Before Smith, Barksdale, and Haynes, Circuit Judges. Jerry E. Smith, Circuit Judge: * In 1998, John Navarro pleaded guilty of attempted sexual assault of a minor in Colorado. In 2013, Navarro moved to Texas. In 2019, law enforcement discovered that Navarro was not registered as a sex offender in Texas and arrested him. Navarro pleaded guilty of failing to register as required by the federal Sex Offender Registration and Notification Act (“SORNA”), a crime under 18 U.S.C. § 2250(a). He completed his term of imprisonment but violated the terms of his supervised release twice and is serving an 11-month revocation sentence. Navarro claims that his guilty plea for failing to register as a sex offender was insufficient as a matter of law because in 2019 he did not have an obligation to register as a sex offender. Agreeing, we vacate the conviction and remand. I. Over twenty years ago, Navarro was convicted of a sex offense in Colorado. State police received disturbing reports from child services in October 1997 and, after investigating further, they arrested Navarro on the suspicion that he had engaged in sexual contact with his two younger half-brothers. Once he was in custody, he waived his Miranda rights and signed a confession. Navarro admitted that he inappropriately touched his half-brothers’ genitals and pressured one of them to perform sexual acts on him. Navarro was nine-teen at the time; his siblings were around six and eight. He pleaded guilty of attempted sexual assault of a child under Colo. Rev. Stat. § 18-3-405 (1998). He was sentenced to three years in prison, beginning July 22, 1998. He served his term of imprisonment. In 2013, Navarro moved to Odessa, Texas.[1] At no point did he register as a sex offender with the county sex registration office or otherwise. In January 2019, a Deputy U.S. Marshal was notified that Navarro was living and working in the state. After confirming that Navarro had been convicted in Colorado of a criminal sexual offense, the Marshals’ Office sought and obtained an arrest warrant. Authorities discovered Navarro at a detention center in Odessa, where he was being held on an out-of-state warrant from Colorado. After he was transferred into federal custody, Navarro was indicted on one count of failure to register as a sex offender under § 2250(a). With the advice of counsel, Navarro entered a voluntary guilty plea before a magistrate judge. The plea was accompanied by a short, one-page document laying out the factual basis for the plea. The document noted Navarro’s conviction for a sex offense, his move to Texas, and his failure to register with the state. The district court accepted his guilty plea. At sentencing, the court adopted the recommendations in the pre-sentence report. According to the report, Navarro’s base offense level was 14, which applies “if the defendant was required to register as a Tier II offender” under SORNA. U.S.S.G. § 2A3.5(a)(2) & n.1. Combining that base offense level with Navarro’s criminal history, the guideline range was 15–21 months’ imprisonment and 5 years’supervised release. The court sentenced Navarro to 21 months and to 5 years of supervised release. Navarro filed a timely notice of appeal, but COVID extensions and issues with Navarro’s appellate counsel delayed briefing and oral argument. In the meantime, Navarro completed his prison sentence. Since then, Navarro has violated the terms of his supervised release twice. The second violation occurred in 2022, when he failed to participate in a required sex offender treatment program. In May 2022, he was given an 11-month revocation sentence with no supervised release. He continues to challenge his original § 2250(a) conviction while he serves his term of imprisonment. He asks this court to vacate the underlying conviction and end his resultant revocation sentence. II. A guilty plea must be supported by a sufficient factual basis. Fed. R. Crim. P. 11(b)(3). “[T]he factual conduct admitted by the defendant” must be “sufficient as a matter of law to establish a violation of the statute to which he entered his plea.” United States v.Trejo, 610 F.3d 308, 313 (5th Cir. 2010) (emphasis removed). Because Navarro challenges the basis of his guilty plea for the first time on appeal, we review for plain error. See United States v. Escajeda, 8 F.4th 423, 426 (5th Cir. 2021); Fed. R. Crim. P. 52(b). We first analyze whether the facts accompanying Navarro’s plea were sufficient to establish guilt under § 2250(a) “as a matter of law.” Trejo, 610 F.3d at 313 (emphasis removed). Concluding the factual basis was insufficient, we then consider whether that was plain error. III. Section 2250(a) has three elements. First, an individual must be a “sex offender” who is “required to register under the Sex Offender Registration and Notification Act.” § 2250(a)(1), (2)(A). Second, he