MANION, Circuit Judge.

After a five-week trial, four defendants were convicted of various drug crimes. The district court later found that the government's star witness had testified falsely, that the government knew this testimony was false, and that the government relied upon it to secure the defendants' convictions. The district court then granted a new trial, and the government appeals. Because the record fully supports the district court's findings that the government knowingly used false testimony and that this testimony affected the jury's verdict, we affirm.

I.

For several years, the government investigated the drug trade in the now-razed Cabrini Green public housing projects. Using video surveillance, garbage pulls, controlled buys, and confidential informants, the government gathered evidence and later secured an indictment against fifteen individuals for various drug-related crimes, including one overarching conspiracy. Ten pleaded guilty, and five went to trial. Of those that went to trial, one was acquitted and the others were convicted of several charges, including the conspiracy charge.

At trial, the government presented a bold case. It alleged that Rondell Freeman was poised at the top of a large drug-trafficking ring. He supplied the drugs and with his lieutenants controlled Cabrini Green's drug trade—the government claimed that no one could sell drugs there without his approval. This was by no means a small operation. Freeman was supposed to have purchased over a kilogram of cocaine a week, which he turned into crack and sold in retail quantities. While no exact figure was produced at trial, one witness speculated that this practice would net Freeman as much as $140,000 a week.

Of course an operation of this size requires help. The government alleged that the co-defendants, Brian Wilbourn, Daniel Hill, and Adam Sanders, all served as Freeman's subordinates, but with a twist. While they all worked for Freeman sometimes selling his drugs at retail, they each also had their own business that competed with, yet was still tied to, Freeman's control and supply of drugs. So, although Freeman would take cocaine and make it into his own "brand" of crack that was sold at retail by his lieutenants, Wilbourn and others would also buy cocaine from Freeman, cook it, and then sell it at retail as well.

Naturally the defendants denied these allegations. Freeman, for his part, did not have much of a defense; he simply put the government to its burden. The others had a different trial strategy: they candidly admitted to dealing drugs but claimed they did so on a very small scale, as independent contractors and not as part of Freeman's operation. In doing so, they denied being tied to him in any way but friendship.

For its part, the government's physical evidence was buttressed by the testimony of three significant, cooperating witnesses. Ralph LaSalle was Freeman's supplier; he testified that Freeman bought at least one and sometimes more than two kilograms of cocaine a week between 2000 through 2005. Demarquis Williams, a co-defendant, worked for Freeman and testified about Freeman's stranglehold over Cabrini Green. The most important testimony, however, came from another co-defendant, Seneca Williams—the central figure in this appeal.

For years Seneca Williams served as Freeman's bagger, a fairly low-level position. In it, Williams would take the large chunks of crack cocaine that formed when the powder is "cooked," and then break and bag it into retail-sized "rocks." Despite such a menial role, he knew much about the operation. He testified about how the operation began and how it grew; he testified about the code words and the drug houses used; and he testified about how Wilbourn, Hill, and Sanders were placed within the operation.

Williams was, however, sketchy on dates, so the timeline for his testimony was based on seasons and landmarks. This is a brief summary of his pertinent testimony.

Williams testified at length about the penthouse, frequently placing Wilbourn there with Freeman and others discussing the drug trade. This included testimony about the defendants "branding" their respective types of crack. This was a particularly damning piece of testimony.

Williams's testimony about the penthouse went beyond that excerpt and provided some of the most detailed evidence of Freeman's operation and the other defendants' role in it.

There was, however, a problem with Williams's testimony about the penthouse, particularly Wilbourn's presence and actions there. From Williams's testimony and the government's other evidence, it is clear that the penthouse was used exclusively in 2003. But Wilbourn was in prison from 2002 until 2005, giving him an obvious alibi.

And this alibi wasn't a surprise for the government. After reading Williams's grand jury testimony, Wilbourn's attorney sent the prosecutors a letter letting them know that Wilbourn was in prison during the time Williams placed him in the penthouse. For some reason—never articulated—the government plowed ahead and still had Williams testify. It solicited testimony about Wilbourn's presence at the penthouse; it even encouraged Williams to specifically detail Wilbourn's participation in Freeman's operation there—including the testimony quoted above. What's more, when Wilbourn's attorney began cross-examining Williams about the impossibility of Wilbourn being at the penthouse, the prosecutor objected, stating in the presence of the jury

"Objection. That's not true."

