This is a sentencing appeal brought by the United States. Noor Mohamed pleaded guilty to one count of being a felon in possession of a firearm, in violation of 18 U.S.C. §§ 922(g)(1) and 924(e). The district court held that, as a matter of law, Mohamed's prior Maine drug trafficking conviction did not qualify as a "controlled substance offense" under *97United States Sentencing Guidelines § 2K2.1(a), essentially adopting the reasoning of another Maine federal judge in another case, United States v. Oliveira, 287 F.Supp.3d 97 (D. Me. 2017).

Although Mohamed has been released from federal custody and is now in state custody on Maine charges, the government tells us it is important we address the issues. Because we determine that Mohamed's prior Maine conviction properly qualified as a "controlled substance offense," we vacate and remand for resentencing.

I.

Mohamed's commission of the federal offense is not contested. This conviction stems from a November 10, 2016, fight outside the Old Port Tavern in Portland, Maine. Mohamed drove a car -- taken without the owner's permission -- the wrong way down a one-way street towards two groups of men who were fighting. Mohamed shot two or three times at some of the men on the street, with one bullet grazing a man's sweatshirt, before Mohamed drove away quickly. A witness saw Mohamed exit the car near a dumpster, and heard a sound consistent with an item being thrown into the dumpster.

Police found a stolen semiautomatic Glock handgun, with a fifteen-round magazine, in the same dumpster on the next day. Forensic testing revealed that the gun had Mohamed's DNA on it. A woman who had been in the car with Mohamed stated that she had seen Mohamed with a handgun earlier that evening, and that she had seen him "pull[ ] the gun out to shoot" after he had driven towards the groups of men. After his arrest, Mohamed's face and hands tested positive for the presence of gunshot residue.

In December 2016, Mohamed was charged with one count of being a felon in possession of a firearm, in violation of 18 U.S.C. §§ 922(g)(1) and 924(e). The indictment listed four prior convictions punishable by imprisonment exceeding one year: three Massachusetts cocaine distribution convictions and one Maine drug trafficking conviction. Under a plea agreement, Mohamed pleaded guilty on November 21, 2017, to one count of being a felon in possession of a firearm.

The first Presentence Report (PSR), dated January 9, 2018, calculated a total offense level (TOL) of thirty and a criminal history category of VI. This PSR stated that Mohamed had nine prior convictions, including three separate 2010 Massachusetts cocaine distribution convictions, and an April 2014 Maine drug trafficking conviction that followed his plea to "unlawful trafficking in a scheduled drug." Me. Stat. tit. 17-A, § 1103(1-A)(A).

The PSR concluded that Mohamed's prior convictions meant he was an armed career criminal under the Armed Career Criminal Act (ACCA). See 18 U.S.C. § 924(e). The guideline imprisonment range was 180 to 210 months' imprisonment.

Before sentencing, Mohamed's three Massachusetts cocaine distribution convictions were vacated due to false or unreliable drug testing involving a former chemist in a Massachusetts crime lab, Annie Dookhan. A revised PSR was prepared, dated February 6, 2018, which included two-level and four-level enhancements for a stolen firearm and for possession of a firearm in connection with another felony offense, respectively. After the Dookhan-infected Massachusetts convictions were vacated, Mohamed no longer qualified as an armed career criminal under ACCA. He had a TOL of twenty-three and a criminal history category of III (which included his Maine trafficking conviction). The resulting *98guideline imprisonment range was fifty-seven to seventy-one months.

Mohamed objected to his Maine trafficking conviction being labeled and used as a "controlled substance offense." He argued that, in light of United States v. Mulkern, 854 F.3d 87 (1st Cir. 2017), and the district court decision in Oliveira,1 this conviction should not qualify as a "controlled substance offense" under the Guidelines. That was because, he argued, the Maine law allowed (but did not mandate) the use of a permissible inference of trafficking where a defendant possessed "4 grams or more of cocaine in the form of cocaine base." Me. Stat. tit. 17-A, § 1103(3).2 The Probation Office initially disagreed and distinguished Mulkern from Mohamed's case, but in its second revised PSR, dated March 23, 2018, the Probation Office agreed with Mohamed and did not recommend counting the Maine trafficking violation as a "controlled substance offense." This second revised PSR reduced Mohamed's TOL to seventeen, and the corresponding guideline imprisonment range to thirty to thirty-seven months.

In his sentencing memorandum, Mohamed acknowledged that the government had properly focused on the elements of the Maine offense, but argued that the relevant Shepard documents, see Shepard v. United States, 544 U.S. 13, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005), did not "show anything beyond the State's reliance on the [Section 1103 permissible] inference based on the quantity possessed." Mohamed argued, again using Oliveira (D. Me.) and Mulkern, that his Maine conviction therefore did not qualify as a "controlled substance offense" under the Guidelines. The government's sentencing memorandum argued that Mulkern could be distinguished, that Oliveira (D. Me.) had been wrongly decided, and that the Shepard documents showed that Mohamed pleaded guilty to a "controlled substance offense" under the Guidelines.

