Appeal from the United States District Court for the Southern District of New York No. 20-Cr-389 (JGK) John G. Koeltl, District Judge, Presiding. (Argued March 23, 2023; Decided September 6, 2023) The government appeals from a judgment of conviction entered against Defendant-Appellee Dave Minter in the United States District Court for the Southern District of New York (Koeltl, J.) after Minter pleaded guilty to being a felon in possession of a firearm, in violation of 18 U.S.C. §§922(g)(1), 924(a)(2), and 2. The District Court sentenced Minter to 72 months’ imprisonment. At sentencing, the District Court rejected the government’s contention that Minter qualified for a sentencing enhancement under the Armed Career Criminal Act (“ACCA”) because his 2014 conviction for possession of cocaine under N.Y. Penal Law §220.39 was a qualifying predicate offense. Specifically, the District Court held that New York’s definition of cocaine is categorically broader than the relevant federal definition. We agree, and therefore, we AFFIRM. BARRINGTON PARKER, C.J. The government appeals from a judgment of conviction entered against Defendant-Appellee Dave Minter in the United States District Court for the Southern District of New York (Koeltl, J.) The District Court concluded that Minter was not a career offender under the Armed Career Criminal Act (“ACCA”), 18 U.S.C. §924(e)(1), and therefore declined to impose a sentencing enhancement sought by the government. The issue presented by this appeal is whether Minter’s 2014 conviction under New York Penal Law §220.39(1) for the sale of cocaine was for a “serious drug offense” and therefore qualifies as a predicate offense for the purposes of a sentencing enhancement under the ACCA. Because we hold that New York’s definition of cocaine is categorically broader than its federal counterpart, Minter’s cocaine conviction cannot serve as a predicate ACCA offense. We therefore affirm the judgment of conviction. BACKGROUND In April 2020, Minter was arrested in the Bronx after discharging a pistol. He was subsequently indicted for one count of being a felon in possession of a firearm, in violation of 18 U.S.C. §§922(g)(1), 924(a)(2), and 2, to which he pleaded guilty in April 2021. The government notified Minter just before he entered his plea that it intended to seek an enhanced mandatory minimum sentence that, it claimed, had been triggered under the ACCA by Minter’s three prior felony convictions in New York. 18 U.S.C. §§924(e)(2)(A)(ii)-(B)(i). Those prior convictions included: (1) a 2004 conviction for robbery in the third degree; (2) a 2009 conviction for robbery in the second degree; and (3) as relevant here, a 2014 conviction for the sale of a controlled substance in the third degree, after being caught with approximately a quarter kilogram of cocaine. Because Minter does not contest and did not contest below that, following United States v. Thrower, 914 F.3d 770, 776 (2d Cir. 2019), his two prior robbery convictions qualified as violent felonies under §924(e)(2)(B)(i) of the ACCA, this appeal concerns only Minter’s third conviction. In seeking the enhancement, the government characterized Minter’s 2014 conviction under New York Penal Law §220.39(1), as a “serious drug offense,” pursuant to 18 U.S.C. §924(e)(2)(A)(ii). The enhancement would have increased Minter’s term of imprisonment from a 10-year maximum (and no minimum) to a mandatory minimum of imprisonment of 15 years. Minter objected to his classification as a career offender on the ground that the New York cocaine offense was categorically broader than its federal counterpart under the Controlled Substances Act (“CSA”), 21 U.S.C. §802. Specifically, Minter argued that the CSA prohibits possession of only optical and geometric isomers of cocaine, while New York’s statute prohibits possession of all cocaine isomers. Because of this categorical mismatch, Minter argued, his 2014 conviction for selling cocaine could not serve as a predicate offense for a sentencing enhancement under the ACCA. The government responded that New York State does not criminalize isomers of cocaine beyond its optical and geometric isomers because those isomers are not chemically equivalent to coca leaves, and because the New York State Legislature could not have intended its definition of cocaine to reach such isomers. The government also argued that the court should apply the “realistic probability test” to find no such probability that the New York statute would ever be applied to prosecute conduct involving a non-optical or non-geometric isomer of cocaine. The District Court was not persuaded by the