must travel in inter-state commerce. § 2250(a)(2)(B). Third, he must “knowingly fail[] to register or update a registration as required by [SORNA].” § 2250(a)(3). Navarro’s central contention is that he did not have a duty to register as a sex offender under the first prong of § 2250(a). Yet our circuit has not been precise about which law determines a sex offender’s duty to register. Sex offender registries are governed by a combination of state and federal law, and Texas and SORNA set different registration requirements. This case requires us to decide whether SORNA (federal law) or Texas (state law) defined Navarro’s duty to register. Navarro maintains that both state and federal law are relevant. In his view, § 2250(a) requires the government to prove that he had an obligation to register under SORNA and under Texas law. In its initial briefing, the United States did not contest that premise, insisting instead that both SORNA and Texas law required Navarro to register. Yet after the briefs were filed (and before oral argument), the United States conceded that Navarro had no obligation to register under Texas state law.[2] Because the government agreed with Navarro’s framing that a state-law duty to register was a necessary component of § 2250(a), it moved to vacate the conviction and remand; it moved separately for an expedited ruling on the motion to vacate. Navarro—for obvious reasons—did not oppose the motions. This panel carried both motions with the case and heard oral argument as scheduled. Despite the parties’ agreement that Navarro’s conviction should be vacated, we are not bound to grant their requested relief on that basis.[3] Notably, the United States has not abandoned its position that Navarro had a duty to register as a sex offender under SORNA. Instead, it contends that even if Navarro was obligated to register under SORNA, the fact that he had no state-level duty to register is sufficient to vacate a § 2250(a) conviction. But that conclusion does not follow from the statute and the caselaw. We write especially to clarify the law in this regard. The government’s concession raises a narrow but nonetheless critical issue of first impression for this circuit: Is a conviction under § 2250(a) in-sufficient merely because the defendant had no duty to register as a sex offender under state law? We conclude that the answer to the question is “no.” Section 2250(a) makes criminal the failure to register under the federal SORNA. States are free to impose stronger or weaker registration requirements on sex offenders, but whether an individual complies with state law has no bearing on whether he has discharged his SORNA obligations. Thus, the United States’s admission that Navarro had no duty to register under state law is not enough to render his conviction ipso facto invalid. A. Whether a person has an obligation to register as a sex offender under § 2250(a) is determined by federal law. Section 2250(a) is clear about which law applies—it incorporates SORNA by reference three separate times.[4] It states in no uncertain terms that individuals are guilty of the offense if they are “required to register under [SORNA]” and fail to do so. § 2250(a). SORNA, in turn, lays out a complex regime for who must register as a sex offender and for how long, depending on the nature of an individual’s sex offense. See 34 U.S.C. §§ 20911–15. Yet the parties put a critical gloss on the statutory scheme. They insist that an individual cannot be convicted under § 2250(a) unless he had both an obligation to register as a sex offender under SORNA and an obligation to register under state law. That interpretation has no basis in the statutory text. Neither § 2250(a) nor SORNA refers to a state’s registration requirements. SORNA applies to “sex offender[s],” a term defined by federal statute. See §§ 20911(1), 20913(a). Those offenders are required to “register, and keep the registration current, in each jurisdiction” where they “reside[].” § 20913(a). SORNA also specifies when the obligation to register begins and when it ends, depending on what kind of sex crime the offender committed. See §§ 20913(b), 20915. To put it another way: SORNA establishes of its own force who must register, where they must register, and for how long they must register. Failure to follow any of those rules is a federal crime. § 2250(a). A state may impose differing obligations on sex offenders, but that has no impact on whether an individual is “required to register under [SORNA].” Id. Navarro points out that SORNA does not create a national sex offender registry and, instead, requires offenders to register in the state in which they live, work, or study. See § 20913(a). Navarro contends that because individual states maintain their own registries, state law necessarily controls whether an individual has an