleisher was vacated because it should never have been granted in the first place, Defendant's suspension order was only vacated because he had come into compliance with the board's requirements. Indeed, rather than suggesting that it had made a mistake in suspending Defendant's license, the board reaffirmed the reasons for the suspension before stating the suspension would be "vacated" because those reasons had now been addressed.

Second, the definition of the term "vacate" does not necessarily mean "to nullify." Webster's Dictionary provides several definitions of "vacate," including both "to make of no authority or validity; make void," and "to make useless, ineffectual, *1240 or without force or significance." Webster's Third New International Dictionary 2527 (1986); see also Weitz Co., LLC v. Mid-Century Ins. Co. , 181 P.3d 309 , 312-13 (Colo. App. 2007) (noting that "[d]ictionaries may be used to assist in the determination of the plain and ordinary meaning of words" and quoting extensively from several editions of Webster's Dictionary). While the first of these definitions might support Defendant's argument that vacatur of his suspension order made it void ab initio , the second definition does not carry the same connotations. An order may be made "useless, ineffectual, or without force or significance" without being retroactively negated. Moreover, even the Black's Law Dictionary definition that Defendant relies on does not necessarily support his argument: something may be "cancelled" without being retroactively erased from existence. See Black's Law Dictionary (10th Ed. 2014) (defining "vacate" as "To nullify or cancel; make void; invalidate"). 2

Third, the director of the medical board testified at Defendant's trial that an order to vacate a suspension "terminates that suspension as of that day," but "does not" erase the suspension as if it never happened. (R. Vol. IX at 808.) Defendant contends that "this lay opinion testimony" is irrelevant to the question of the legal effect of the vacatur order. (Appellant's Reply Br. at 13.) Given the potential ambiguity in the term "vacate," however, we are not persuaded that testimony from the medical board as to what the medical board meant when it used this term is irrelevant to the question of what legal effect the medical board's order should be given.

Furthermore, the director of the medical board's testimony is entirely consistent with the language of the pertinent orders themselves. For instance, at the end of the suspension order, the medical board used the term "lifted" interchangeably with the term "vacated" to describe the conditions under which the suspension would no longer "remain in effect." (R. Supp. Vol. I at 3.) Lifting a suspension would remove its force or significance, by allowing the doctor to return to practicing medicine again, but the term "lift" does not suggest that the suspension would be nullified or voided altogether. The medical board's treatment of vacatur as synonymous with lifting a suspension thus strongly suggests that the medical board had the second definition in mind when it used the term "vacate." Likewise, the fact that the vacatur was made effective on the date the vacatur order was entered, rather than being made retroactively effective on the date of the suspension, further suggests that the medical *1241 board did not intend for the vacatur to make the suspension void and as if it had never existed, but rather simply intended to lift the suspension so that Defendant could return to the practice of medicine. Thus, the documents themselves strongly support the district court's conclusion that the term "vacate" as used by the medical board did not nullify Defendant's suspension ab initio , making it as if the suspension had never occurred, but simply ended the suspension and thus permitted him to again practice medicine.

Finally, we note that the Colorado medical board's enabling statute is the Colorado Medical Practice Act, which was enacted "in the interests of public health, safety, and welfare ... to the end that the people shall be properly protected against unauthorized, unqualified, and improper practice of the healing arts in this state," and must "be construed in conformity with this declaration of purpose." Colo. Stat. Ann. §§ 12-36-102(1); see also Cross v. Colo. State Bd. of Dental Examiners , 37 Colo.App. 504 , 552 P.2d 38 , 41 (1976) ("The Dental Practice Law does not mention surrender of a license. Accordingly, we are guided by the fundamental rules of statutory construction that the legislative intent is to be ascertained and given effect, and that a statute should be given a construction which will render it effective in accomplishing the purpose for which it was enacted."). Although this case does not raise an issue of statutory interpretation, we nonetheless find it appropriate to construe the board's vacatur order in light of the board's statutory mandate to protect the public "against the unauthorized, unqualified, and improper practice of the healing arts." Defendant contends that vacatur of the suspension of a medical license makes it as though the license had never been suspended. Thus, by Defendant's reasoning, a doctor would face no repercussions for practicing on a suspended license so long as the suspension was ultimately vacated. But surely this cannot be correct. We cannot believe that the Colorado medical board or Colorado courts would countenance the unauthorized practice of medicine by a doctor operating under a suspended license, even if the suspension was ultimately vacated. We are not persuaded that we should adopt an interpretation of the medical board's order that would frustrate the board's statutory mandate to protect the public, particularly where such an interpretation would be inconsistent both with the rest of the language in the pertinent documents and with the trial testimony that the board used the term "vacate" to refer only to cancelling or terminating the suspension, not to nullifying it altogether.

In light of all of these considerations, we see no error in the district court's ruling that Defendant's answer on the DEA application was false as a matter of law. Defendant's license had indeed been suspended, and the vacatur of the suspension order did not effectively remove it from historical existence and permit Defendant to state that his license had never been suspended. We pause to note that, just as before, this holding does not prevent Defendant from contesting the mens rea element of the offense: he remains free on retrial to again attempt to convince the jury that he honestly, albeit mistakenly, believed his answer was true based on the vacatur of his suspension. However, our holding that his answer was in fact false as a matter of law will remain the law of the case on remand. See United States v. Monsisvais , 946 F.2d 114 , 115 (10th Cir. 1991) ("The law of the case doctrine posits that when a court decides upon a rule of law, that decision should continue to govern the same issues in subsequent stages in the same case." (internal quotation marks omitted) ).

*1242 Finally, we dismiss as moot Defendant's challenge to the procedural reasonableness of his sentence. Defendant's arguments on this point, if credited, would affect only the length of his sentence. However, Defendant is no longer serving that sentence: he completed his term of incarceration and was released from prison in December 2017. 3 See Fed. Bureau of Prisons Inmate Locator, https://www.bop.gov/inmateloc/ (last visited Apr. 27, 2018). "We cannot modify his sentence now that it has been completed. And we are not allowed to give him a judicial make-up call by shortening his supervised release term." Rhodes v. Judiscak , 676 F.3d 931 , 935 (10th Cir. 2012). Thus, because we "can no longer issue a judgment [as to sentencing] that has a more-than-speculative chance of affecting [Defendant's] rights," we dismiss his sentencing arguments as moot. See id. ; see also United States v. Meyers , 200 F.3d 715 , 721 n.3 (10th Cir. 2000) (en banc footnote).

We therefore AFFIRM Defendant's conviction on the six controlled-substance counts and REVERSE AND REMAND his conviction on the false-statement count. His challenge to the district court's sentencing decision is DISMISSED AS MOOT .