
665 F.3d 344 (2011)
UNITED STATES of America, Appellee,
v.
Robin Eddie RIVERA-MARTÍNEZ, Defendant, Appellant.
No. 09-1766.
United States Court of Appeals, First Circuit.
Submitted December 2, 2011.
Decided December 20, 2011.
*345 Jean C. LaRocque, by appointment of the court, on supplemental brief for appellant.
Lanny A. Breuer, Assistant Attorney General, Greg D. Andres, Acting Deputy Assistant Attorney General, Vijay Shanker, Attorney, Appellate Section, Criminal Division, United States Department of Justice, Rosa Emilia Rodríguez-Vélez, United States Attorney, Nelson Pérez-Sosa, Assistant United States Attorney (Appellate Chief), and Julia M. Meconiates, Assistant United States Attorney, on supplemental brief for appellee.
Before TORRUELLA, SELYA and HOWARD, Circuit Judges.
SELYA, Circuit Judge.
In United States v. Rivera-Martínez (Rivera-Martínez I), 607 F.3d 283 (1st Cir.2010), we affirmed a district court decision finding the defendant ineligible for a sentence reduction under certain retroactive amendments to the federal sentencing guidelines. Id. at 286-88. The defendant petitioned for a writ of certiorari. While that petition was pending, the Supreme Court decided Freeman v. United States, ___ U.S. ___, 131 S.Ct. 2685, 180 L.Ed.2d 519 (2011). The Court then granted the petition in Rivera-Martínez I, vacated the judgment, and remanded for reconsideration in light of Freeman. Rivera-Martínez v. United States, ___ U.S. ____, 131 S.Ct. 3088, 180 L.Ed.2d 910 (2011) (mem.).
The task committed to us requires a careful parsing of the three opinions filed in Freeman, an identification of Freeman's holding, and a fresh determination of the defendant's eligibility for the sought-after sentence reduction. We conclude that Justice Sotomayor's concurring opinion embodies the Freeman Court's holding and that under its strictures the defendant remains ineligible for a reduced sentence.

I. BACKGROUND
On March 6, 2000, defendant-appellant Robin Eddie Rivera-Martínez pleaded guilty to conspiring to possess with intent to distribute more than five kilograms of crack cocaine. See 21 U.S.C. §§ 841(a)(1), 846. His plea was entered pursuant to a plea agreement (the Agreement) forged under Federal Rule of Criminal Procedure 11(c)(1)(C). Such a vehiclea so-called C-type plea agreementallows the parties to bind the district court to a pre-agreed sentence if the court accepts the plea. See, e.g., Rivera-Martínez I, 607 F.3d at 284; United States v. Teeter, 257 F.3d 14, 28 (1st Cir.2001).
Here, the Agreement stipulated that the defendant was accountable for over 1.5 kilograms of cocaine base.[1] On the date of the plea, this drug quantity corresponded to a base offense level of 38. After walking through various guideline adjustments, the Agreement arrived at a total offense *346 level of 37. Although the parties agreed to a 240-month sentence, the Agreement said nothing about either the defendant's criminal history category or his guideline sentencing range.
Sentencing took place on September 12, 2000. The district judge rehearsed the guideline calculations limned in the presentence investigation report, accepted the Agreement, and sentenced the defendant to 240 months in prison.
We fast-forward to 2007, when the Sentencing Commission modified the quantities of crack cocaine that suffice to trigger certain base offense levels. See USSG App. C, Amend. 706 (Supp.2007) (modifying USSG § 2D1.1); see also USSG App. C, Amend. 711 (Supp.2007). The Commission soon made these amendments retroactive. See USSG App. C, Amend. 713 (Supp.2008).
Seizing upon these developments, the defendant moved for a sentence reduction under 18 U.S.C. § 3582(c)(2>).[2] The district court denied the motion. We affirmed. See Rivera-Martínez I, 607 F.3d at 288. We determined that "[a]bsent an express statement in the plea agreement making the sentence dependent upon a guideline calculation, a sentence imposed pursuant to a C-type plea agreement is based on the agreement itself, not on the guidelines." Id. at 287.[3]
The defendant petitioned for a writ of certiorari. On June 23, 2011, the Supreme Court decided Freeman. A few days later, it granted the defendant's certiorari petition, vacated this court's judgment, and remanded for reconsideration in light of Freeman.