The court overruled the objection, but later noted it "forcibly muted what might otherwise have been [a] devastating impeachment."

At the time, the government disputed that Wilbourn had been in prison during this period. The prosecutors felt that Wilbourn's arrest and incarceration records were unclear on his time in prison. They are not. That aside, the government did not resolve this issue before trial. Nor did it quickly attempt to clarify the conflict when it was raised during the trial. Eventually near the end of the trial and without further comment or testimony, it stipulated that Wilbourn was in prison from April 2002 until September 2005. And at the close of the government's case, the stipulation was read to the jury—twelve days after Williams testified.

Despite the certainty the stipulation provided, problems stemming from Williams's testimony arose again during closing arguments. In its summation, the government still relied on his testimony for a number of factual issues, including connecting Wilbourn to the conspiracy through his use of the orange-striped bags. It also used the rebuttal portion of closing argument to confuse rather than clarify the time conflict in Williams's testimony. It argued that Williams had not lied about Wilbourn and the others at the penthouse—Williams was just imprecise or mildly mistaken about the dates (and presumably the location) on which some events occurred. In essence, it claimed Williams's testimony about the penthouse was, in fact, true—it just happened earlier than he claimed, and in a different place.

During that line of argument, the court sustained several objections from the defense. And it informed the government that its argument was both inaccurate and an attempt to bolster Williams's testimony. The court later found that this constituted prosecutorial misconduct.

The jury eventually convicted four of the five defendants on various charges, including the conspiracy charge. The defendants were, however, acquitted of several others. After the verdict, the defendants moved for a new trial, arguing that Williams's false testimony violated their due process rights. In a very thorough order, the district court agreed and granted the defendants a new trial on count 1, the conspiracy charge. It also granted Wilbourn a new trial on counts 10 and 11, and Freeman a new trial on count 11— counts 10 and 11 were charges of possession with intent to distribute. Concerning those counts, it found that the prosecutor's misconduct during closing argument affected the verdict.

II.

When the government obtains a conviction through the knowing use of false testimony, it violates a defendant's due process rights. Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959); United States v. Bagley, 473 U.S. 667, 679 n. 8, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985) (discussing the evolution of the rule in Napue). To obtain a new trial, the defendant must establish: (1) that there was false testimony; (2) that the government knew or should have known it was false; and (3) that there is a likelihood that the false testimony affected the judgment of the jury. United States v. Saadeh, 61 F.3d 510, 523 (7th Cir.1995). The district court found all three criteria and granted the defendants a new trial, and we review that decision for an abuse of discretion. United States v. Are, 590 F.3d 499, 508 (7th Cir.2009). The district court abuses its discretion when it makes an error of law or when it makes a clearly erroneous finding of fact. United States v. Tingle, 183 F.3d 719, 728 (7th Cir.1999).

A.

There are several layers to the government's argument on appeal. As an initial point, it argues that the district court misapplied Napue, because Napue only applies when the truthfulness of a witness's testimony can be verified or refuted. It characterizes Williams's testimony as a choice between competing inferences, "rather than a matter of demonstrable truth or falsity." And it argues that since the truth of Williams's testimony cannot be verified or refuted, the possibility remains that he was mistaken. Thus, under its understanding, Napue does not apply. The government also argues that Seneca Williams did not testify falsely and that the district court erred by finding Williams's testimony was false.

There are two problems with the government's argument. First, it does not acknowledge or understand the effect that stipulating to Wilbourn's prison sentence had on its evidence. See Wright & Miller, 22 Fed. Practice & Proc.: Evidence § 5194 (1st ed. 1978); see also Keller v. United States, 58 F.3d 1194, 1199 n. 8 (7th Cir. 1995). Williams puts Wilbourn in one place when he discusses the drug trade and the branding of the crack: the penthouse. But the penthouse was only used in 2003. On cross-examination, Williams did not equivocate or waver on this; he stuck to his story: Wilbourn was at the penthouse, dealing drugs, and splitting up the Cabrini Green drug trade with Freeman. And after finally stipulating that Williams's testimony was inaccurate— nothing could have occurred with Wilbourn at the penthouse—the government did not re-call Williams for him to provide an explanation. To be clear, there was no testimony that any of the events that Williams testified about taking place in the penthouse took place elsewhere or at another time.

