In his written plea agreement to being a felon in possession of a firearm, James Davis accepted certain limits on his right to appeal. When he attempted to appeal in a way that potentially contradicted that plea agreement, his federal public defender, Jason Hawkins, moved to withdraw as counsel pursuant to Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967), and United States v. Acquaye, 452 F.3d 380 (5th Cir.2006).1
In United States v. Davis, 530 F.3d 318 (5th Cir.2008) (per curiam), we ordered Hawkins to submit a letter “stating the government’s position with respect to the plea agreement’s appellate-waiver provisions.” He responded by stating that he “spoke with Assistant United States Attorney Susan B. Cowger and she informed me that the government will be asserting the appellate-waiver provision in James Davis’s plea agreement.”
Anders’s purpose is “to vindicate the constitutional right to appellate counsel.... ” Smith v. Robbins, 528 U.S. 259, 273, 120 S.Ct. 746, 145 L.Ed.2d 756 (2000). Under Anders, before withdrawing as court-appointed counsel, a lawyer must undertake a “conscientious examination” of the case, and if he finds the appeal “wholly frivolous,”2 *he must “request permission to withdraw” and submit a “brief referring to anything in the record that might arguably support the appeal.” Anders, 386 U.S. at 744, 87 S.Ct. 1396.3 After we assess the brief submitted by counsel, and after we examine any points raised by the appellant speaking on his own behalf and independently and thoroughly review the record, we may grant the request to withdraw and dismiss the appeal as frivolous. *565Id. “On the other hand, if [we] find[ ] any of the legal points arguable on the merits (and therefore not frivolous) [we] must, prior to decision, afford the indigent the assistance of counsel to argue the appeal.” Id.
Here, we have reviewed Hawkins’s Anders brief and his supplemental letter, and, having also conducted our own investigation of the record, we agree that any argument raised by Davis as to whether the plea was voluntary, or whether he has a claim of ineffective assistance of counsel, would be wholly frivolous. We disagree, however, that every potential argument he could raise regarding whether his sentence exceeds the statutory maximum punishment, or whether there was calculation error in his sentence, also necessarily would be frivolous. Because Hawkins has not briefed everything “in the record that might arguably support the appeal,” id., as is required under Anders, we deny the motion to withdraw.
The problem is this: Our review of the record suggests that it may not be wholly frivolous to argue that Davis’s Arizona convictions for second-degree burglary, attempted burglary in the second degree, and aggravated robbery are not “violent felon[ies]” for purposes of the Armed Career Criminal Act, 18 U.S.C. § 924(e), and thus that the court committed plain error in calculating Davis’s sentence to be 180 months (the statutory minimum under § 924(e)(1)). Because Davis reserved the right to appeal both “a sentence exceeding the statutory maximum” and “an arithmetic error at sentencing,” each of which arguably encompasses the right to appeal § 924(e)’s application, it potentially would not be frivolous to argue that Davis was improperly sentenced.4
To be sentenced under § 924(e)(1), as Davis was, “a person [must first] violate[ ] section 922(g) of this title” and must have “three previous convictions by any court referred to in section 922(g)(1) of this title *566for a violent felony or a serious drug offense, or both, committed on occasions different from one another.” We agree that it is not debatable that Davis violated § 922(g)(1) — he unambiguously pleaded guilty to it.
The next question is whether Davis has “three previous convictions by any court referred to in section 922(g)(1) of this title for a violent felony or a serious drug offense, or both, committed on occasions different from one another.” Under § 922(g)(1), it is “unlawful for any person ... who has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year ... to ship or transport in interstate or foreign commerce, or possess in or affecting commerce, any firearm or ammunition....” As part of his plea agreement, Davis concedes that he has been convicted at least three independent times in Arizona for “felony offenses punishable by imprisonment for a term in excess of one year.”