obligation to register. Yet in § 20913(a), SORNA merely tells sex offenders where to register; it does not give states the power to decide whether offenders must register as a matter of federal law. If § 20913(a) really delegated such power to states— or implicitly incorporated states’ registration requirements—it would obviate the rest of SORNA’s registration scheme. It would mean that even where SORNA required an individual to register for a period of years, if a state imposed a lesser obligation on that offender (or even no obligation at all), he would not violate SORNA and could not be convicted under § 2250(a). Indeed, the parties all but concede that their view makes SORNA’s registration requirements superfluous. The United States represented at oral argument that if state registration requirements are different from the federal ones, the state requirements “trump[].”[5]So too, Navarro’s counsel agreed that even though § 2250(a) criminalizes a failure to register under SORNA, SORNA mandates that sex offenders follow their respective states’ registration requirements.[6] Again, however, SORNA does not merely direct sex offenders to follow state law registration rules: It sets up its own requirements for which sex offenders have to register and when. §§ 20911–15. It is inconceivable that Congress would go to the trouble of devising SORNA’s elaborate scheme only for a state’s weaker registration requirements to supplant the federal ones. Instead of the statutory text, the parties rely on United States v. Shepherd, 880 F.3d 734 (5th Cir. 2018) (Smith, J.). The Shepherd panel summarized the requirements of § 2250(a) by stating that a “defendant is subject to SORNA’s provisions if . . . he or she . . . knowingly fails to register or update his or her registration as required by state law.” Id. at 740 (quoting United States v. LeTourneau, 534 F. Supp. 2d 718, 720 (S.D. Tex. 2008)) (emphasis added). The parties place all their weight on that final phrase. To them, Shepherd means that a defendant has a duty to register as a sex offender for the purposes of § 2250(a) only if state law requires him to register. But Shepherd does not go as far as the parties say. First, the quoted language is accurate in the narrow sense that sex offenders must register in the state where they reside, work, or go to school—that much SORNA says. Compare id., with § 20913(a). Sex-offender registries are creatures of state law. Therefore, “SORNA requires sex offenders to register with state-run sex-offender registries and to keep their registrations current.” United States v. Torres, 767 F.3d 426, 427 (5th Cir. 2014) (emphasis added). SORNA does not, however, adopt states’ separate requirements for who must register and when—SORNA sets its own rules for when sex offenders must register with state authorities. Second, and more importantly, Shepherd does not control this dispute because it did not directly interpret the meaning of § 2250(a) or SORNA. Though the defendant in Shepherd was convicted under § 2250(a), his appeal was based on a 28 U.S.C. § 2255 motion that sought to invalidate his guilty plea because of ineffective assistance of counsel. Shepherd, 880 F.3d at 737. The court dealt only with the ineffective-assistance claim and explicitly declined to determine whether Shepherd was actually innocent under § 2250(a). Id. at 740. In resolving the ineffective-assistance question, the court emphasized that counsel in Shepherd was abnormally inept: He advised the defendant to plead guilty, even though state caselaw suggested that the defendant had no duty to register in the state. Id. at 741–43. The attorney later testified that he would have advised his client to plead differently if he had done further research. Id. at 743. The Shepherd court held that such failure was ineffective assistance of counsel because it would have demonstrably changed the attorney’s recommendation to plead guilty. Id. at 746. Critically, this court did not hold that Shepherd’s conviction under § 2250(a) was invalid just because he had no duty to register under Texas law—the question of actual innocence was left open. See id. There is thus no Fifth Circuit precedent that justifies a departure from SORNA’s unambiguous language. The weight of additional authority confirms our limiting reading of Shepherd. In direct appeals of SORNA convictions, both our court and the Supreme Court have articulated the requirements of § 2250(a) in a way that makes certain that federal law determines whether an individual has a duty to register as a sex offender under SORNA (not state law).[7] Meanwhile, our sister circuits have consistently held that an individual can be convicted of failing to register under SORNA even if the state does not require him to register.