After review of the Shepard documents, the district court stated that the "controlled substance offense" issue was "very close," and acknowledged that by "go[ing] with [ Oliveira (D.Me.) ] ... I think we could be back here on a resentencing." The district court then adopted much of the reasoning in Oliveira (D. Me.), focusing on the "amount that would be deemed under Maine law to be enough to constitute trafficking" based on the amount required for the Section 1103 permissible inference. It also said, and the government vigorously disputes, that four grams of cocaine base "probably wouldn't be enough" to constitute trafficking or allow for such an inference under federal law. Accordingly, the district court accepted the second revised PSR, including the guideline imprisonment range of thirty to thirty-seven *99months' imprisonment. The district court sentenced Mohamed to thirty-seven months' imprisonment, as well as thirty-six months' supervised release. The government timely appealed.3

II.

"Whether a prior conviction qualifies as a predicate offense under U.S.S.G. § 4B1.1 is a question of law that we review de novo." United States v. Davis, 873 F.3d 343, 345 (1st Cir. 2017) (quoting United States v. Almenas, 553 F.3d 27, 31 (1st Cir. 2009) ).

We first lay out the federal and state statutes at issue, before briefly explaining the modified categorical approach, which binds us, as it applies to prior convictions under divisible statutes. We then turn to Mohamed's conviction, and determine that it properly qualifies as a "controlled substance offense." We finally consider federal drug trafficking prosecutions.

For 18 U.S.C. § 922(g) and other statutes, the Sentencing Guidelines establish enhanced Base Offense Levels (BOLs) for particular aggravating factors, including when a defendant has been convicted of a prior "controlled substance offense." U.S.S.G. § 2K2.1(a). A "controlled substance offense" under § 2K2.1(a)"has the meaning given that term in § 4B1.2(b) and Application Note 1 of the Commentary to § 4B1.2," id. § 2K2.1 cmt. 1:

an offense under federal or state law, punishable by imprisonment for a term exceeding one year, that prohibits the manufacture, import, export, distribution, or dispensing of a controlled substance ... or the possession of a controlled substance ... with intent to manufacture, import, export, distribute, or dispense.

Id. § 4B1.2(b). We have held that the definition of " 'controlled substance offense' requires that the statute under which the defendant was charged involve[ ] an intent to distribute or other indicia of trafficking." United States v. Bryant, 571 F.3d 147, 157 (1st Cir. 2009). The government bears the burden of demonstrating that a prior conviction properly qualifies as a predicate offense. United States v. Dávila-Félix, 667 F.3d 47, 55 (1st Cir. 2011).

Mohamed had pleaded guilty in 2014 to the following Maine law offense:

[A] person is guilty of unlawful trafficking in a scheduled drug if the person intentionally or knowingly trafficks in what the person knows or believes to be a scheduled drug, which is in fact a scheduled drug, and the drug is:

A. A schedule W drug.

Me. Stat. tit. 17-A, § 1103(1-A)(A). Under Maine law, cocaine base is a schedule W drug. Id. § 1102(1)(F). Maine law defines "traffick" in multiple alternative ways:

A. To make, create, manufacture;

B. To grow or cultivate, except for marijuana;

C. To sell, barter, trade, exchange or otherwise furnish for consideration;

*100D. To possess with the intent to do any act mentioned in paragraph C[.]

Id. § 1101(17).4 Subsections (A), (B), (C), and (D) track closely the Guidelines definition of a "controlled substance offense."

Maine law also allows a permissible inference regarding trafficking, based on the quantity of particular drugs possessed by a defendant, including cocaine base:

Proof that the person intentionally or knowingly possesses any scheduled drug that is in fact of a quantity, state or concentration as provided in this subsection, gives rise to a permissible inference under the Maine Rules of Evidence, Rule 303 that the person is unlawfully trafficking in scheduled drugs: ...