In fact, it was not until the prosecutor's statements at closing argument that the jury heard that Williams was mildly mistaken and the events described at the penthouse really took place one year earlier, in a different location. See Seventh Circuit Pattern Instruction 1.06 (instructing that "the lawyers' statements to [the jury] are not evidence."); accord Whiting v. Westray, 294 F.3d 943, 946 (7th Cir.2002). In its order, the district court rejected the government's argument on this point as a "glib assertion." And we agree. The stipulation establishes that Wilbourn was never in the penthouse. If he had never been there, those conversations could not have taken place—there is no competing inference from such an impossible event. Therefore, the evidence fully supports the district court's finding that Williams's testimony was false.

Second, the government's legal argument misconstrues the holding in Napue and our precedent. The government seizes on several cases where we have upheld the denial of a motion under Napue when there were contradictions in testimony. Saadeh, 61 F.3d at 523; United States v. Smith, 223 F.3d 554, 574 (7th Cir.2000); Simental v. Matrisciano, 363 F.3d 607, 615 (7th Cir.2004). It argues that those cases dictate that Napue is inapplicable when there can be competing inferences about whether a witness is lying. That is, Napue only applies when the truth or falsity of the testimony can be established.

The government's argument is misplaced. For one, Williams's false testimony was conclusively established. But even if weren't, none of those cases limits a defendant's due process rights to situations where it can be conclusively established that the government witness was lying. In fact, we have held the opposite. In Boyd, we noted that Napue does not require that the witness could be successfully prosecuted for perjury. United States v. Boyd, 55 F.3d 239, 243 (7th Cir. 1995). In this area of the law, the governing principle is simply that the prosecutor may not knowingly use false testimony. This includes "half-truths" and vague statements that could be true in a limited, literal sense but give a false impression to the jury. Id. ("It is enough that the jury was likely to understand the witness to have said something that was, as the prosecution knew, false."). To uphold the granting of a new trial, there does not need to be conclusive proof that the testimony was false or that the witness could have been prosecuted for perjury; all that matters is that the district court finds that the government has knowingly used false testimony. Thus, we reject the government's argument that a claim under Napue can only be made when it can be established that the witness is lying.

B.

The central issue then becomes whether the government knew or should have known that Williams's testimony was false. Saadeh, 61 F.3d at 523. On this point, it is obvious that when the government received the letter from Wilbourn's attorney, it knew there were problems with Williams's testimony—problems that it should have cleared up well before Williams was allowed to testify.

The government's duty to assure the accuracy of its representations has been well stated, many times before. Berger v. United States, 295 U.S. 78, 88, 55 S.Ct. 629, 79 L.Ed. 1314 (1935); Alcorta v. Texas, 355 U.S. 28, 31, 78 S.Ct. 103, 2 L.Ed.2d 9 (1957); United States ex rel. Wilson v. Warden Cannon, 538 F.2d 1272, 1277 (7th Cir.1976); see also United States v. LaPage, 231 F.3d 488, 492 (9th Cir.2000) ("A prosecutor has a special duty commensurate with a prosecutor's unique power, to assure that defendants receive fair trials."). This means that when the government learns that part of its case may be inaccurate, it must investigate. United States v. Price, 566 F.3d 900, 910 n. 11 (9th Cir.2009) (noting "[w]hen a prosecutor suspects perjury, the prosecutor must at least investigate further" (quotation omitted)). It cannot simply ignore evidence that its witness is lying. See United States v. Young, 20 F.3d 758, 764 (7th Cir.1994) (noting "a prosecutor's office cannot get around Brady by keeping itself in ignorance" (quotation omitted)); United States v. Wallach, 935 F.2d 445, 457 (2d Cir.1991) ("We fear that given the importance of [the witness's] testimony to the case, the prosecutors may have consciously avoided recognizing the obvious—that is, that [the witness] was not telling the truth." (emphasis added)). Here, the government abdicated its responsibility by failing to investigate and determine whether Wilbourn could have been at the penthouse as Williams claimed he was.

This notice of Wilbourn's incarceration establishes that the government should have known that Williams's testimony was false. Even more, once the government finally stipulated that Wilbourn was in prison the entire time the penthouse was used, that meant the government knew Williams's testimony was false. Yet despite first using and then admitting that Williams's testimony was false, the government relied on it during closing arguments. In sum, the district court did not err in finding that the government knowingly used false testimony.