[8] Similarly, in its most recent rulemaking, the Justice Department clarified that “SORNA’s registration requirements are independent of state law registration requirements,” so “SORNA requires sex offenders to register in states whose own laws do not require registration by those offenders.”[9] In short, a § 2250(a) conviction imposes a duty to register under SORNA. And SORNA sets federal registration requirements that are independent of state law.[10] Although we accept the government’s concession that Navarro did not have a duty to register under Texas law, that has no bearing on whether he had a duty to register under § 2250(a). B. Because Navarro was convicted for failing to register “under [SORNA],” § 2250, we cannot vacate his conviction unless we determine that he had no duty to register under SORNA. After carefully parsing our precedents, we conclude that Navarro had no duty to register under SORNA in 2019. 1. There is no dispute that Navarro initially fell within the ambit of SORNA. Because he was a “sex offender” within the meaning of the statute,[11] Navarro had a duty to register beginning at the conclusion of his first prison sentence. See § 20913(a)–(b); see also 28 C.F.R. § 72.7(a)(1). Navarro was convicted of his predicate sex offense in July 1998. Given his three-year sentence, his obligation to register began (at the latest) around July 2001. 2. The more difficult issue is how long Navarro’s registration requirement lasted. SORNA divides the universe of sex offenders into three “tiers,” and the length of an offender’s duty to register depends on his assigned “tier.” See §§ 20911, 20915. A tier I offender must keep his registration current for 15 years; a tier II offender must do so for 25 years; a tier III offender’s registration obligation lasts for life. § 20915(a). A defendant’s “tier” is dictated by the nature of his underlying offense. Tier I is the baseline—all offenders who are not tier II or tier III offenders are tier I offenders by default. § 20911(2). A tier II offender is an individual who, among other things, was convicted of an offense “against a minor” that “is comparable to or more severe than” a list of enumerated federal crimes. See § 20911(3). An offender is tier III if he is convicted of an offense that “is comparable to or more severe than” a list of more egregious federal sex crimes. See § 20911(4). If Navarro was a tier II offender, then his 25-year registration obligation would have run from 2001 to 2026, and he would have been required to register in Texas in 2019. But Navarro contends that he was a tier I offender. If he is correct, then his 15-year registration obligation would have expired in 2016, three years before he was federally indicted for failure to register. The district court treated Navarro as a tier II offender.[12] Recall that an offender qualifies as tier II if his sex offense was “committed against a minor” and “is comparable to or more severe than” a list of federal crimes, including, “abusive sexual contact (as described in section 2244 of Title 18).” § 20911(3)(A)(iv) (emphasis added). “[A]busive sexual contact,” in turn, is defined as any of six additional federal crimes. 18 U.S.C. § 2244(a). Two of those six crimes are relevant here: 1. 18 U.S.C. § 2243(a), which criminalizes “knowingly engag[ing] in a sexual act” with a “minor” who is at least twelve but not yet sixteen, so long as the victim is at least four years younger than the perpetrator. 2. 18 U.S.C. § 2241(c), which prohibits “knowingly engag[ing] in a sexual act with another person who has not attained the age of 12 years.” Because Navarro’s conduct would satisfy the second of those two federal offenses (§ 2241(c))—his half-brothers were both younger than twelve when he abused them—the United States asserts that Navarro’s predicate crime was “comparable” to”abusive sexual contact” and was thus a tier II offense. Though that approach is facially plausible, it is not how our circuit has interpreted and applied SORNA. To determine whether an offender’s predicate offense is “comparable” to a crime listed in SORNA, we use the “categorical approach” that is familiar to federal criminal law. United States v. Escalante, 933 F.3d 395, 398 (5th Cir. 2019); United States v. Young, 872 F.3d 742, 745–46 (5th Cir. 2017). Under the categorical approach, the specific circumstances of a defendant’s crime are irrelevant. All that matters is whether the elements of the state crime match the elements of the federal crime. Descamps v. United States, 570 U.S. 254, 260–61 (2013). If the state crime “sweeps more broadly” than the federal offense, it is not comparable and, therefore, cannot be a predicate offense. United States v. Montgomery, 966 F.3d 335, 338 (5th Cir. 2020) (quoting Descamps, 570 U.S. at 261). A crime “sweeps more broadly” when it criminalizes more conduct than the federal crime would reach by its terms. See id.