B. ... 4 grams or more of cocaine in the form of cocaine base.

Id. § 1103(3). This permissible inference need not be invoked by the State. State v. Peakes, 440 A.2d 350, 355 (Me. 1982) ("The State cannot be required to invoke the presumption of section 1103(3) when the evidence which it presents makes reliance upon the presumption unnecessary."). Where a case goes to trial and the permissible inference is invoked, the permissible inference requires the jury to come to its own conclusion based on the evidence before it, and respects the State's burden of proof beyond a reasonable doubt. See Me. Jury Instr. Manual, § 6-13 (2013).5

In addition, Maine Rule of Evidence 303, referenced directly by the permissible inference provision, contains two qualifications. First, "[t]he court may not direct a verdict against an accused based on a presumption or statutory provisions that certain facts are prima facie evidence of other facts or of guilt." Me. R. Evid. 303(b). And second,

[t]he charge must include an instruction that the jurors may draw reasonable inferences from facts proved beyond a reasonable doubt and may convict the accused in reliance upon an inference of fact if they conclude that such inference is valid and if the inference convinces them of guilt beyond a reasonable doubt and not otherwise.

Id. 303(c). Maine courts must use the term "inference" rather than "presumption" when referring to inferences and instructing the jury. See State v. Liberty, 478 A.2d 1112, 1116-17 (Me. 1984) ; State v. King, 379 A.2d 131, 134 (Me. 1977).

*101A. The Modified Categorical Approach

The Supreme Court has held that a sentencing court should use a categorical or modified categorical approach when considering sentencing enhancements based on prior offenses. See, e.g., Mathis v. United States, --- U.S. ----, 136 S.Ct. 2243, 2249, 195 L.Ed.2d 604 (2016) ; Taylor v. United States 495 U.S. 575, 588, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990). The categorical or modified categorical approach "applies not just to jury verdicts, but also to plea agreements." Descamps v. United States, 570 U.S. 254, 262-63, 133 S.Ct. 2276, 186 L.Ed.2d 438 (2013). Despite the criticisms and defenses of the categorical approach, it is binding on us, and thus there is no reason not to apply it here.

The Maine trafficking statute at issue here is divisible because there are a number of distinct ways to "traffick." See Me. Stat. tit. 17-A, §§ 1101(17), 1103. Some, including the one involved here, explicitly require an intent to distribute as an element of the crime. For divisible statutes, or those "that contain several different crimes, each described separately," Moncrieffe v. Holder, 569 U.S. 184, 191, 133 S.Ct. 1678, 185 L.Ed.2d 727 (2013), the Supreme Court has "approved [use of] the 'modified categorical approach.' " Mathis, 136 S.Ct. at 2249. When taking the modified categorical approach, "a sentencing court looks to a limited class of documents ... to determine what crime, with what elements, a defendant was convicted of." Id. These are known as Shepard documents, and include "the indictment, jury instructions, or plea agreement and colloquy." Id. We conclude from these permissible documents that Mohamed's Maine conviction falls under a provision requiring intent to distribute as an element.

This case is not about the wisdom of the categorical approach, and whether the reasons for it are convincing or not is simply irrelevant.

B. Mohamed's Maine Conviction

In August 2013, a Maine grand jury indicted Mohamed on several charges, including several counts of aggravated trafficking in scheduled drugs and one count of unlawful trafficking of scheduled drugs. At the plea colloquy, after the indictment had been modified, the State judge described to Mohamed the unlawful trafficking charge as "intentionally and knowingly traffic[king] in what you knew or believed to be a scheduled drug, which was, in fact, cocaine [base], a schedule W drug." Mohamed stated that he understood this charge, and pleaded guilty to an intent crime.

The intent element in Maine law Sections 1101(17)(C) and (D) is not stripped away by the existence of the Maine law Section 1103 permissible inference. The government first argues that the Shepard documents establish that the State relied on those sections requiring intent as an element, and that ends the matter. It argues that the district court strayed from the proper modified categorical approach. It contends that the permissible inference in any event still means that the prior offense is a controlled substance offense and does not negate the required finding of the element of an intent to distribute. The government also distinguishes this court's decision in Mulkern on a number of grounds, and says Oliveira (D. Me.) was both wrongly decided and did not follow from this court's decision in Mulkern.

Mohamed rests much of his argument on the reasoning of the district court opinion in Oliveira (D. Me.), and argues that the permissible inference means that the Maine legislature intended to proscribe "as trafficking the mere possession of a tiny amount ... of a mixture containing cocaine *102base."6 We disagree with this purported reading of Maine law. A corollary is his argument that such an amount is not enough to raise a rational inference of intent to distribute, as required for a "controlled substance offense."

Assuming arguendo that the district court correctly performed the modified categorical approach, we turn to the underlying legal issue: whether Section 1103's permissible inference means that a conviction under Section 1103(1-A)(A), based on the definition of trafficking in Section 1101(17)(C)-(D), cannot constitute a "controlled substance offense." We determine first that Mohamed's conviction was under a section requiring intent (and did not, in any event, rest on the permissible inference). We determine second that the permissible inference does not mean that a conviction under Section 1103 based on the definition of trafficking in Section 1101(17)(C)-(D) is not a "controlled substance offense."

