Dean Doutt pled guilty to receiving child pornography. The district court enhanced his sentence because it found that he had engaged in a "pattern of activity involving the sexual abuse or exploitation of a minor." U.S. Sentencing Guidelines Manual § 2G2.2(b)(5) (U.S. Sentencing Comm'n 2016). But the district court used the wrong legal standard when it applied this enhancement, so we vacate and remand for resentencing.

I.

Dean Doutt thought he could secretly obtain child pornography online using a video-conferencing application. He was wrong. Turns out, the federal government was monitoring that application. So the government charged him with receipt of child pornography.

Before pleading guilty, Doutt agreed to undergo a polygraph examination. The examiner asked Doutt about any sexual relations he previously had with minors. Among other incidents, Doutt admitted that he had engaged in sexual activity with a neighborhood boy, M.R., nearly forty years earlier. Doutt stated that he was sixteen and M.R. was "a year or two younger" than Doutt when the activity first started. R. 42, Pg. ID 199. But when pressed by the examiner, Doutt changed his response and recalled that M.R. was eleven or twelve. These sexual encounters with M.R. continued over the next several years.

At sentencing, the government recommended an enhancement for a "pattern of activity involving the sexual abuse or exploitation of a minor" based on Doutt's encounters with M.R. U.S.S.G. § 2G2.2(b)(5). Over Doutt's objections, the district court agreed and applied the enhancement. Doutt now appeals, and we review the district court's interpretation of the sentencing enhancement de novo. United States v. Gawthrop , 310 F.3d 405 , 408 (6th Cir. 2002).

II.

Doutt claims that the district court used the wrong legal standard when it determined that he engaged in a "pattern of activity involving ... sexual abuse." U.S.S.G. § 2G2.2(b)(5). Under the Sentencing Commission's commentary to this enhancement, a "pattern of activity" means "any combination of two or more separate instances of ... sexual abuse ... of a minor." U.S.S.G. § 2G2.2 cmt. n.1. "Sexual abuse" is defined by reference to various criminal statutes-including one that forbids sexual activity with a minor between the ages of twelve and sixteen "if the perpetrator was at least four years older than" the minor. 18 U.S.C. § 2243 (a) ; Esquivel-Quintana v. Sessions , --- U.S. ----, 137 S. Ct. 1562 , 1570-71, 198 L.Ed.2d 22 (2017). The district court concluded that Doutt was at least four years older than M.R. because Doutt said he had sexual relations with M.R. when Doutt was sixteen and M.R. was either eleven or twelve. Since there was no other evidence of M.R.'s or Doutt's actual ages, the district court based its conclusion entirely on Doutt's statement.

Doutt argues that the district court erred when it simply took his age (sixteen), subtracted M.R.'s age (eleven or twelve), and concluded that Doutt was four years older than M.R. Doutt is correct, but to understand why we must look behind the numbers. On the one hand, Doutt could have been one day shy of his seventeenth birthday, and M.R. could have just turned twelve-essentially a five -year age difference. But on the other hand, Doutt could have just celebrated his sixteenth birthday the day before M.R. turned thirteen-essentially a three- year age difference. Most people would understand a distinction between these two worlds. Yet the district court's standard would apply the same punishment for Doutt's conduct in either situation-in a way that is "random and somewhat meaningless." United States v. Black , 773 F.3d 1113 , 1117 (10th Cir. 2014).