II. ANALYSIS
To comply with the Supreme Court's mandate, we must identify Freeman's holding, chart its contours, and apply the insights gleaned from those inquiries to the defendant's circumstances. This undertaking requires us to step back for a moment.
As a general rule, a sentencing court cannot revisit a final sentence. 18 U.S.C. § 3582(c). Section 3582(c)(2) provides an exception to this general rule:
[I]n the case of a defendant who has been sentenced to a term of imprisonment based on a sentencing range that has subsequently been lowered by the Sentencing Commission ... the court may reduce the term of imprisonment, after considering the factors set forth in section 3553(a) to the extent that they are applicable, if such a reduction is consistent with applicable policy statements issued by the Sentencing Commission.
Id. § 3582(c)(2) (emphasis supplied). The question before the Freeman Court was whether a defendant who was sentenced pursuant to a C-type plea agreement can be eligible for section 3582(c)(2) relief.
The court of appeals had held that, in the absence of a miscarriage of justice, entering into a C-type plea agreement presented a categorical bar to section 3582(c)(2) relief. United States v. Goins, 355 Fed.Appx. 1, 2-3 (6th Cir.2009), rev'd in part sub nom., Freeman v. United States, ___ U.S. ___, 131 S.Ct. 2685, 180 L.Ed.2d 519 (2011). Five Justices concluded *347 that no such bar existed. But those five Justices reached this conclusion in different waysand therein lies the rub.
A four-member plurality found determinative the analytic framework that undergirds the decisionmaking process employed by sentencing judges in federal criminal cases. Freeman, 131 S.Ct. at 2692-94 (Kennedy, J., with whom Ginsburg, Breyer, and Kagan, JJ., joined). The sentencing guidelines are integral to that process. Even in cases in which sentencing follows the execution of a C-type plea agreement, the sentencing judge is required to take the guidelines into account when deciding whether to accept the agreement and impose the agreed sentence. Id. at 2692-93. Viewed through this prism, a judge's decision to accept a C-type plea agreement will almost always be based on the guidelines, thereby rendering the defendant eligible for section 3582(c)(2) relief when those guidelines are amended and made retroactive. Id. at 2695.
Four votes, however, do not make a majority on a nine-judge court. To achieve the magic number, the plurality depended upon Justice Sotomayor, who also found the defendant eligible for section 3582(c)(2) relief. But Justice Sotomayor's approach differed sharply from that of the plurality. She concluded that a term of imprisonment imposed by a court pursuant to a C-type plea agreement is based on the agreement, not on the sentencing judge's assessment of the guidelines. Id. at 2695 (Sotomayor, J., concurring).
Withal, Justice Sotomayor carved out an exception for cases in which a C-type plea agreement "expressly uses a Guidelines sentencing range applicable to the charged offense to establish the term of imprisonment, and that range is subsequently lowered." Id. In that event, "the term of imprisonment is `based on' the range employed and the defendant is eligible for sentence reduction under § 3582(c)(2)." Id. The sentence imposed in Freeman came within this exception.
The four dissenting Justices, like Justice Sotomayor, concluded that sentences imposed pursuant to C-type plea agreements are based on the agreement, not on the guidelines. See id. at 2700 (Roberts, C.J., with whom Scalia, Thomas, and Alito, JJ., joined, dissenting). But unlike Justice Sotomayor, the dissenters argued that the imposition of a sentence pursuant to a C-type plea agreement always precluded section 3582(c)(2) relief. Id. at 2700-05.
These opinions leave some doubt as to the controlling rule. To allay this doubt, our first recourse is to Marks v. United States, 430 U.S. 188, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977). There, the Supreme Court explained that "[w]hen a fragmented Court decides a case and no single rationale explaining the result enjoys the assent of five Justices, the holding of the Court may be viewed as that position taken by those Members who concurred in the judgments on the narrowest grounds." Id. at 193, 97 S.Ct. 990 (internal quotation marks omitted). This "narrowest grounds" approach is useful when it can be applied straightforwardly, but it is sometimes unworkable. See, e.g., United States v. Johnson, 467 F.3d 56, 63-64 (1st Cir. 2006).
The defendant asserts that Freeman is not amenable to the Marks "narrowest grounds" approach. As a default measure, he invites us to apply the plurality's reasoning. In support, he relies on our decision in Johnson.