government’s arguments. It concluded that New York’s definition of cocaine, without any textual limitation on the types of isomers it reaches, was categorically broader than the federal definition, which expressly limits itself to only optical and geometric isomers. Finding the predicate for a sentencing enhancement under the ACCA unmet, the District Court then sentenced Minter to 72 months’ imprisonment.1 This appeal followed. We review de novo whether a prior conviction qualifies as a “serious drug offense” under ACCA. United States v. Ojeda, 951 F.3d 66, 69 (2d Cir. 2020). DISCUSSION Under the ACCA, a defendant who has three prior convictions for violent felonies or serious drug offenses is subject to a mandatory minimum sentence of fifteen years if convicted of possessing a firearm or ammunition that has been transported in interstate commerce. 18 U.S.C. §924(e)(1). The term “serious drug offense” is defined as: (i) an offense under the Controlled Substances Act (21 U.S.C. 801 et seq.), the Controlled Substances Import and Export Act (21 U.S.C. 951 et seq.), or chapter 705 of title 46, for which a maximum term of imprisonment of ten years or more is prescribed by law; or (ii) an offense under State law, involving manufacturing, distributing, or possessing with intent to manufacture or distribute, a controlled substance (as defined in section 102 of the Controlled Substances Act (21 U.S.C. 802)), for which a maximum term of imprisonment of ten years or more is prescribed by law. 18 U.S.C. §924(e)(2)(A). If a state statute of conviction is broader than its federal counterpart — that is, if the state statute criminalizes conduct that is not criminalized under the analogous federal law — the state conviction cannot be used to enhance a defendant’s sentence under the ACCA. Cf. United States v. Townsend, 897 F.3d 66, 72 (2d Cir. 2019). We apply the categorical approach to determine whether a state law matches conduct involving a controlled substance as defined under federal law. See Mathis v. United States, 579 U.S. 500, 504 (2016); see also Taylor v. United States, 495 U.S. 575, 602 (1990). “‘Under the categorical approach, courts identify the minimum criminal conduct necessary for conviction under a particular statute’ by ‘looking only to the statutory definitions — i.e., t he elements — of the offense, and not to the particular underlying facts.’” Hylton v. Sessions, 897 F.3d 57, 60 (2d Cir. 2018) (quoting United States v. Hill, 890 F.3d 51, 55 (2d Cir. 2018)). The categorical approach “is concerned with the existence of a valid prior conviction and the statute of conviction,…[i.e.] ‘to the fact that the defendant has been convicted of crimes falling within certain categories, and not to the facts underlying the prior conviction.’” United States v. Thompson, 961 F.3d 545, 550 (2d Cir. 2020) (quoting Taylor, 495 U.S. at 600). “When [a] state law is facially overbroad” — even by a minimal amount — “we look no further.” Hylton, 897 F.3d at 65 (internal quotation marks omitted). That proposition applies to the identity of prohibited substances, as “the state law must criminalize only those substances that are criminalized under federal law.” Townsend, 897 F.3d at 74. A state’s criminalization of a single substance not also prohibited by the CSA is often enough to prevent a prior conviction from triggering a federal sentencing enhancement. See id. (finding New York’s criminalization of human chorionic gonadotropin categorically overbroad compared to the CSA, which does not list that substance); cf. Hylton, 897 F.3d at 59, 63 (holding that federal law punishing as a felony a “small amount” of marijuana, defined as thirty grams, is a categorical mismatch t o New York’s law, which overbroadly punished as a felony only twenty-five grams of marijuana). Here, the relevant offense is Minter’s 2014 conviction for the sale of cocaine, a violation of New York Penal Law §220.39(1). That section provides, in relevant part, that “[a] person is guilty of criminal sale of a controlled substance in the third degree when he knowingly and unlawfully sells…a narcotic drug.” N.Y. Penal Law §220.39(1). A “narcotic drug” is defined as “any controlled substance listed in schedule I(b), I(c), II(b) or II(c) other than methadone.”2 N.Y. Penal Law §220.00(7). Since 1978, Schedule II(b) of the New York Public Health Law, in turn, defines “cocaine” and related substances as: Coca leaves and any salt, compound, derivative, or preparation of coca leaves, and any salt, compound, derivative, or preparation thereof which is chemically equivalent or identical with any of these substances including cocaine