JOHN K. BUSH, Circuit Judge.

ON BRIEF: Andrew N. Wise, FEDERAL COMMUNITY DEFENDER OFFICE, Detroit, Michigan, for Appellant. Patricia Gaedeke, UNITED STATES ATTORNEY'S OFFICE, Detroit, Michigan, for Appellee.

Before: STRANCH, BUSH, and READLER, Circuit Judges.

JOHN K. BUSH, Circuit Judge.

The difference between waiver and forfeiture has long bedeviled lawyers and judges alike. Lawyers often split the difference, using the terms interchangeably or even offering a formulation like "my opponent waived and/or forfeited that argument." Sometimes they will also invoke invited error, which falls within the continuum between forfeiture and waiver. But the terms have different meanings and, especially in criminal cases, different consequences. For Edres Montgomery, the difference is dispositive. At his resentencing hearing, the district court applied the wrong Criminal History Category, placing Montgomery in a higher Sentencing Guidelines range. Had Montgomery waived the right to challenge that error, he would be stuck with the sentence he received under the incorrect range. But he only invited the error, which means that we have discretion to review it if the interests of justice demand that we do so. Here, they do. We therefore vacate Montgomery's sentence and remand for resentencing under the correct Guidelines range.

I.

In 2007, a jury convicted Montgomery of conspiracy to distribute cocaine or cocaine base, distribution of cocaine base, and witness tampering. United States v. Montgomery , 358 F. App'x 622, 625 (6th Cir. 2009). At the time, the conspiracy conviction required a mandatory sentence of life in prison, on top of which he received a separate 360-month sentence for the distribution count. Id. Then, three years later, Congress passed the Fair Sentencing Act of 2010, which changed the sentencing scheme for offenses involving crack cocaine. United States v. Boulding , 960 F.3d 774, 777 (6th Cir. 2020). But the Fair Sentencing Act did not make those changes retroactive, so they did not help Montgomery. Id. More recently, in 2018, Congress passed the First Step Act, which made the Fair Sentencing Act's changes to crack-cocaine offenses retroactive, allowing defendants like Montgomery to move for a reduced sentence. Id. He did so in 2019, initially proceeding pro se. In reviewing Montgomery's motion, the district court had to re-calculate Montgomery's Guidelines range to ensure that it sentenced him under the Guidelines as they existed at the time of resentencing. Id. at 784. It determined that he remained in Criminal History Category VI, but that his base offense level had dropped for each offense, giving him a lower Guidelines range. His new ranges were, according to the district court, 292–365 months for the conspiracy count and 151–88 for the distribution count. After considering the relevant sentencing factors, the district court granted Montgomery's motion and varied downwards from those ranges, reducing his sentences to 275 months for the conspiracy conviction and 145 months for the distribution conviction. Montgomery now appeals, arguing that the district court plainly erred when it placed him in Criminal History Category VI instead of category V. The government offers two arguments in response. First, it argues that Montgomery waived his right to challenge his criminal history categorization. Second, it argues that the district court's error was not plain because the district court's obligation to sentence Montgomery under the correct Guidelines range was not clear.

II.

First, we must clarify the difference between waiver, invited error, and forfeiture and explain their different consequences in the criminal law setting. As we have noted recently, our cases discussing waiver and forfeiture are not a model of clarity. See United States v. Petlechkov , 922 F.3d 762, 767 (6th Cir. 2019) (noting that our cases sometimes use the terms interchangeably); United States v. Wooden , 945 F.3d 498, 503 (6th Cir. 2019) (same), cert. granted on other grounds , ––– U.S. ––––, 141 S. Ct. 1370, 209 L.Ed.2d 118 (2021). Our discussion of invited error fares no better—we call it a "branch of the doctrine of waiver," Harvis v. Roadway Exp., Inc. , 923 F.2d 59, 61 (6th Cir. 1991), but we treat it more like "waiver-light," giving ourselves discretion to forgive it, see United States v. Savoires , 430 F.3d 376, 381 (6th Cir. 2005).