[13] Using the categorical approach, we readily conclude that Navarro’s Colorado statute of conviction is broader than either of the federal crimes listed in tier II of SORNA. Navarro’s crime of conviction proscribes sexual contact with a child younger than fifteen, so long as the offender is at least four years older than the victim. Colo. Rev. Stat. § 18-3-405(1) (1998). The two relevant federal statutes criminalize slightly different conduct— § 2243(a) criminalizes sexual acts with a minor between the ages of twelve and sixteen so long as the victim is at least four years younger than the offender, and § 2241(c) prohibits all sexual acts with children younger than twelve. There is some overlap between those statutes, as the government points out. Nevertheless, under the categorical approach, overlap is not enough. Colorado’s statute is broader than § 2243(a) because it criminalizes sexual contact with children younger than twelve, while § 2243(a) only criminalizes contact with children between twelve and sixteen years of age. Meanwhile, the Colorado statute is broader than § 2241(c) because it covers illicit sexual contact with twelve-to fourteen-year-olds, but § 2241(c) stops before age twelve. In short, the Colorado statute “sweeps more broadly” than either of the comparable federal statutes. Descamps, 570 U.S. at 261.[14] Our conclusion follows directly from Escalante, in which this court held that a Utah sex offense was not “comparable” to any of the federal crimes in SORNA’s tier II. 933 F.3d at 400–01. Escalante was convicted under a Utah statute that criminalized consensual sexual activity with some-one aged fourteen to fifteen. See id. at 397 n.3. The only federal crime in SORNA’s tier II that was theoretically comparable was § 2243(a), which criminalizes sex with twelve-to fifteen-year-olds. But the federal statute “requires, as an element, that the government prove at least a four-year age differential” between the offender and the victim. Escalante, 933 F.3d at 400. In other words, “[T]he Utah statute criminalized consensual sexual activity between an 18-year-old and a 15-year-old,” while the federal statute did not. Id. at 401. Therefore, the court held that “under the categorical approach, the Utah offense ‘sweeps more broadly’ than the comparable federal offense and cannot serve as a proper predicate for a SORNA tier II sex offender designation.” Id. at 402 (quoting Descamps, 570 U.S. at 261). This case presents the same situation—by criminalizing conduct that the federal statutes do not, Colorado’s statute sweeps too broadly to serve as a predicate SORNA offense. Escalante also rebuts the government’s contention that Navarro’s crime is “comparable” to a tier II offense because it is narrower than some of the offenses listed in SORNA. Namely, § 2243(a) criminalizes sex with fifteen-year-olds where there is a four-year age gap between the participants whereas the Colorado statute does not. Compare § 2243(a), with Colo. Rev. Stat. § 18-3-405 (1998). But the state statute in Escalante was narrower in the same sense—the relevant federal statutes criminalized some conduct that the Utah statute did not. See Escalante, 933 F.3d at 397 n.3. Nevertheless, Escalante held that the Utah statute swept “more broadly” because it criminalized more conduct than the federal statute. Id. at 402 (quotation omitted). Similarly, the Colorado statute criminalizes conduct that neither § 2243(a) nor § 2241(c) criminalizes. That over-inclusiveness means the statutes are not “comparable.” Escalante, 933 F.3d at 402. Navarro’s claim finds additional support in United States v. Walker, 931 F.3d 576 (7th Cir. 2019) (Barrett, J.). Walker was convicted under the same Colorado statute as Navarro and failed to register after he was released. Id. at 578. The Seventh Circuit had to decide whether the Colorado statute was “comparable” to any of the offenses in SORNA’s tier II. Id. (quoting § 20911(3)(A)(iv)). After adopting the categorical approach, Judge Barrett held that it was not. Id. at 580, 582. As in this case, the United States in Walker suggested that the Colorado statute prohibited the same conduct as did §§ 2243(a) and 2241(c). Id. at 582. Still, the court reasoned that “the Colorado statute sweeps more broadly than § 2243(a) because it covers sexual contact against some victims under 12, and § 2243(a) does not.” Id. Mean-while, Colorado’s statute is broader than § 2241(c) because the state law “covers some victims between the ages of 12 and 15, and § 2241(c) does not.” Id. In other words, “a conviction under the Colorado statute doesn’t necessarily satisfy the elements of either federal offense and so fails the categorical analysis.” Id. The Seventh Circuit’s persuasive conclusion is equally applicable here. In sum, Navarro had no federal duty to register as a sex offender in 2019. He was a tier