and ecgonine, their salts, isomers, and salts of isomers, except that the substances shall not include…decocainized coca leaves or extraction of coca leaves, which extractions do not contain cocaine or ecgonine. N.Y. Pub. Health Law §3306, Schedule II(b)(4). By contrast, Schedule II of the federal CSA defines cocaine as: Coca leaves…and any salt, compound, derivative or preparation of coca leaves (including cocaine…and ecgonine…and their salts, isomers, derivatives and salts of isomers and derivatives), and any salt, compound, derivative, or preparation thereof which is chemically equivalent or identical with any of these substances, except that the substances shall not include…decocainized coca leaves or extraction of coca leaves, which extractions do not contain cocaine or ecgonine. 21 C.F.R. §1308.12(b)(4). Unlike New York’s undefined use of the term “isomer,” the federal regulation further defines “isomer” to mean only “any optical or geometric isomer” of cocaine. Id. §1300.01(b). Isomers are “[c]hemical compounds that have the same composition but differ in the chemical arrangement of their constituents.” Merck Eprova AG v. Gnosis S.p.A, 760 F.3d 247, 252 (2d Cir. 2014). There are two broad types of isomers: stereoisomers — isomers in which the atoms are joined in the same order, but in a different spatial arrangement — and constitutional isomers, which are all other isomers, including what are termed “positional isomers.” See United States v. Phifer, 909 F.3d 372, 377-78 (11th Cir. 2018) (“Unlike in stereoisomers, the atoms in constitutional isomers differ in how they are connected.”). The CSA includes only stereoisomers — optical and geometric — in its definition of cocaine, but includes certain constitutional isomers in its definitions of other drugs. See, e.g., 21 C.F.R. §1308.11(d) (defining hallucinogens to include its “optical, positional, or geometric” isomers (emphasis added)). In comparison, the New York definition of cocaine does not limit itself to optical or geometric isomers. That is so even though the New York schedules supply specific definitions of criminalized isomers of other types of drugs. See, e.g., N.Y. Public Health Law §3306, Schedule I(d) (defining isomers of hallucinogenic substances “only” to “include[] the optical, position and geometric isomers”); see also id. §3306, Schedule I(g) (same, for synthetic cannabinoids). Without such an express limitation, New York law criminalizes conduct — specifically conduct involving cocaine isomers other than optical or geometric isomers — that the CSA does not. The plain text of the two statutes thus compels the conclusion that New York’s definition of cocaine is categorically broader than the federal definition. We do not find the government’s arguments to the contrary persuasive. The government argues first that the New York statute does not, on its face, include non-optical and geometric isomers of cocaine. The government contends that because the New York statute does not define “chemically equivalent or identical,” or “isomers,” that the face of the statute cannot be read to include all isomers. But a plain reading of the statute indicates that “cocaine and ecgonine, their salts, isomers and salts of isomers” are all defined as chemically equivalent to “coca leaves” or any “salt, compound, derivative or preparation thereof” and are thus controlled substances under New York law. “Isomers,” in other words, are specifically included in the subset of substances that are chemically equivalent or identical to coca leaves or any salt, compound, derivative or preparation thereof.3 See N.Y. Pub. Health Law §3306, Schedule II(b)(4) (listing as controlled substances “[c]oca leaves and any salt, compound, derivative, or preparation of coca leaves, and any salt, compound, derivative, or preparation thereof which is chemically equivalent or identical with any of these substances including…isomers” of cocaine (emphasis added)). We are also unpersuaded that we should rewrite New York’s definition of cocaine because the New York Legislature could not have intended to include all isomers in its definition of cocaine. The New York statute governing cocaine was amended in response to the growing problem of the “isomer defense,” which relied on the chemical difference between two particular isomers of cocaine, l-cocaine and d-cocaine. See United States v. Ross, 719 F.2d 615, 617 (2d Cir. 1983). Statutes all over the country during the 1970s and 80s prohibited “l-cocaine” or “levo-cocaine,” which is “natural” cocaine, but not “d-cocaine” or “dextro-cocaine,” which is a chemically synthesized compound wherein