In the district court, both of Montgomery's briefs used the Guidelines range that the district court ultimately applied (292–365 months). His second supplemental brief also said that he had a Criminal History Category of VI. We must determine whether that briefing waived his challenge to the Criminal History Category, invited the error, or merely forfeited the argument.

A. THE DIFFERENT DOCTRINES

Waiver, invited error, and forfeiture are best understood as operating on a continuum.

At one extreme is waiver. "[W]aiver is the ‘intentional relinquishment or abandonment of a known right.’ " United States v. Olano , 507 U.S. 725, 733, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (quoting Johnson v. Zerbst , 304 U.S. 458, 464, 58 S.Ct. 1019, 82 L.Ed. 1461 (1938) ). A plea agreement, for example, typically waives an array of rights. United States v. Smith , 960 F.3d 883, 886 (6th Cir. 2020). But waiver need not be quite that direct. Take United States v. Jackson , 995 F.3d 476 (6th Cir. 2021). There, Jankie Jackson's attorney explicitly told the district court that he "couldn't have, in good faith, objected to his leadership role," and therefore the leadership role enhancement was proper. Id. at 484. That is waiver. Id. Because a defendant can only waive a right that he knows of and actively abandons, true waiver will be relatively rare. As such, it comes with the strictest consequences: waiver "extinguishes an ‘error’ under Rule 52(b)," so we cannot review the supposed error at all. Olano , 507 U.S. at 733, 113 S.Ct. 1770 ; Jackson , 995 F.3d at 484 ("[W]e may not review waived claims at all." (quoting United States v. Hall , 373 F. App'x 588, 591–92 (6th Cir. 2010) )).

Forfeiture is at the other end of the spectrum. It is the passive failure to make a timely assertion of a right. Olano , 507 U.S. at 733, 113 S.Ct. 1770. If a defendant fails to object to a district court's ruling at trial, for example, he forfeits the argument. See, e.g. , United States v. Ford , 761 F.3d 641, 653 (6th Cir. 2014) ; see also Black v. United States , 561 U.S. 465, 474, 130 S.Ct. 2963, 177 L.Ed.2d 695 (2010) ("[B]y properly objecting to the honest-services jury instructions at trial, Defendants secured their right to challenge those instructions on appeal."). The same is true if a defendant fails to object to the way the Sentencing Guidelines are applied to him. See United States v. Mabee , 765 F.3d 666, 671 (6th Cir. 2014). But in criminal cases, it is forfeiture in name only— Federal Rule of Criminal Procedure 52(b) allows us to consider such unpreserved arguments for plain error. See United States v. Simmons , 587 F.3d 348, 358 n.6 (6th Cir. 2009) (noting that an argument was forfeited "only in the sense that the claim is subject to a more deferential standard of review on appeal").

Finally, covering much of the space in the middle is invited error. A litigant invites error when he contributes in some way to the district court's error without intentionally relinquishing his rights. See United States v. Barrow , 118 F.3d 482, 490 (6th Cir. 1997) (discussing error that the party "himself invited or provoked the court or the opposite party to make"). In Barrow , we applied the invited-error doctrine to a defendant's challenge to jury instructions to which he had originally stipulated. Id. at 490–91. And in United States v. Thompson , we applied it when a defendant "specifically recommended (along with the government) that the district court apply" two sentencing enhancements. 509 F. App'x 449, 451–52 (6th Cir. 2012) ; see also United States v. Jallad , 468 F. App'x 600, 607–08 (6th Cir. 2012). Because in such circumstances a defendant is more responsible for the district court's error than when he merely forfeits an argument, but has not made the conscious choice to waive the argument, the consequences fall in between those for forfeiture and waiver. We do not review invited errors as a matter of course, but we are also not foreclosed from reviewing them; instead, we review for plain error when "the interests of justice demand" it. United States v. Howard , 947 F.3d 936, 945 (6th Cir. 2020) (quoting United States v. Latham , 358 F. App'x 661, 664–65 (6th Cir 2009) (per curiam)). That crucial difference means that although we have said that invited error is a branch of waiver, it is best to keep the two analytically distinct.