1. The Permissible Inference and Mohamed's Maine Conviction

First, there is no evidence from the Shepard documents that Mohamed's Maine conviction rested on anything other than his intentional distribution plea. Also, the State prosecution is under no burden to rely upon or use the permissible inference. See Peakes, 440 A.2d at 355. Even assuming to Mohamed's benefit that the permissible inference impacted, in some unspoken way, his decision to plead guilty to the Maine charge -- although nothing in the record suggests this -- the State was prepared to offer and rely on evidence of intentional trafficking (other than the inference), which it would have sought to prove at trial.

Aware of the circumscribed scope of the modified categorical approach, we look to the plea colloquy here not to determine "the facts presented or admitted to by the defendant," United States v. Kennedy, 881 F.3d 14, 22 (1st Cir. 2018), but to discern on which portion of the divisible statute the State charged and proceeded. It is undisputed that the "brute facts" of the crime, id. at 21 (quoting Mathis, 136 S.Ct. at 2251 ), are not relevant to this case. In discerning which portion of a divisible statute is involved, the facts that the government said it would have sought to prove at trial demonstrate the portion of the divisible statute under which the State proceeded.7

*103Here, State prosecutors made clear the plea was to intentional trafficking. Indeed, they never mentioned the permissible inference during the plea colloquy. Instead, during the recitation of facts that the government would have sought to prove at trial, the State prosecutor explained the amount of cocaine base involved: 5.7 gross grams found in a glassine bag near Mohamed. The prosecutor did not connect this amount to the permissible inference regarding trafficking. The prosecutor instead told the court that "we would show that the $ 582 [found on Mohamed] was or could be proved to be part of drug proceeds," "based on the interview with [a man walking with Mohamed at the time of arrest], as well as ... [a] previous investigation that took place on May 6 and interviews done with people that had come into contact with Mr. Mohamed." In addition, the prosecutor stated the drugs were packaged for distribution:

I should also point out that we would ... show trafficking because of the way the baggie [containing cocaine base] was packed; it had individual baggies within it; to show that there was an intent to distribute it, rather than just for personal use. That's essentially the State's case.

The State prosecutor also laid out other evidence with which the State would have sought to prove intentional drug distribution, including defendant's possession of a bag with several firearms. We look to the plea colloquy to determine whether the portion of the statute involved distributive intent, which, as a matter of Maine law, it does.

In this same hearing, the State judge had explained to Mohamed that:

On the trafficking charge, the state is required to prove that ... you acted intentionally, that it was your conscious act to do so or knowingly, you were aware ... [and] certain that your actions would cause this result in trafficking, and to traffic[k] is to sell, buy, to trade, exchange, or otherwise furnish to another, and to furnish is to ... give, dispense, deliver, or otherwise transfer to another what you knew or believed to be a scheduled drug, which was in fact a scheduled drug, which was, in fact, cocaine-base[ ], a Schedule[ ] W drug.

Mohamed pled to that offense. The judge made no mention of the Section 1103 permissible inference.

A statutory presumption -- where a "statute by its terms applies to those who do not intend to distribute as long as they possess the requisite quantity," United States v. Brandon, 247 F.3d 186, 195 (4th Cir. 2001) -- is qualitatively different from the permissible inference under Section 1103, where the final inquiry remains whether a defendant intended to distribute the drug at issue (considering all of the evidence).8 As the Maine Supreme Judicial Court held in Peakes, the possession of an amount of a drug (there, marijuana) that would allow the permissible inference under Section 1103(3) "is not a necessary element of the crime of trafficking; it is a means by which the crime may be proved." 440 A.2d at 354. The permissible inference does not negate the distributive intent element *104of the crime. See Me. Stat. tit. 17-A, § 1101(17)(C)-(D).9 Thus, as a matter of Maine law, a jury must find distributive intent, whether it uses the permissible inference or not.

Accordingly, Oliveira (D. Me.) is wrong that, for the purposes of considering a "controlled substance offense" under the Sentencing Guidelines, "Maine's permissive inference instruction for cocaine [in subsection (D) ] demands similar treatment to its conclusive presumption for heroin and fentanyl addressed in Mulkern." 287 F.Supp.3d at 106. A Maine conviction for trafficking resting on the definition in Section 1101(17)(D) ("To possess with the intent to do any act mentioned in paragraph C [sell, barter, trade, exchange or otherwise furnish for consideration]") qualifies as a "controlled substance offense."

In summary, the Shepard documents establish that Mohamed's Maine conviction rested on intentional distribution, to which he pled. The elements of the statute at issue -- when taking into account the definitions of "traffick" relevant here, see Me. Stat. tit. 17-A, § 1101(17)(C)-(D) -- include intent to distribute. This element is not swept away by the existence of a permissible inference. Again, the statutory elements here closely track the "controlled substance offense" definition in the Guidelines. Mohamed's Maine conviction is properly a "controlled substance offense" under the Guidelines.