The difficult question is whether the Arizona convictions were for “violent felon[ies].” In relevant part, the statute defines “violent felony” as “any crime punishable by imprisonment for a term exceeding one year,” provided that “it has as an element the use, attempted use, or threatened use of physical force against the person of another; or is burglary, arson, or extortion, involves use of explosives, or otherwise involves conduct that presents a serious potential risk of physical injury to another.... ” 18 U.S.C. § 924(e)(2)(B). To determine whether Davis’s Arizona convictions count for purposes of applying § 924(e)(1), we employ the so-called categorical approach of Taylor v. United States, 495 U.S. 575, 110 5. Ct. 2143, 109 L.Ed.2d 607 (1990). Because Davis did not object at sentencing, our review is for plain error. See, e.g., United States v. Dupre, 117 F.3d 810, 817 (5th Cir.1997).5
Davis, as noted, admits that he has been convicted five times in the past for Arizona felonies “punishable by imprisonment for a term in excess of one year.” These include three convictions for burglary in the second degree (in 1995, 1990, and 1987), one for aggravated robbery (in 1982), and one for attempted burglary in the second degree (in 1981).6 For Davis to satisfy § 924(e), therefore, at least one of his eligible prior convictions must have been for second-degree burglary, else the number does not add up to three. Given this case’s procedural posture, we consequently focus exclusively on the burglary convictions. Under Taylor, for a state statute to constitute generic burglary (such that § 924(e) applies), it must “hav[e] the basic elements of unlawful or unprivileged entry into, or remaining in, a building or structure, with intent to commit a crime.” 495 U.S. at 599,110 S.Ct. 2143.
It appears that no published decision from this court has addressed whether Arizona’s second-degree-burglary statute is a “violent felony” under Taylor. In United States v. Garcia-Lopez, 262 Fed. Appx. 584, 585 (5th Cir.2008), concerning the analogous sentencing guidelines, we stated that “[w]e have not previously de*567cided whether a district court may enhance a sentence based on a prior conviction of second-degree burglary under Arizona law.” We noted, however, that the Ninth Circuit, in the § 924(e) context, has “observed ... that Arizona’s courts ha[ve] broadened the statute to allow for conviction if criminal intent was formed after entering a residential structure or if entry was privileged,” id, (citing United States v. Bonat, 106 F.3d 1472, 1475 (9th Cir.1997)), even though the Arizona statute’s text merely states that “ ‘[a] person commits burglary in the second degree by entering or remaining unlawfully in or on a residential structure with the intent to commit any theft or felony therein,’ ” id. (quoting Ariz.Rev.Stat. Ann. § 13-1507).
Given that the question was one of first impression, we held that “[a]s the law of this circuit was ... uncertain at the time of Garcia-Lopez’s sentencing, any error by the district court in enhancing Garcia-Lopez’s sentence could not have been plain.” Id. (citing United States v. Garcia-Rodriguez, 415 F.3d 452, 455-56 (5th Cir.2005)). Although Garcictr-Lopez is unpublished and therefore not binding precedent, if one were to follow its logic there is a compelling argument that any appeal by Davis as to whether his burglary convictions should have been counted as “violent felon[ies]” should also be rejected as not constituting plain error.
Notwithstanding the force of such an argument, the question before us is not whether Davis is likely to prevail if he presents a counter-argument, but instead only whether there is a non-frivolous counter-argument that even can be offered. Here, there is such a non-frivolous argument, at least potentially. “[I]f a defendant’s theory ‘requires the extension of precedent, any potential error could not have been “plain.” ’ ” Garcia-Rodriguez, 415 F.3d at 455 (quoting United States v. Hull, 160 F.3d 265, 272 (5th Cir.1998)). This, of course, in some sense begs the question, for where is the dividing line between the rote application of precedent and the extension of precedent? Any instance in which precedent is applied to new facts could be considered an “extension,” but that begrudging interpretation of our plain error analysis would nullify the entire endeavor. More concretely, what if, in a case involving another state with a burglary statute very similar to Arizona’s, we ruled that a conviction was not a “violent felony” because it could be committed in ways outside of the elements of generic burglary? Though our consideration of state statutes under the categorical approach is — at least ordinarily— state-specific, we cannot say that drawing an analogy between Davis’s case and that hypothetical opinion would be frivolous.