C.

Since Williams's testimony was false and the government knew or should have known it was false, the issue becomes whether the district court erred in finding that there was a "reasonable likelihood that the false testimony could have affected the judgment of the jury." Griffin v. Pierce, 622 F.3d 831, 841-42 (7th Cir.2010) (quoting United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976)). This standard is much friendlier for defendants and "sets a lower threshold for determining materiality." Braun v. Powell, 227 F.3d 908, 920 & n. 11 (7th Cir.2000) (discussing the distinction and surveying cases); United States v. Morris, 498 F.3d 634, 640 (7th Cir.2007) (noting the standard for false testimony is "[t]he easier standard for the defendant to meet"). The diminished burden reflects the fact that the knowing use of false testimony corrupts "the truth-seeking function of the trial process." Agurs, 427 U.S. at 104, 96 S.Ct. 2392; accord Bagley, 473 U.S. at 680, 105 S.Ct. 3375. At this point in the analysis, we also weigh whether the defendants had an adequate opportunity to expose the false testimony on cross-examination. Saadeh, 61 F.3d at 523; Shasteen v. Saver, 252 F.3d 929, 933 (7th Cir.2001).

Given all the evidence in this case, granting a new trial is a difficult question. But we re-emphasize our standard of review: The issue is not whether we are convinced that the defendants are guilty but whether the district court clearly erred when it determined that there was any reasonable likelihood that Williams's false testimony affected the verdict. Powell, 227 F.3d at 920. In a trial like this, much of what occurred in the courtroom can be lost in the transcript. Compared to the trial judge who handled all the evidence, our understanding of the testimony and its impact is limited. We can't see the witnesses, and we have no idea how the jury reacted to them: what we may dismiss as a clumsy moment on the transcript could very well be a clever piece of advocacy, delivered at a pivotal moment in the trial. See United States v. Van Eyl, 468 F.3d 428, 436 (7th Cir.2006). For five weeks, the district judge listened to this case; she had a feel for it that we can't replicate, and that fact is not lost in our review of her decision. Boyd, 55 F.3d at 242.

The government argues that since Williams was cross-examined extensively and it stipulated about Wilbourn's time in prison, the jury knew about Williams's false testimony. Thus, his false testimony could not have affected the jury. In the judge's order, she addressed both of these arguments. Concerning the cross-examination of Williams, she noted that "[w]hen Wilbourn's counsel attempted to confront Williams with the dates of Wilbourn's incarceration [] the government objected, stating, `Objection. That's not true.'" And this improper objection "forcibly muted what might otherwise have been [a] devastating impeachment." Concerning the stipulation, the judge found that it did not cure the false testimony. It was read twelve full days after Williams's testimony and at the end of a tedious, five-week trial. Given the judge's view of the trial, we cannot conclude that she clearly erred in finding that the stipulation and the cross-examination did not cure the harm of Williams's false testimony.

Nor do we agree with the government that the evidence was so overwhelming that it was unreasonable for the district court to find that Williams's false testimony affected the verdict. To be sure, there was much evidence of the defendants' guilt, some of it very strong. After all, the defendants did candidly admit to being drug dealers. But despite that, there were three critical impressions affecting the evidence that inform our holding. First, when reading the transcript and the judge's order there is an impression that the case promised by the government—a large and profitable conspiracy—was not what it delivered. Second, Williams's testimony filled in many necessary details that gave flesh and context to the government's evidence. Third, the other parts of the government's case were not so strong that Williams's testimony was mere surplusage.

The government claimed that Freeman was a kingpin, taking a kilo or two of cocaine a week—sometimes more—and turning it into Cabrini Green's retail market. Yet the evidence did not fully support this claim. This was unlike the previous cases concerning control of Cabrini Green, with the hierarchy, wealth, and power exercised by the Gangster Disciples. E.g., United States v. Jackson, 207 F.3d 910 (7th Cir.2000); Smith, 223 F.3d at 560-62; United States v. Wilson, 237 F.3d 827, 830 (7th Cir.2001). When the police officers made several controlled stops of Freeman and his associates, sometimes hoping to find the defendants with bags of money, they had a few hundred or a thousand dollars on them. Similarly, the recorded phone calls were not those of kingpins controlling large areas of vice; rather, they bordered on the comical. At one point at the height of Freeman's "empire," he was recorded calling around trying to scrounge up five dollars from several associates. The same can be said of the other defendants and the evidence against them. Indeed, the transcript does not reveal the markings of the operation the government alleged.