2. Assuming the Use of the Permissible Inference

Second, even were we not allowed to refer to these documents and were required to assume that this is a case involving the permissible inference because it might have impacted Mohamed's plea, despite all the evidence to the contrary, we would reach the same result. Importantly, the Supreme Court has held that "[a] permissive inference does not relieve the State of its burden of persuasion because it still requires the State to convince the jury that the suggested conclusion should be inferred based on the predicate facts proved." Francis v. Franklin, 471 U.S. 307, 314, 105 S.Ct. 1965, 85 L.Ed.2d 344 (1985).10 Maine law is not to the contrary. The relevant jury instruction in Maine states: "You may reject an inference if you wish. The ultimate decision is up to you .... [Y]ou must remember that the burden remains on the State to prove each element of the offense beyond a reasonable doubt." Me. Jury Instr. Manual, § 6-13 (2013) (emphasis added). And distributive intent is an element.

Our decision in Mulkern is clearly distinguishable from this case. In Mulkern we held, among other things, that the defendant's Maine drug trafficking conviction did not qualify as an ACCA predicate "serious drug offense" because intent to distribute could not be inferred from the title of the Maine trafficking statute nor from merely possessing two grams or more of heroin. 854 F.3d at 96. There, the defendant *105had pleaded guilty to trafficking in Maine in 2004, based on the provision of the Maine trafficking statute containing a statutory presumption of trafficking in subsection (E) based only on the amount, either in grams or receptacles, of heroin possessed ("To possess 2 grams or more of heroin or 90 or more individual bags, folds, packages, envelopes or containers of any kind containing heroin," Me. Stat. tit. 17-A, § 1101(17)(E)). Mulkern, 854 F.3d at 94. The trafficking provision at issue in Mulkern does not require that the government prove any other element of intent, such as the intent to "sell, barter, trade, exchange or otherwise furnish for consideration," Me. Stat. tit. 17-A, § 1101(17)(C)-(D); it must only show mere possession of a set amount of heroin or receptacles containing heroin.

In Mulkern, then, this court addressed arguments concerning the inference of trafficking from the title of a statute, and presumption of illegality from drug quantity or containers alone, neither of which are presented here. That is, distributive intent was not a necessary element of the portion of the crime to which the defendant in Mulkern pleaded guilty. In contrast, the crime to which Mohamed pleaded guilty did require distributive intent, as demonstrated in the plea colloquy, a permissible Shepard document.

So this case does not raise what the Mulkern court called the "difficult question" of "what is the right amount of drugs a person must possess 'before this presumption of an intent to distribute is appropriate.' " 854 F.3d at 96 (emphasis added) (quoting Brandon, 247 F.3d at 192 ). Mohamed's Maine conviction does not fall into this category of cases involving a statutory presumption, and the permissible inference does not require courts or juries to infer distributive intent from amount possessed. See Me. Jury Instr. Manual, § 6-13 (2013).

C. Drug Weight and Relationship to Drug Trafficking

We asked for, and received, additional filings from the parties, including data on federal drug trafficking convictions where the amount of cocaine base was less than or close to four grams and further discussion on drug quantity as it related to personal use versus intent to distribute.

The district court stated in the sentencing hearing that four grams of cocaine base "probably wouldn't be enough" to constitute trafficking under federal law or allow an inference of trafficking. This is incorrect. The government has provided data from the United States Sentencing Commission demonstrating hundreds of examples of federal drug trafficking convictions involving less than 2.8 grams of cocaine base (and a corresponding BOL of twelve),11 including forty-three in district courts of this circuit between 2013 and 2017. The government also cited several circuit cases -- albeit mostly unpublished opinions -- affirming or sustaining federal drug trafficking convictions involving less than four grams of cocaine base. See, e.g., United States v. Moore, 481 F.3d 1113, 1115 (8th Cir. 2007). These cases cannot be ignored.

Further, for federal drug trafficking crimes under 21 U.S.C. § 841(a)(1), the Pattern Criminal Jury Instructions for the District Courts of the First Circuit allow for a permissible inference of drug trafficking that is not linked to any numerical drug quantity: "Intent to distribute may *106... be inferred from a quantity of drugs larger than that needed for personal use .... The law does not require you to draw such an inference, but you may draw it." Pattern Criminal Jury Instructions for the District Courts of the First Circuit § 4.21.841(a)(1)A (2018).