Johnson cannot bear the weight that the defendant loads upon it. The language upon which the defendant reliesthat "Marks is workable ... only when one *348 opinion is a logical subset of other, broader opinions," id. at 63 (quoting King v. Palmer, 950 F.2d 771, 781 (D.C.Cir.1991) (en banc))signifies only that "the narrowest opinion must represent a common denominator of the Court's reasoning; it must embody a position implicitly approved by at least five Justices who support the judgment." King, 950 F.2d at 781. Adhering to this standard, Freeman is fertile soil for a Marks analysis.
To be sure, Freeman's plurality and concurrence agree on very little. The plurality looks to the analytic framework underlying a district judge's decision to accept a C-type plea agreement, see 131 S.Ct. at 2692-95 (plurality op.), whereas Justice Sotomayor's concurrence looks to the plea agreement to determine whether a particular sentence is based on an identifiable guideline sentencing range, see id. at 2695-98 (Sotomayor, J., concurring). The disconnect between these views is accentuated by the plurality's observation that the Sentencing Commission's policy statements and commentary require the district judge in every case to consult the guidelines and determine whether a sentence set forth in a C-type plea agreement is appropriate before accepting the agreement. Id. at 2692 (plurality op.). In the plurality's view, therefore, "the court's acceptance [of a C-type plea agreement] is itself based on the Guidelines." Id.
The gap between the plurality and the concurrence is wide, but it is still possible to tease out a common denominator. In light of its perceived "consult the guidelines" requirement, the plurality would surely agree that in every case in which a defendant's C-type plea agreement satisfies the criteria for Justice Sotomayor's exception by "expressly us[ing] a Guidelines sentencing range applicable to the charged offense to establish the term of imprisonment," id. at 2695 (Sotomayor, J., concurring), the sentencing judge's decision to accept that sentence is based on the guidelines. Thus, Justice Sotomayor's concurrence delineates the narrowest grounds on which at least five Justices agree. It is, therefore, the controlling opinion. See Marks, 430 U.S. at 193-94, 97 S.Ct. 990.
In reaching this conclusion, we do not write on a pristine page. In the uncertain wake of Freeman, two other courts of appeals have published opinions addressing this question. Both agree with our conclusion. See United States v. Smith, 658 F.3d 608, 611 (6th Cir.2011); United States v. Brown, 653 F.3d 337, 340 & n. 1 (4th Cir.2011), petition for cert. filed, (U.S. Sept. 14, 2011) (No. 11-6385).
It remains for us to decide whether the defendant is eligible for a sentence reduction under the rationale of the concurrence. Justice Sotomayor allows for eligibility when the agreement itself expressly indicates that the term of imprisonment is based on a guideline sentencing range that has subsequently been reduced by the Sentencing Commission. See Freeman, 131 S.Ct. at 2695 (Sotomayor, J., concurring). She has identified two scenarios in which this phenomenon will occur. The firsta scenario in which a C-type plea agreement calls for a sentence within an identified sentencing range, id. at 2697 does not exist here.
The second scenario requires more elaboration. Justice Sotomayor wrote:
[A] plea agreement might ... make clear that the basis for [a] specified term [of imprisonment] is a Guidelines sentencing range applicable to the offense to which the defendant pleaded guilty. As long as that sentencing range is evident from the agreement itself, for purposes of § 3582(c)(2) the term of imprisonment imposed by the *349 court in accordance with that agreement is "based on" that range.
Id. at 2697-98. The defendant's fallback argument is that he is eligible for section 3582(c)(2) relief under this scenario.
This argument assumes that the second scenario requires "an analysis of the reasons that motivated or informed the parties' decision" to enter into the plea agreement. Appellant's Supp. Br. at 9. Starting from this premise, he notes that the Agreement mentions some guideline components (including a total offense level) as well as a specified drug quantity. These references, the defendant says, make it hard to believe that the guidelines did not figure into the agreed sentence.