the base molecule is a mirror image of l-cocaine. See United States v. Hall, 552 F.2d 273, 275 (9th Cir. 1977); United States v. Gutierrez-Campos, No. 21 Cr. 40 (JPC), 2022 WL 281582, at *15 (S.D.N.Y. Jan. 31, 2022); United States v. Holmes, No. 21 Cr. 147 (NGG), 2022 WL 1036631, at *9 (E.D.N.Y. Apr. 6, 2022). Standard laboratory tests did not distinguish between l-and d-cocaine, and defendants could therefore argue that they could not be convicted for cocaine offenses beyond a reasonable doubt absent proof that the substance at issue in their case was in fact l-cocaine. In 1978, New York’s definition of cocaine was amended in response to this “isomer defense” problem. See App’x 89 (memorandum by the bill sponsor in support of the 1978 amendment, explaining “[t]he purpose of the bill is to assure that the dextro isomer of cocaine is included as a controlled substance,” and closing that “statutory loophole” by “includ[ing] all isomers of cocaine and ecgonine in the schedule of controlled substances”). The government contends “isomers” has a specific meaning targeted to that problem, because it was “widely understood” at the time of the 1978 amendment that cocaine has eight isomers: natural cocaine (l-cocaine) and its seven optical and geometric isomers, which included the problematic d-cocaine. Appellant’s Br. 35. According to the government, limiting New York’s definition to only eight isomers also helps to avoid the absurd result of including thousands of isomers of cocaine in New York’s definition, including some drugs approved by the Food and Drug Administration. That argument is unavailing. Constitutional isomers “were known to exist when the New York Legislature added the term ‘isomers’ to the definition of cocaine in 1978.” Holmes, 2022 WL 1036631 at *8 (citing Robert L. Clarke & Sol J. Daum, ß-Cocaine, 18 J. Med. Chemistry 102, 102-03 (1975)). The New York Legislature, like at least two other state legislatures to address the same isomer-defense issue,4 nevertheless made a policy choice to define cocaine as broadly as possible, without any limitation on the types of cocaine isomers it includes. See People v. Burnett, 666 N.Y.S.2d 658, 659 (2d Dep’t 1997) (“[A] controlled substance under Schedule II of Public Health Law §3306 includes cocaine and all of its isomers.” (emphasis added)). Given the plain text and purpose of the New York statute, we cannot rewrite the law to conform it to what the government contends is a realistic picture of actual cocaine prosecutions. Such arguments are better directed to the state legislature.5 Finally, the government argues, under Gonzalez v. Duenas-Alvarez, 549 U.S. 183, 193 (2007), that even if the New York definition of cocaine is broadly construed to criminalize all its isomers, Minter must show a “realistic probability, not a theoretical possibility,” that New York’s statute is broader in practice. “The categorical match inquiry is modified by the so-called realistic probability test when the state statute of conviction is of indeterminate scope in its application and so leaves open the possibility that it does not in practice match the federal statute; otherwise said, that the federal and state statutes appear from their texts alone to be a categorical match, but their enforcement may diverge in practice.” Williams v. Barr, 960 F.3d 68, 77 (2d Cir. 2020) (internal quotation marks omitted). “To demonstrate such a mismatch ‘requires a realistic probability, no t a theoretical possibility, that the State would apply its statute to conduct that falls outside the generic definition of a crime.”" Id. (quoting Duenas-Alvarez, 549 U.S. at 193). But as we have recently explained, the realistic probability test applies only “as a backstop when a [state] statute has indeterminate reach.” Hylton, 897 F.3d at 63. It has no place where, as here, the statute’s scope is plain. See Williams, 960 F.3d at 78 (“The ‘realistic probability’ test articulated in Duenas-Alvarez has no role to play in the categorical analysis…when the state statute of conviction on its face reaches beyond the generic federal definition.”); Hylton, 897 F.3d at 63-64 (“Here, the elements of the crime of conviction are not the same as the elements of the generic federal offense. The Supreme Court has never conducted a ‘realistic probability’ inquiry in such a case.” (citations omitted)). Here, the New York statute applies on its face to all cocaine isomers; the CSA does not. “When the state law is facially overbroad, we look no further.” Hylton, 897 F.3d at 65 (internal quotation marks and brackets omitted). CONCLUSION The judgment of the district court is affirmed.