I offender under SORNA, and so his 15-year duty to register ended in 2016 and was no longer operative at the time of his indictment. Therefore, Navarro could not be convicted of a § 2250(a) offense, and, as the government now concedes (albeit for a different, flawed reason), the factual basis supporting his guilty plea was insufficient as a “matter of law.” Trejo, 610 F.3d at 313. IV. Our final consideration is whether Navarro’s faulty conviction is “plain error.” To succeed under plain-error review, a defendant must establish four things. First, the district court must err. Greer v. United States, 141 S. Ct. 2090, 2096 (2021). Second, the error must be “plain,”id., “clear[,] or obvious, rather than subject to reasonable dispute.” Puckett v. United States, 556 U.S. 129, 135 (2009). Third, “the error must affect ‘substantial rights,’ which generally means that there must be ‘a reasonable probability that, but for the error, the outcome of the proceeding would have been different.’” Greer, 141 S. Ct. at 2096 (quoting Rosales-Mireles v. United States, 138 S. Ct. 1897, 1904–05 (2018)). Finally,”[i]f those three requirements are met, an appellate court may grant relief if it concludes that the error had a serious effect on ‘the fairness, integrity or public reputation of judicial proceedings.’” Id. at 2096–97 (quoting Rosales-Mireles, 138 S. Ct. at 1905). Even though plain error is an exacting standard, see, e.g., United States v. Young, 470 U.S. 1, 15 (1985), all four elements are met here. First, the district court erred. Greer, 141 S. Ct. at 2096. Navarro did not have an obligation to register “under [SORNA]” in 2019. § 2250(a). The admitted facts were insufficient to establish his guilt as a matter of law. Trejo, 610 F.3d at 313; see also Fed. R. Crim. P. 11(b)(3). Second, the error was “plain.” Greer, 141 S. Ct. at 2096. It is well-established that this circuit takes a categorical approach to interpreting SORNA’s tiers.[15] Nevertheless, the district court treated Navarro as a tier II offender without any meaningful comparison of the state and federal statutes. The government suggests that the categorical approach to comparing SORNA offenses may not have been evident to the district court at the time it accepted Navarro’s guilty plea. See United States v. Olano, 507 U.S. 725, 734 (1993) (noting that a district court’s mistake cannot be plain error if the law was unclear). Yet on plain-error review, we determine whether the law was “settled” based on the law at the time of the appeal, not the time of conviction. United States v. Escalante-Reyes, 689 F.3d 415, 423 (5th Cir. 2012) (en banc). As of this appeal, the Fifth Circuit has stated, in at least three precedential opinions, that we use the categorical approach to compare offenses under SORNA. See Young, 872 F.3d at 746; Escalante, 933 F.3d at 398; Montgomery, 966 F.3d at 338. Our most recent opinion made clear that any predicate state offense that criminalizes more conduct than a related federal offense “sweeps more broadly” and therefore cannot be “comparable.” Montgomery, 966 F.3d at 338 (quotations omitted). In treating Navarro’s Colorado conviction as a tier II offense, the district court departed from that established mandate. Third, the error affects substantial rights. Greer, 141 S. Ct. at 2096. A defendant challenging the sufficiency of a guilty plea under Rule 11 must show “a reasonable probability that, but for the error, he would not have entered the plea.” United States v. Dominguez Benitez, 542 U.S. 74, 83 (2004). It is hard to deny that Navarro would not have pleaded guilty if he had correctly understood the tier of his predicate sex offense. Similarly, the district court would likely not have accepted the guilty plea if it had known Navarro had failed to satisfy the first element of the crime.[16] Indeed, in Montgomery, this court held that the failure correctly to classify a defendant’s tier under SORNA was “plain error” both because the correct tiering was “clear under current law” and because the mistake “resulted in [the defendant's] serving additional time in prison.” 966 F.3d at 339. The same is true here.[17] Finally, affirming Navarro’s conviction would undermine the integrity of judicial proceedings by permitting the continued punishment of a man who is not guilty of the crime charged. See Greer, 141 S. Ct. at 2097. We have been instructed to”correct a plain forfeited error that causes the conviction or sentencing of an actually innocent defendant.” See Olano, 507 U.S. at 736. We accordingly conclude that the error is reversible. * * * The judgment of conviction is VACATED. The motions carried with the case are DENIED as moot, and the case is REMANDED for the district court to ensure the termination of Navarro’s revocation sentence and for any other proceedings not inconsistent with this opinion.