Before Ho, Duncan, and Oldham, Circuit Judges. Andrew S. Oldham, Circuit Judge: A Texas state court convicted Michael Ray Senn of sexual assault and prohibited sexual conduct with his intellectually disabled daughter. The state court sentenced Senn to life in prison. In this federal habeas case, Senn con-tends that his sentence offends the Equal Protection Clause. We deny relief. I We describe (A) Senn’s trial in state court, (B) his state court appeals, and (C) his postconviction proceedings in state and federal court. A “Brenda”[1] is Senn’s intellectually disabled biological child. She has a tested IQ of 64. According to a psychologist’s testimony in the record, Brenda has the competence of a “preteen.” A nurse testified that Brenda has a “very childlike” demeanor. In 2011, Senn raped Brenda. Brenda understood neither that what happened to her was sex nor that sex could result in pregnancy. Brenda be-came pregnant after the assault. In January 2012, she gave birth to a child. DNA testing showed a high statistical probability that Senn was thebiological father. In 2015, a Texas jury found Senn guilty of felony sexual assault for raping and impregnating Brenda. Sexual assault is generally a felony of the second degree subject to a statutory maximum sentence of 20 years. Tex. Penal Code §§ 22.011(f), 12.33(a). But sexual assault is a felony of the first degree—and the statutory maximum is life imprisonment—when the victim is “a person whom the actor was prohibited from marrying or purporting to marry or with whom the actor was prohibited from living under the appearance of being married under Section 25.01.” Tex. Penal Code §§ 22.011(f)(1)(A), 12.32(a). We refer to this provision as the Section 22.011(f) enhancement. Texas sought the Section 22.011(f) enhancement for Senn’s conduct, arguing that Senn was prohibited from marrying his daughter because he was already married—namely, to Brenda’s stepmother.[2] The jury agreed. After the guilty verdict, Senn was sentenced to life imprisonment for a first-degree felony under the Section 22.011(f) enhancement and to an additional concur-rent term of 20 years’ imprisonment for prohibited sexual conduct. B Senn then litigated a series of unsuccessful appeals in the Texas state court system. First, the appellate court affirmed Senn’s conviction on direct appeal. Senn v. State (Senn I), 551 S.W.3d 172, 183 (Tex. App.—Fort Worth, 2017). Second, the Texas Court of Criminal Appeals granted Senn’s petition for discretionary review, vacated Senn I, and remanded the case for reconsid-eration in light of its recent decision in Arteaga v. State, 521 S.W.3d 329 (Tex. Crim. App. 2017), superseded by statute, Tex. Penal Code § 22.011(f)(1)(B), as recognized in Lopez v. State, 600 S.W.3d 43, 46 (Tex. Crim. App. 2020).[3] See State v. Senn (Senn II), No. PD-0145-17, 2017 WL 5622955 (Tex. Crim. App. Nov. 22, 2017). In Arteaga, the Texas Court of Criminal Appeals held that Section 22.011(f) enhanced sexual assault from a second-degree felony to a first-degree felony only when the State “prove[d] facts constituting bigamy.” Arteaga v. State, 521 S.W.3d 329, 336 (Tex. Crim. App. 2017). The court reasoned that Section 22.011(f) and Texas’s bigamy statute, Tex. Penal Code § 25.01, which Section 22.011(f) incorporates by reference, “should be read together.” Arteaga, 521 S.W.3d at 336. Third, the court of appeals rendered, and subsequently withdrew on rehearing, an opinion applying Arteaga on remand. See Senn v. State (Senn III), No. 02-15-00201-CR, 2018 WL 2248673 (Tex. App.—Fort Worth, May 17, 2018). Fourth, the court of appeals’ substitute opinion held that there was insufficient evidence to support Senn’s Section 22.011(f) enhancement. Senn v. State (Senn IV), 614 S.W.3d 130, 138 (Tex. App.—Fort Worth, 2018). Reasoning that Arteaga required Texas to prove that Senn’s actions constituted bigamy under Section 25.01 to trigger a Section 22.011(f) enhancement, the court remanded for a new sentence because “no facts exist[ed] that Senn committed a bigamy offense” when he sexually assaulted Brenda. Senn IV, 614 S.W.3d at 138. Fifth, Texas petitioned the Court of Criminal Appeals for review of that decision, seeking clarification on “whether the State must prove com-mission of bigamy in order to enhance punishment of sexual assault under Penal Code Section 22.011(f).” Lopez, 600 S.W.3d at 44. In Lopez, which consolidated three cases, including Senn IV, the Court of Criminal Appeals held that it did not. Id. at 47. To trigger the Section 22.011(f) enhancement, Texas need prove only that “the defendant was legally married to someone other than the victim at the time of the sexual assault.” Id. at 47–48. Accord-ingly, the fact that Senn was married to Brenda’s stepmother when he raped his daughter was sufficient to trigger the enhancement. Id. at 49–50. Sixth, in Senn V, on remand from Lopez, the court of appeals affirmed the trial court’s original judgment and rejected Senn’s sufficiency-of-the- evidence claim. Senn v. State (Senn V), No. 02-15-00201-CR, 2020 WL 6065926, at *2 (Tex. App.