By the 2016 Sentencing Guidelines' Drug Equivalency Tables in effect at the time of Mohamed's federal sentencing in April 2018, four grams of cocaine base was equivalent to 14,284 grams of marijuana, or about 504 ounces. U.S.S.G. § 2D1.1 cmt. 8(D) (2016). Turning to our caselaw, in United States v. Oliveira, this court affirmed a sentencing enhancement regarding distribution where under eight grams of marijuana was found (among other evidence reasonably related to drug trafficking, such as packaging in small baggies). 907 F.3d 88, 92 (1st Cir. 2018). That is, a far smaller amount of marijuana than the marijuana equivalency of four grams of cocaine base has sufficed to support a sentencing enhancement based on drug distribution. Based on the Guidelines and our caselaw, four grams of cocaine base is an amount rationally related to drug distribution.12 See United States v. Henry, 848 F.3d 1, 14 (1st Cir. 2017) (finding approximately three grams of cocaine base "consistent with an intent to distribute").

Finally, to the extent Mohamed evinces concern with a small amount of cocaine base being found in a mixture weighing over four grams, that neither negates our earlier reasoning nor distinguishes Maine law from federal law. The Sentencing Guidelines were, and are, clear on this point: "Unless otherwise specified, the weight of a controlled substance set forth in the [drug equivalency] table refers to the entire weight of any mixture or substance containing a detectable amount of the controlled substance." U.S.S.G. § 2D1.1 n.A. Similarly, in considering penalties for drug trafficking and manufacturing under 21 U.S.C. § 960, the statute considers amounts "of a mixture or substance ... which contains cocaine base," not of isolated cocaine base. Id. §§ 960(b)(1)(C), 960(b)(2)(C). Maine law is not contrary to federal law regarding the calculation of the quantity of cocaine base involved in an offense.

III.

So long as it is taken into consideration, our result -- that Mohamed is eligible for an increased guideline imprisonment range based on a prior "controlled substance offense" -- does not affect the sentencing judge's discretion as to the sentence imposed on remand. See 18 U.S.C. § 3553 ; United States v. Stone, 575 F.3d 83, 89 (1st Cir. 2009) (recognizing "district courts['] discretion to disagree with many guidelines").

We vacate Mohamed's sentence and remand to the district court for resentencing consistent with this opinion.

*107Once again, we confront a challenge to the application of a federal sentencing enhancement to a defendant's prior state law conviction. Once again, we must try to divine whether the conviction triggers the enhancement. We have confronted this issue many times in the context of crimes of violence. We do so here in the context of a drug offense: trafficking cocaine base in violation of Maine law. See Me. Stat. tit. 17-A, §§ 1101(17), 1103(1-A).

The government contends that, because Noor Mohamed was convicted of the prong of this offense that requires proof of possession of cocaine base with an intent to "sell, barter, trade, exchange or otherwise furnish [it] for consideration," see id. § 1101(17)(C)-(D), he is subject to a sentencing enhancement under the United States Sentencing Guidelines, U.S.S.G. § 2K2.1(a). That enhancement is triggered by a conviction for a "controlled substance offense," id., which the Guidelines elsewhere define, in relevant part, to be only an offense that prohibits the "possession of a controlled substance ... with intent to manufacture, import, export, distribute or dispense," id. § 4B1.2(b).

Under prevailing precedent, we must use the so-called "categorical approach" to determine whether Mohamed's conviction for his Maine drug trafficking offense triggers this enhancement. See United States v. Dávila-Félix, 667 F.3d 47, 55 (1st Cir. 2011) (applying the categorical approach to federal Sentencing Guidelines); Maj. Op. 101. Thus, only if the least of the conduct that this Maine offense criminalizes would itself qualify as a "controlled substance offense" under § 2K2.1(a) may a court apply this federal sentencing enhancement to Mohamed. See Moncrieffe v. Holder, 569 U.S. 184, 190-91, 133 S.Ct. 1678, 185 L.Ed.2d 727 (2013) ("[W]e must presume that the conviction 'rested upon nothing more than the least of the acts' criminalized, and then determine whether even those acts are encompassed by the generic federal offense." (quoting Johnson v. United States, 559 U.S. 133, 137, 130 S.Ct. 1265, 176 L.Ed.2d 1 (2010) (alterations omitted)); see also Dávila-Félix, 667 F.3d at 55-56 ).

Maine law permits a jury to draw an inference of the distributive intent that is required under Me. Stat. tit. 17-A, § 1101(17)(D) based on the mere possession of a relatively small amount of a mixture that contains even a speck of cocaine base. See id. § 1103(3); id. § 1101(25)(B) (defining "cocaine" to mean a "mixture" including "any quantity of" "cocaine" or "cocaine base"); State v. McLaughlin, 189 A.3d 262, 268 (Me. 2018) (construing "cocaine base" to mean a mixture including "any quantity of cocaine base" for purposes of Maine's drug trafficking statute, including for various quantitative thresholds in that statute). Thus, that minimal possessory conduct is the least of the conduct that the Maine offense at issue criminalizes.