Of course, there will be cases that sit on the hazy border between invited error and waiver. In United States v. Aparco-Centano , for example, Aparco-Centano's counsel explicitly agreed that two of his prior offenses were aggravated felonies for sentencing purposes. 280 F.3d 1084, 1088 (6th Cir. 2002). Doing so, we said, waived his challenge to the district court's decision to treat them as such. Id. But we went on to say that we review "waived" arguments when the interests of justice demand it. Id. That phrasing was imprecise—better stated, we review invited errors when the interests of justice demand it, Barrow , 118 F.3d at 491 ; we do not review waived arguments at all, Olano , 507 U.S. at 732–33, 113 S.Ct. 1770. So were we wrong (or at least inexact) to say that Aparco-Centano waived the challenge, or wrong to raise the possibility that we could review it anyway? More likely it was the former—a labeling error on our part. Nothing in our reasoning there shows that Aparco-Centano was aware that the statuses of his prior crimes were subject to dispute. Thus, the situation in Aparco-Centano is better understood as a case of invited error.

B. APPLICATION TO MONTGOMERY

Laying out the three doctrines makes clear where Montgomery's incorrect briefing falls. He did not intentionally relinquish a known right, as he would have to do to affirmatively waive that right. See Olano , 507 U.S. at 733, 113 S.Ct. 1770. But he did more than passively stand by as the district court erred, so he did not just forfeit his challenge to the Guidelines calculation either. See Mabee , 765 F.3d at 671. By telling the district court in his briefing that he was in Criminal History Category VI, and that his Guidelines range was therefore 292–365 months, Montgomery invited the district court to reach those erroneous conclusions. We must therefore decide whether the interests of justice demand that we consider the district court's error.

III.

Whether the interests of justice demand that we review an invited error is left largely to our discretion. Barrow , 118 F.3d at 491. We have said, for example, that the interests of justice will typically favor reviewing an argument where the government and the defendant are equally at fault and the defendant claims a violation of his constitutional rights. Id. ; see also Howard , 947 F.3d at 945. But our discretion to review invited errors is not limited to constitutional violations; we can review any error of sufficient gravity if failing to do so would result in manifest injustice. See United States v. Demmler , 655 F.3d 451, 458–59 (6th Cir. 2011). Here, we conclude that the interests of justice demand that we consider Montgomery's challenge to the district court's Guidelines calculation.

First, Montgomery was no more culpable for the error than the government. They both uncritically assumed that his Criminal History Category had not changed since his first sentencing. That favors review. See Barrow , 118 F.3d at 491 ("Most importantly, assuming that error occurred, the government was as much at fault for inviting the error as the defendant since the parties stipulated to the same instructions."). It also differentiates Montgomery's case from other Guidelines-related invited-error cases, like United States v. Hanna , where the district court made the error "directly in response to Hanna's urging that it take that very course." 661 F.3d 271, 293 (6th Cir. 2011).