—Fort Worth, Oct. 15, 2020). The court also rejected Senn’s as-applied equal protection challenge to Section 22.011(f). Id. at *8. In Senn V, the court of appeals held that Section 22.011(f) did not vio-late the Equal Protection Clause of the Fourteenth Amendment as applied to Senn. Id. at *8. Relying on a Court of Criminal Appeals precedent, the court noted that Section 22.011(f) was not facially unconstitutional. Ibid. (citing State v. Rosseau, 396 S.W.3d 550, 558 (Tex. Crim. App. 2013)). The court reasoned that Section 22.011(f) as applied to Senn was rationally related to the State’s interest in protecting children from sexual exploitation. Ibid. (citing Estes v. State, 546 S.W.3d 691, 700 (Tex. Crim. App. 2018)). In Estes, the Court of Criminal Appeals upheld the application of Section 22.011(f) to a married man who had been convicted of sexually assaulting a 14-year-old girl, crediting as rational “the idea that marriage bestows upon its partici-pants a certain aura of trustworthiness, specifically in regard to children.” 546 S.W.3d at 702. The Senn V court reasoned that the “basic facts” in Senn’s case were the same as those in Estes. 2020 WL 6065926, at *8. Seventh, on May 12, 2021, the Court of Criminal Appeals of Texas re-fused Senn’s petition for discretionary review of Senn V. C On September 30, 2022, Senn filed a state habeas application, arguing that Texas’s application of Section 22.011(f) to him violated the Equal Pro-tection Clause of the Fourteenth Amendment because it exposed married persons to a higher rangeof punishment than unmarried persons for thesame offense. The court denied Senn’s application without written order, holding that Senn’s equal protection challenge was barred because it had been raised and rejected on direct appeal in Senn V. Next, Senn petitioned for a writ of habeas corpus in federal district court. Senn again asserted his as-applied equal protection challenge to Sec-tion 22.011(f). The district court held that Senn’s petition was barred by the Anti-Terrorism and Effective Death Penalty Act of 1996 (“AEDPA”), 28 U.S.C. § 2254(d). The district court noted that Texas state courts had heard and rejected Senn’s equal protection challenge on the merits, and it agreed that Section 22.011(f) did not violate the Equal Protection Clause as applied to Senn.Thedistrictcourt held thatSenn had not shown that the”statecourt adjudication was incorrect in any respect” and that he had “certainly . . . not met his burden under § 2254(d).” Senn timely noticed his appeal. Wegranted him a certificateof appeal-ability on his as-applied equal-protection challenge to Section 22.011(f). II We affirm. We first (A) explain AEDPA’s demanding strictures and then (B) hold that Senn cannot satisfy them. A To succeed under AEDPA, a petitioner must show that the state court’s adjudication of the relevant claim “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). The Supreme Court calls this provision the “reliti-gation bar.” Harrington v. Richter, 562 U.S. 86, 100 (2011). As its name sug-gests, the relitigation bar imposes a nearly “complete bar on federal-court relitigation of claims already rejected in state proceedings.” Id. at 102. Under AEDPA, habeas corpus serves as a “guard against extreme malfunctions in the state criminal justice systems, not [as] a substitute for ordinary error cor-rection through appeal.” Ibid. (quoting Jackson v. Virginia, 443 U.S. 307, 332, n.5 (1979) (Stevens, J., concurring in the judgment)) (quotation omitted). As relevant here, AEDPArequires a state prisoner to “shoehorn” his claim into one of two narrow exceptions. Langley v. Prince, 926 F.3d 145, 155 (5th Cir. 2019) (en banc). First, a petitioner can show that the state court decision was “contrary to” clearly established federal law. 28 U.S.C. § 2254(d)(1). “A state court decision is ‘contrary to’ clearly established federal law only if it arrives at a conclusion opposite to that reached by the Supreme Court on a question of law or if it resolves a case differently than the Supreme Court has on a set of materially ‘indistinguishable’ facts.” Langley, 926 F.3d at 156 (quoting Wil-liams v. Taylor, 529 U.S. 362, 413 (2000)) (quotation omitted). Second, a petitioner can show that the state court decision involved an “unreasonable application of” clearly established federal law. 28 U.S.C. § 2254(d)(1). This standard requires a prisoner to “show far more than that the state court’s decision was merely wrong or even clear error.” Shinn v. Kayer, 592 U.S. 111, 118 (2020) (per curiam) (quotation omitted). Instead, the petitioner must show that the state court’s “determination was unreason-able—a substantially higher threshold.” Schriro v. Landrigan, 550 U.S. 465, 473 (2007) (emphasis added). To clear the relitigation bar, the complained-of unreasonable application by the state court must be “so lacking in justifi-cation that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement.” Woods v. Etherton, 578U.S. 113, 117 (2016) (per curiam) (quoting White v. Woodall, 572U.S.415, 420 (2014)). Finally, even if a petitioner can shoehorn his claim into one of the re-litigation bar’s exceptions, he “still must show, on de novo review, that he is in custody in violation of the Constitution or laws or treaties of the United States.” Langley, 926 F.3d at 156 (quoting Salts v. Epps, 676 F.3d 468, 480 (5th Cir. 2012); 28 U.S.C. § 2254(a)) (quotation omitted). B Senn’s equal protection claim satisfies neither exception, so he cannot clear the relitigation bar. We consider each of the relitigation bar’s relevant provisions in turn. 1 We begin with the relitigation bar’s contrary-to prong. It requires Senn to identify “clearly established Federal law, as determined by the Su-preme Court of the United States.” 28 U.S.C. § 2254(d)(1); see also Langley, 926 F.3d at 156. Senn must identify a Supreme Court case that is “materially indistinguishable” from his own. Williams, 529 U.S. at 413. He offers only one: Eisenstadt v. Baird, 405 U.S. 438 (1972). In Eisen-stadt, the Supreme Court evaluated the constitutionality of a Massachusetts statute that criminalized the distribution of certain contraceptives to unmar-ried persons. See id., 405 U.S. at 440–42. Applying rational basis review, the Court held that the contraceptive ban’s differential treatment of married and unmarried persons violated the Equal Protection Clause of the Fourteenth Amendment because the Commonwealth had no rational interest in deter-ring premarital sex or promoting health that was served by the discrimination. Id. at 447. The State of Texas has an obvious and eminently rational basis for enhancing Senn’s sentence: he was married, namely to Brenda’s stepmother, which is one of the many aggravating factors of his heinous crime. It should go without saying that this case bears zero resemblance to Eisenstadt. And it bears even less resemblance to a violation of AEDPA’s contrary-to prong. 2 Next, the unreasonable-application prong. This part of the relitigation bar requires Senn to show that no fairminded jurist could agree with the state court’s application of clearly established Supreme Court precedent. See Woodall, 572 U.S. at 427. If “disagreement is possible, then the petitioner’s claim must be denied.” Sexton v. Beaudreaux, 585 U.S. 961, 965 (2018). Fur-thermore, “if a habeas court must extend a rationale before it can apply to the facts at hand, then by definition the rationale was not clearly established at the time of the state-court decision.” Woodall, 572 U.S. at 426 (quotation omitted). Senn cannot come close to showing that all fairminded jurists would believe that Eisenstadt‘s rule—or rational basis review generally—forecloses Section 22.011(f)’s enhancement for bigamous rapists. Eisenstadt held that a stateinterest in deterring premarital sex or promoting health could not justify a ban on the sale of contraceptives on the basis of marital status. 405 U.S. at 447. It said nothing about a married man raping his own child. And, as the state court held, Eisenstadt did nothing “to discard as ‘irrational’ the idea that marriage bestows upon its participants a certain aura of trustworthiness, specifically in regard to children.” Estes, 546 S.W.3d at 702. True, Brenda was technically an 18-year-old adult when Senn raped and impregnated her. And it is also true that Estes said the Section 22.011(f) enhancement was principally designed to “protect[] children from sexual abuse.” Id. at 700. But no part of Section 22.011(f) requires a juvenile victim. As the Court of Criminal Appeals emphasized: [M]uch of [Estes'] reasoning would apply equally to an adult victim of sexual assault. As Estes points out, there is a strong societal connection between the union of marriage and the ideas of family, home, safety, stability, and security. A married defendant may abuse these deeply-rooted beliefs even if hisvic-tim is an adult. Lopez, 600 S.W.3d at 47. This is all the more true where, as here, the victim has the competence of a “preteen” and a “very childlike” demeanor. Accordingly, the Section 22.011(f) enhancement rests on an unquestionably rational basis. Eisenstadt thus does nothing to undermine the State’s reasons for specially punishing married rapists. At a minimum, Senn’s contention requires a monumental extension of Eisenstadt, which would undermine “AEDPA’s carefully constructed framework.” Woodall, 572 U.S. at 426. We decline that invitation. * * * Judgment AFFIRMED. Habeas DENIED.