In my view, the federal government has not met its burden, Dávila-Félix, 667 F.3d at 55, to show that such minimal possessory conduct manifests the "intent to manufacture, import, export, distribute or dispense" that is necessary to trigger the application of the Guidelines enhancement for having a prior conviction for a "controlled substance offense." U.S.S.G. §§ 2K2.1(a), 4B1.2(b). Accordingly, I conclude, like the District Court, but unlike my colleagues, that the enhancement does not apply here.

In arguing otherwise, the federal government first contends that the Maine trafficking offense for which Mohamed was convicted necessarily triggers the federal sentencing enhancement, because that Maine offense itself contains a distributive *108intent element. Our precedent makes clear, however, that, under the categorical approach, we must inquire into how loosely Maine defines that element. Only by doing so can we ensure that the offense criminalizes no more conduct than the federal sentencing enhancement's triggering offense. See United States v. Mulkern, 854 F.3d 87, 96 (1st Cir. 2017) (rejecting the government's argument that an offense involved possession with intent to distribute because the state legislature "designates the copped-to crime as 'trafficking' ").

The government separately attempts to meet its burden to show that the Maine offense does not sweep too broadly to trigger the enhancement by reference to materials that show the type of evidence that suffices to prove the distributive intent element of 21 U.S.C. § 841(a)(1), a federal drug crime. The government suggests that these materials are relevant for present purposes because the Guidelines' definition of a "controlled substance offense" necessarily encompasses conduct that suffices to satisfy the distributive intent element of that federal drug crime.13

The materials to which the government refers do not, however, help its cause. They include references to precedents in which courts determined that the possession of more than four grams of cocaine base did not, on its own, suffice to prove such distributive intent. See United States v. Nealy, 221 F. App'x 329, 333 (5th Cir. 2007) (per curiam) (unpublished) (explaining that, under 21 U.S.C. § 841(a)(1), testimony presented by the government showed that while 5.01 grams of cocaine base "suggested drug dealing," it also "indicated that this quantity is not clearly inconsistent with personal use" and thus "additional evidence [was] necessary to show intent to distribute" (emphasis added)); United States v. Hunt, 129 F.3d 739, 742 (5th Cir. 1997) (holding that, under 21 U.S.C. § 841(a)(1), possession of 7.998 grams of cocaine base alone was insufficient to prove intent to distribute beyond a reasonable doubt because it was "consistent with personal use"). Nor does the government identify a single case that indicates that -- as Maine's drug trafficking offense allows -- the mere possession of a mixture that contains a speck of cocaine base may, on its own, suffice to prove the requisite distributive intent under 21 U.S.C. § 841(a)(1).

The federal government does direct our attention to the drug quantity tables that are set forth in the Sentencing Guidelines and to sentencing data from each of the circuits that shows the "Base Offense Levels for Drug Trafficking in Each Drug Type." But, the tables purport only to relate to the calculation of the Guidelines sentencing range for a person convicted of a federal drug crime. See U.S.S.G. § 2D1.1(c). They thus give no insight into the least of the conduct criminalized by those federal drug crimes. The sentencing data does identify the conduct of defendants convicted of federal drug crimes, but that data, too, does not purport to give insight into the key issue that, under the *109categorical approach, we must resolve: whether possession of a four-gram substance containing cocaine base in and of itself can suffice to establish an "intent to manufacture, import, export, distribute or dispense" within the meaning of the Guideline's definition of a "controlled substance offense." See U.S.S.G §§ 2K2.1(a), 4B1.2(b).

The majority, for its part, points to one of the § 841(a) cases on which the government relies -- United States v. Moore, 481 F.3d 1113 (8th Cir. 2007) -- to contend that the government has met its burden to show that the Guidelines enhancement encompasses even possessory conduct of the minimal sort that the Maine trafficking offense at issue here criminalizes. Maj. Op. 106. But, that case did not involve a sufficiency challenge -- let alone one that directly addresses the type of possessory conduct that, in and of itself, might suffice to prove distributive intent under 21 U.S.C. § 841(a)(1). Thus, that case cannot demonstrate what it must for the government to be able to prevail on its § 841 -based argument under the categorical approach.

I close by making two additional observations.

The first concerns how we apply the categorical approach. The majority emphasizes -- repeatedly -- that the Shepard documents, see Shepard v. United States, 544 U.S. 13, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005), reveal that prosecutors did not need to, and in fact did not, rely on the permissible inference to secure Mohamed's conviction for the trafficking offense. See Maj. Op. 102-04.