Second, the Supreme Court has offered instruction on the gravity of Guidelines-calculation errors. In Rosales-Mireles v. United States , the Court took up the question whether a district court erroneously placing a defendant in Criminal History Category VI instead of Category V (as happened here) is the kind of error that "seriously affects the fairness, integrity, or public reputation of judicial proceedings" for purposes of plain error analysis. ––– U.S. ––––, 138 S. Ct. 1897, 1905–06, 201 L.Ed.2d 376 (2018) (quoting Olano , 507 U.S. at 736, 113 S.Ct. 1770 ). The Court concluded that it was. Id. at 1908. It explained that "[t]he risk of unnecessary deprivation of liberty particularly undermines the fairness, integrity, or public reputation of judicial proceedings in the context of a plain Guidelines error because of the role the district court plays in calculating the range and the relative ease of correcting the error." Id. At the end of the day, "who wouldn't hold a rightly diminished view of our courts if we allowed individuals to linger longer in prison than the law requires only because we were unwilling to correct our own obvious mistakes?" Hicks v. United States , ––– U.S. ––––, 137 S. Ct. 2000, 2001, 198 L.Ed.2d 718 (2017) (mem.) (Gorsuch, J., concurring).

The Supreme Court's logic in Rosales-Mireles applies with equal force in this context. It is difficult to see how the interests of justice would be served by requiring Montgomery to linger longer in prison because no one in the district court, the court itself included, noticed that the way we calculate a defendant's Criminal History Category had changed between his two sentencings. It is true, as the government notes, that the sentence the district court imposed falls within his correct Guidelines range. But the Court heard and rejected that same argument in Rosales-Mireles , 138 S. Ct. at 1910, because the Guidelines range is the starting point for the district court's analysis. On remand, the district court can decide whether, starting from the correct Guidelines range, a downward variance remains appropriate.

IV.

We review Montgomery's challenge for plain error. To show plain error, a defendant must satisfy four prongs: (1) error occurred; (2) that error was obvious; (3) it affected the defendant's substantial rights; and (4) it affected the fairness, integrity, or public reputation of judicial proceedings. Mabee , 765 F.3d at 673–74. Montgomery has made that showing.

To the first prong, at Montgomery's first sentencing, he received one extra criminal history point for committing the offense for which he was being sentenced within two years of release from prison. That point tipped him into Criminal History Category VI. But a few years later, in 2010, the Sentencing Commission amended the Guidelines to eliminate that recency penalty. U.S.S.G. Supp. App. C, Admt. 742 (effective Nov. 1, 2010). So, under the current Guidelines, Montgomery would be in Criminal History Category V. And, for the second prong, that error would have been readily apparent had anyone recalculated his Criminal History Category before his new sentencing.

For the third and fourth prongs, the Supreme Court has forcefully indicated that those prongs typically favor correcting Guidelines errors. In Molina-Martinez v. United States , the Court explained that "[t]he Guidelines’ central role in sentencing means that an error related to the Guidelines can be particularly serious." ––– U.S. ––––, 136 S. Ct. 1338, 1345, 194 L.Ed.2d 444 (2016). For that reason, a Guidelines error will affect substantial rights unless the record indicates that the district court would have chosen the sentence it imposed regardless of the Guidelines range. Id. at 1346–47. We have no such indication here. And, as we discussed above, the Court held in Rosales-Mireles that a Guidelines error will typically satisfy the fourth prong of the plain error analysis. 138 S. Ct. at 1906–08. Both cases addressed the same Guidelines error we face—placing someone in Criminal History Category VI instead of V. Id. at 1905 ; Molina-Martinez , 136 S. Ct. at 1344.

The government's sole argument in response is that even though the Guidelines error itself was readily apparent, the district court's obligation to apply the correct Guidelines range was not. It cites our decision in United States v. Alexander , which explained that a sentence-reduction hearing under the First Step Act does not require a de novo resentencing hearing. 951 F.3d 706, 708 (6th Cir. 2019). But there is a dramatic difference between requiring a district court to re-weigh all aspects of the defendant's circumstances, which Alexander rejected, and applying the correct Guidelines range. The Guidelines are the "lodestar" of most federal sentencing proceedings, Molina-Martinez , 136 S. Ct. at 1346, and correctly calculating the Guidelines range is the starting point of the resentencing hearing, see Boulding , 960 F.3d at 783. The government's argument is therefore unpersuasive.

V.

For the above reasons, we vacate Montgomery's sentence and remand for resentencing.