A more straightforward, precise standard is available. A "year" means either "twelve calendar months" or "[a] consecutive 365-day period." See Black's Law Dictionary (10th ed. 2014). As early as 45 B.C., Julius Caesar recognized the need for a 365-day year (with an extra day added on every four years for leap years). Plutarch, The Life of Julius Caesar , in Plutarch's Lives, Volume II 237 (Arthur Hugh Clough ed. 2001); Adrian Goldsworthy, Caesar: Life of a Colossus 479 (2006). Although Pope Gregory XIII modified Caesar's calendar in 1582 and made some adjustments to leap years, one thing remained the same: a year under the pope's calendar still consisted of 365 days. Steve Hendrix, On New Year's, Our Calendar's Crazy History, and the Switch that Changed Washington's Birthday , Wash. Post (Dec. 31, 2017), https://www.washingtonpost.com/news/retropolis/wp/2017/12/31/on-new-years-our-calendars-crazy-history-and-the-switch-that-changed-washingtons-birthday/?utm_term=.89197ee9eb77. 1 For over two thousand years, then, a year has meant 365 days. While other countries have adopted different calendars at different times, a year has never meant anything less in the United States. That unbroken history makes the statute in this case clear: "at least four years" older means at least 1,461 days (365 multiplied by four, plus one leap day) or 48 months older. Two of our sister circuits have adopted this days-and-months standard when calculating age differences under analogous statutes. Black , 773 F.3d at 1115 ; United States v. Brown , 740 F.3d 145 , 149-50, 150 n.8 (3d Cir. 2014). One state court was so precise that its calculation came down to the hours of birth. See Commonwealth v. Price , 189 A.3d 423 , 431-32 (Pa. Super. Ct. 2018) (vacating the convictions of twin brothers for sexual assault when the statute required that the twin brothers be "four years older" and the brothers were only 3 years, 364 days, and 10 hours older than the victim). Thus, this straightforward days-and-months approach applies to 18 U.S.C. § 2243 .

What is not straightforward, however, is whether Doutt was at least 1,461 days older than M.R. If we had both Doutt's and M.R.'s birthdays, we could easily compute the age difference. Cf. Black , 773 F.3d at 1114 . But we do not have those dates. Instead, we have one statement: Doutt said that he was sixteen years old, and M.R. was "closer to 11 or 12 years of age." 2 R. 42, Pg. ID 199. That statement is simply not enough to conclude that Doutt was "at least four years" older than M.R. Again, the age difference could have been merely three years and one day. Cf. Black , 773 F.3d at 1116-17 .

The government does not tackle this argument head-on but rather argues that plain error review applies because Doutt did not raise this argument before the district court. But Doutt did raise this argument: he explicitly stated that there could have been a mere "three-year age difference" between him and M.R. R. 42, Pg. ID 204. Although he never used the words "days" and "months" to explain his argument, Doutt did contend that there was insufficient evidence to show a four-year age difference. That was enough to preserve his argument, and under de novo review, the district court erred by applying the enhancement without precisely calculating the age difference between Doutt and M.R.

One final point: on remand, the government may introduce further evidence to prove that Doutt was "at least four years" older than M.R. Sometimes the government is precluded from presenting new evidence at resentencing. United States v. Goodman , 519 F.3d 310 , 323 (6th Cir. 2008). Yet the origins of this ban are murky. See United States v. Matthews , 278 F.3d 880 , 887-88 (9th Cir. 2002) (en banc). Thus, we have noted that "special circumstances" can permit the government to introduce new evidence on remand. Goodman , 519 F.3d at 323 (quoting United States v. Leonzo , 50 F.3d 1086 , 1088 (D.C. Cir. 1995) ). This case presents one such special circumstance. The government had no reason to present evidence about the days separating Doutt and M.R. because the district court did not apply a days-and-months approach. When a district court applies the wrong legal standard at sentencing, the government may introduce additional evidence on remand that comports with the appropriate legal standard. United States v. Baker , 559 F.3d 443 , 455 & n.10 (6th Cir. 2009) ; cf. Matthews , 278 F.3d at 888-89 . Because we hold for the first time that an age difference under 18 U.S.C. § 2243 (a) must be calculated using days and months-not whole years-the government can introduce new evidence at resentencing to bolster its claim that Doutt was "at least four years" older than M.R.

* * *

Dean Doutt might very well have been "at least four years" older than M.R. But the district court did not make this determination using the correct legal standard. Accordingly, we vacate Doutt's sentence and remand for resentencing consistent with this opinion.