We have not conducted an extensive state-by-state survey of this court’s construction of burglary statutes; that is work best done by a zealous advocate. Nonetheless, in United States v. OrtegaGonzaga, 490 F.3d 393, 395-96 (5th Cir.), cert, denied, — U.S.-, 128 S.Ct. 410, 169 L.Ed.2d 287 (2007), we held that a conviction under a California burglary statute was not a “crime of violence” under the sentencing guidelines because the statute did not require that the entry be “unlawful or unprivileged” and that under Taylor, “statutes, like the one at issue, that do not require an ‘unlawful or unprivileged entry into, or remaining in’ are broader than the common definition of ‘burglary.’” Id. at395.
In Ortega-Gonzaga, we also explained that entering with an intent to commit a crime is not identical to an unprivileged entry, for “a cable repairman may enter a house with intent to rape, but because he enters lawfully and with privilege, there is no ‘burglary.’ Likewise, a shoplifter who lawfully enters a store with the intent to *568steal may later commit theft, but not burglary.” Id. Consistent with the approach laid out in Ortega-Gonzaga, we held in United States v. Herrera-Montes, 490 F.3d 390, 391 (5th Cir.2007), that a Tennessee conviction for aggravated burglary was not a “crime of violence,” because it could “be committed even if, at the time of unlawful entry, [the person] had no intent to commit a crime.”7
Moreover, here, during the sentencing hearing, the government argued that “second-degree burglary in Arizona has been deemed by the 9th Circuit a crime of violence for armed career criminal purposes. The 5th Circuit hasn’t considered it.” Based on this statement, it is not utterly frivolous to contend that the court was on notice that it ought to peruse the Ninth Circuit’s opinion before deciding Davis’s sentence. If the court would have done so, it would have learned that the Ninth Circuit’s opinion was not as categorically unyielding as the government’s brief obliquely suggested. Instead, “the [second-degree burglary] statute as construed by the Arizona courts expands the definition of burglary beyond generic burglary” such that a conviction in Arizona for second-degree burglary only can constitute a “violent felony” if it falls “in [that] ‘narrow range of cases where a jury was actually required to find all the elements of generic burglary.’ ” Bonat, 106 F.3d at 1475-76 (quoting Taylor, 495 U.S. at 602, 110 S.Ct. 2143).
Of course, it is possible that Hawkins has reviewed Davis’s underlying Arizona convictions and their respective sentencing documents and has determined that under Taylor it would be frivolous to argue that the enhancement is inapplicable.8 If so, we have not been apprised, contrary to Hawkins’s duty under Anders. We therefore direct Hawkins promptly to file a supplemental brief addressing whether, in light of the respective documents of conviction, it would be frivolous to appeal Davis’s sentence under § 924(e). We DENY the motion to withdraw, subject to reconsideration pending receipt of the supplemental filing consistent with this order.
Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. The agreement permits Davis to appeal his sentence only if it exceeds the statutory maximum, if there is an arithmetic error at sentencing, if there is a question as to the voluntariness of the plea agreement, or for a claim of ineffective assistance of counsel.
. Frivolous is defined as "[backing a legal basis or legal merit; not serious; not reasonably purposeful.” Black's Law Dictionary 677 (7th ed.1999).
. See also United States v. Cordero, 18 F.3d 1248, 1253 (5th Cir.1994) ("The attorney must isolate possibly important issues and must furnish the court with references to the record and legal authorities to aid it in its appellate function. After the defendant has had an opportunity to raise any additional points, the court fully examines the record and decides whether the case is frivolous.”) (internal citations and quotations omitted).