If the majority emphasizes this point merely to shore up the uncontested fact that Mohamed was convicted of the portion of the Maine trafficking offense to which the permissible inference provision -- rather than the irrebuttable presumption provision at issue in Mulkern, 854 F.3d at 96 -- applies, then I have no quarrel. Maj. Op. 102-03 n. 7. But, the majority appears to suggest that the Shepard documents are also relevant to our analysis because they show that Mohamed was convicted of his trafficking offense based on conduct that was more severe than the least of the conduct that this offense criminalizes. See Maj. Op. 103-04, 104-05. If so, it seems to me that the majority is engaging in precisely the kind of inquiry into the "brute facts" of Mohamed's means of committing the offense that the categorical approach makes irrelevant. See Mathis v. United States, --- U.S. ----, 136 S.Ct. 2243, 2251, 195 L.Ed.2d 604 (2016).

After all, the permissible inference provision does not establish an element of the offense for which, all parties agree, Mohamed was convicted. See id. at 2248 ("[Elements] are what the defendant necessarily admits when he pleads guilty[.]"). The permissible inference provision merely sets forth a method for proving the conduct that could satisfy an element of that offense -- namely, the one that concerns Mohamed's distributive intent. See Me. Stat. tit. 17-A, § 1103(3).

The second observation concerns the sense in applying the categorical approach at all. My colleagues agree that, just as our precedent instructs, the categorical approach does apply here. Maj. Op. 101. That point, therefore, is not at issue in this appeal.

I am aware, though, that the categorical approach has received its fair share of criticism for the counter-intuitive results that it often yields. See United States v. Faust, 853 F.3d 39, 61 (1st Cir. 2017) (Lynch, J., concurring) (collecting statements). I am aware, as well, that an outcome like the one that I am convinced that we must reach here -- in which we would *110deem a drug "trafficking" offense not to constitute a "controlled substance offense" -- might well add to that criticism. I thus think it important to explain both that I do not share the oft-expressed concern that the categorical approach is too counter-intuitive to have been contemplated by those who drafted these enhancements, see id. at 61-66 (Barron, J., concurring), and that the outcome that I believe that approach requires in this case does not lead me to see new merit to that concern.

Sentencing enhancements are often written in terms that comfortably invite a categorical inquiry, see id. at 62-65, and that is certainly true of the one before us, see U.S.S.G. § 4B1.1(b). In my view, when enhancements are written in terms that invite such an inquiry, there is no reason to presume that their drafters could not have intended for judges to determine the scope of such enhancements by inquiring into the least of the conduct criminalized by the predicate offense.

I say that because the decision to restrict (even if not to eliminate) a sentencing judge's discretion to determine a sentence on an individualized basis -- as sentencing enhancements such as the one before us necessarily do -- is a consequential one. I thus see no reason to presume that the drafters of such enhancements made that type of decision in a manner that would define the class of persons subject to them on the basis of merely the name that a state gives to an offense or with no appreciation of the difficulty of ensuring, retrospectively, that a defendant had engaged in conduct more severe than the least of what the offense of his conviction criminalized. Rather, it seems to me entirely sensible to presume that, in choosing words that invite judges to use the categorical approach to define an enhancement's scope, the drafters of the enhancement chose to ensure that it would accord with principles of lenity, cf. United States v. Santos, 553 U.S. 507, 514, 128 S.Ct. 2020, 170 L.Ed.2d 912 (2008) ("The rule of lenity requires ambiguous criminal laws to be interpreted in favor of the defendants subjected to them."), just as the categorical approach ensures. See Faust, 853 F.3d at 65 (Barron, J., concurring).

Consistent with these conclusions about the likely intent of the drafters of these enhancements, I note that, despite the criticism that the categorical approach has engendered, no changes have been made to this one by its drafters that would require us to use a different approach. That is no doubt in part because of the serious problems that inhere in the alternative means that have been suggested to define the scope of sentencing enhancements that are predicated on prior state offenses. See ids="12276892" index="117" url="https://cite.case.law/f3d/853/39/#p61">id. at 61-66.

Thus, I wish to emphasize that the result that I would reach here demonstrates to me the sense that inheres in the categorical approach -- insofar as there is any sense in establishing such enhancements -- rather than the merit of the critiques that have been lodged against it. For, I can see no good reason to conclude that the drafters of U.S.S.G. §§ 2K2.1(a)(2), 4B1.2(b), in establishing a sentencing enhancement for defendants who have been convicted of drug offenses that require proof of distributive intent, actually intended for it to a apply to a defendant convicted of a drug offense that -- though labeled as one for "trafficking" -- requires proof of nothing more than possessory conduct of a most minimal sort.

On this understanding, I respectfully dissent.