And while there was certainly evidence of drug dealing going on, much of the strongest evidence that Freeman was in league with these defendants in this massive conspiracy came from Seneca Williams—he was the inside man. His testimony made up for some of the other deficiencies in the government's case. Indeed, his testimony about Wilbourn and Sanders, supposedly at the penthouse, gave them a prominent role in the conspiracy, far beyond the impression that any other testimony created.

Moreover, the transcript does not reveal evidence so overwhelming that Williams's testimony could be viewed as mere surplusage. United States v. Beck, 625 F.3d 410, 421-22 (7th Cir.2010). The defense attorneys' cross-examination was, at times, effective in qualifying, minimizing, or casting doubt on the testimony of Demarquis Williams and Ralph LaSalle. Indeed, all of the testimony and evidence here does not strongly convince us that the district court was mistaken in finding that Williams's false testimony affected the defendants' convictions on the conspiracy charge.2 Accordingly, the district court did not abuse its discretion by granting the defendants a new trial on that count.

III.

The government also appeals the granting of the new trial for Wilbourn on count 10 and for both Freeman and Wilbourn on count 11. Williams's role in these counts amounted to translating the codes that were being used by Wilbourn and Freeman during some recorded conversations. These recorded conversations served as the principal evidence against them on these counts. The district court found that the verdict on those counts was affected by the government's bolstering of Williams's false testimony during closing argument. To be clear, no one suggests that Williams's testimony concerning those counts was false.

The district court has broad discretion in deciding whether to grant a new trial based on prosecutorial misconduct. United States v. Cheska, 202 F.3d 947, 949-50 (7th Cir.2000). The inquiry is two-fold: first, whether there was prosecutorial misconduct; second, whether it prejudiced the defendant. United States v. Serfling, 504 F.3d 672, 677 (7th Cir.2007). The district court found that the prosecutor's comments during closing argument, that Williams was truthful about his testimony but mistaken on the dates, was improper. See United States v. White, 222 F.3d 363, 370 (7th Cir.2000) (noting "[a]rgument referencing facts not in evidence is clearly improper"). We agree. The comment was not only inaccurate, it also gave the impression that the prosecutor knew something outside the evidence—namely, that Williams had, outside the presence of the jury, clarified his position and that it was now clear that he was just mistaken on the dates. This was, to say the least, improper. Morris, 498 F.3d at 642 (noting a "prosecutor may not imply that facts not before the jury lend a witness credibility").

To determine whether the district court erred in finding those comments prejudiced Wilbourn and Freeman, we look at several factors, including the efficacy of curative instructions, the defendant's opportunity to rebut the false statements, and the weight of the evidence. United States v. Corley, 519 F.3d 716, 727 (7th Cir.2008) (listing all six factors). But "[u]ltimately, the inquiry turns on whether the improper statement so infected the trial with unfairness as to make the resulting conviction a denial of due process." Id. (quotation marks and citation omitted). Again, we reverse only if we have a "strong conviction of error." Cheska, 202 F.3d at 950 (quotation omitted).

The comments at issue were made during the rebuttal portion of the government's closing argument, so there was no opportunity for the defense to counter the statement. And a curative instruction would have had little effect. Indeed, even if the prosecutor's statements were the product of gross negligence, rather than an intentional act, we fully agree with the district court that in a case like this, the harm was not cured—instead it left an indelible impression on the jury. While there was other evidence to support Wilbourn's and Freeman's convictions on counts 10 and 11, Williams's testimony was a substantial part of the evidence: he translated the code and told the jury precisely what the defendants were discussing on the tapes. In other words, his credibility was important to the government's proof. Thus, the district court's findings are well supported in the record, and it was not an abuse of discretion to grant the defendants a new trial on these counts as well.

IV.

After a full review of the record, we hold that the district court did not err in finding that the government knowingly used false testimony and that there was a reasonable likelihood that the false testimony affected the jury's verdict on the conspiracy charge. Nor did the district court abuse its discretion in granting the defendants a new trial. In addition, the district court did not abuse its discretion by granting a new trial for the counts affected by the government's statements made in closing arguments. Accordingly, the judgment of the district court is affirmed.