. As part of his plea agreement, Davis reserved the right to appeal "an arithmetic error at sentencing.” The meaning of the term "arithmetic error” is not straightforward. It could be read to mean that the reserved right applies only to calculations of which sentence to impose under § 924(e) and not whether § 924(e) itself applies at all; the latter question seems substantive in character, but the term “arithmetic” suggests procedure. When it is also considered that Davis was indicted under both 18 U.S.C. § 922(g)(1) and § 924(e) and that he purportedly pleaded guilty to both, the argument that "arithmetic error” has a narrow definition becomes stronger still.
There is, however, a non-frivolous argument that can be made that "arithmetic error” also encompasses whether the prerequisites of § 924(e) itself have been satisfied. The argument is based on the fact that the plea agreement expressly refers to whether "the defendant has three previous valid convictions of a violent felony or a serious drug offense,” in which case a fifteen-year sentence is required, but also that "if the defendant does not qualify for enhancement under ... § 924(e),” the sentence will be "for a period not to exceed ten ... years.” The fact that the plea agreement explicitly contemplates § 924(e)'s not applying suggests that the reserved right to appeal any “arithmetic error[s]" is sufficiently broad so as to include whether § 924(e) applies at all. We also note that in the "factual resume” submitted by Davis in conjunction with his plea agreement, he conceded that he had been convicted of sundry felonies, but he did not concede that they were "violent felonpesj," further suggesting that he has not waived that argument, as does the fact that during his plea entry, the court did not ask expressly whether he pleaded guilty to § 924(e).
We do not resolve which of these constructions of “arithmetic error” is correct, because it is sufficient to observe that there are non-frivolous arguments supporting both. We likewise note that if Davis was improperly sentenced under § 924(e), he arguably received a sentence greater than the statutory maximum, because without the enhancement, his plea agreement states that his imprisonment cannot be greater than ten years.
. Under United States v. Olano, 507 U.S. 725, 730-36, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993), "this court may reverse only if: (1) there was error (2) that was clear and obvious and (3) that affected a defendant's substantial rights.'' Dupre, 117 F.3d at 817. "When these elements of plain error are present, a court may exercise its discretion to correct the error if it seriously affects the fairness, integrity, or public reputation of judicial proceedings." Id. (internal citations and quotations omitted).
. The presentence report lists several other adult convictions, which are not listed in the factual recitation that accompanied the plea agreement.
. Ortega-Gonzaga and Herrera-Montes were decided after Davis was sentenced and thus could not have been considered by the district court. Because, however, those decisions relied extensively on Taylor and the Model Penal Code, it is not frivolous to argue that they are mere applications of Taylor.
Likewise, in Ortega-Gonzaga, we noted that United States v. Garcia-Mendez, 420 F.3d 454, 456 (5th Cir.2005), involving a Texas burglary statute, supported the position that both lack of consent and unlawful intent at time of entry are necessary for a burglary conviction to fall under the generic definition. In Garcia-Mendez, we specifically observed that ”[t]he Texas statute states that a person commits burglary if he enters a building closed to the public, or a habitation, without the consent of the owner, with the intent to commit a felony, theft, or an assault.” Id. (citing Tex. Penal Code § 30.02(a)(1)) (emphasis added). It thus could be urged that the principles set forth in Ortega-Gonzaga and Herrera-Montes predated our explicit elucidation of them. Again, such an argument may not be successful, but that is not the Anders standard.
. Under Taylor, a sentencing court may consider “statutory elements, charging documents, and jury instructions to determine whether an earlier conviction after trial was for generic burglary,” notwithstanding the potential breadth of the statute of conviction. Shepard v. United States, 544 U.S. 13, 16, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005). Where the prior conviction involved a guilty plea, the court may look to “the statutory definition, charging document, written plea agreement, transcript of plea colloquy, and any explicit factual finding by the trial judge to which the defendant assented.” Id.