The defendant's reasoning is plausible, but he is answering the wrong question. Justice Sotomayor's concurrence expressly rejects an inferential approach. She acknowledges that a term of imprisonment in a C-type plea agreement will most often be negotiated by reference to the relevant guideline provisions. Freeman, 131 S.Ct. at 2697 (Sotomayor, J., concurring). Yet under the rationale of the concurrence, this linkage is not enough to warrant a finding that the ensuing sentence is "based on" the guidelines. Justice Sotomayor makes it pellucid that the proper focus is neither the guideline calculations that the judge may perform before deciding whether to accept the agreement, id. at 2695-97, nor the "mere fact that the parties ... may have considered the Guidelines in the course of their negotiations," id. at 2697. Rather, it is the terms contained within the four corners of the plea agreement that matter. See id. at 2697-98; see also Smith, 658 F.3d at 612-13.
Silhouetted against this backdrop, the concern that we voiced in Rivera-Martínez I echoes still. The Agreement does not identify any guideline sentencing range. Moreover, the Agreement does not contain any information about the defendant's criminal history category. See Rivera-Martínez I, 607 F.3d at 287 & n. 4. This silence about a criminal history category makes it impossible to conclude from the Agreement alone that the proposed sentence is based on a specific sentencing range. See id. at 287 n. 4. The integers needed to trigger the exception carved out by Justice Sotomayor are not present here.
A comparison of the Agreement with the plea agreement in Freeman is telling. The latter agreement contained an explicit stipulation to both an offense level and a criminal history category. See Freeman, 131 S.Ct. at 2699-2700 (Sotomayor, J., concurring). When Justice Sotomayor turned to the sentencing table with these coordinates in hand, she could identify with certainty a particular sentencing range. See id. In this case, the Agreement does not permit such certitude. As we have explained, one of the two essential coordinates is missing.[4]
The short of it is that we cannot identify a referenced sentencing range from the Agreement alone. We would have to supplement the Agreement with either the parties' background negotiations or the facts that informed the sentencing judge's decision to accept the plea. Justice Sotomayor's concurrence forbids us from making such an archeological dig. See id. at 2696-98. We therefore conclude that the *350 defendant is not eligible for a sentencing reduction under section 3582(c)(2).[5]
There is one loose end. The parties have agreed that the district court made a clerical error when it entered the amended judgment. The judgment describes the offense of conviction as "[p]ossess[ion] with intent to distribute in excess of 5 kg of cocaine, and in excess of 5 kg of cocaine base Schedule II Narcotic Drug Controlled Substances." This is not the crime to which the defendant admitted his guilt. The judgment therefore should be amended to reflect that the defendant pleaded guilty only to conspiracy, not to the underlying substantive offense. Accordingly, we remand for the limited purpose of correcting this clerical error. See Fed.R.Crim.P. 36; see also United States v. Arboleda, 929 F.2d 858, 871 (1st Cir.1991).

III. CONCLUSION
We need go no further. For the reasons elucidated above, we again conclude that the defendant is ineligible for a sentence reduction under 18 U.S.C. § 3582(c)(2). We therefore reinstate our judgment affirming the denial of the defendant's motion while at the same time remanding for the limited purpose of correcting the district court's judgment.
So Ordered.
NOTES
[1]  For present purposes, cocaine base is crack cocaine, and we use the terms interchangeably.
[2]  A further amendment, which post-dates the filing of the defendant's sentence reduction motion, has increased the quantities of crack cocaine needed to trigger certain base offense levels. See USSG App. C, Amend. 750, Pt. A & comment. (backg'd.) (Supp.2011).
[3]  We also stated that Rule 11(c)(1)(C) prohibits a district court from altering a sentence "unless the terms of the plea agreement explicitly authorize it to do so." Rivera-Martínez I, 607 F.3d at 287. Freeman forecloses this rationale. See 131 S.Ct. at 2690.
[4]  Even if we were free to work backward, that effort would prove fruitless. When we look to the sentencing table armed with a 240-month sentence and an offense level of 37, the defendant's sentence places him in two distinct guideline sentencing ranges. See USSG Ch.5, Pt.A (sentencing table).
[5]  Justice Sotomayor herself foreshadowed this result. In explaining why she rejected absolutist approaches to the eligibility of individuals sentenced pursuant to C-type plea agreements for sentence reductions under retroactive guideline amendments, she cited our decision in Rivera-Martínez I with apparent approval. See Freeman, 131 S.Ct. at 2698 & n. 3 (Sotomayor, J., concurring). In that decision, we had advocated a flexible approach similar to that subsequently delineated by Justice Sotomayor. See Rivera-Martínez I, 607 F.3d at 287.
