
512 F.3d 1 (2007)
UNITED STATES of America, Appellee,
v.
Virgilio JIMENEZ, Defendant, Appellant.
No. 06-1553.
United States Court of Appeals, First Circuit.
Submitted October 11, 2007.
Decided December 27, 2007.
*2 Elaine Pourinski, on brief, for appellant.
Robert Clark Corrente, United States Attorney, Donald C. Lockhart and Stephen G. Dambruch, Assistant United States Attorneys, on brief, for appellee.
Before LIPEZ, Circuit Judge, SELYA, Senior Circuit Judge, and HOWARD, Circuit Judge.
SELYA, Senior Circuit Judge.
In this criminal appeal, defendant-appellant Virgilio Jimenez ascribes a litany of errors to the district court proceedings that resulted in his conviction and sentence on a drug-trafficking charge. Finding none of his arguments compelling, we affirm the judgment below.
Because the appellant's conviction and sentence followed the entry of a guilty plea, we draw the essential facts from the change-of-plea colloquy and the uncontroverted portions of the presentence investigation report (PSI Report). See United States v. Dietz, 950 F.2d 50, 51 (1st Cir. 1991).
On June 15, 2002, a federal grand jury sitting in the District of Rhode Island returned a single-count indictment charging the appellant with possession of five grams or more of cocaine base with intent to distribute. See 21 U.S.C. § 841(a)(1). The indictment followed a warrant-backed search of the appellant's home, during which the authorities discovered approximately 39.22 grams of cocaine base hidden inside a can of "Carpet Fresh." The same search revealed a digital scale, drug-packaging supplies, and video surveillance equipment. After being advised of his Miranda rights, see Miranda v. Arizona, 384 U.S. 436, 444, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966), the appellant confessed to his involvement in a drug-trafficking enterprise and admitted ownership of the cocaine base and drug paraphernalia.
*3 Despite these admissions, the appellant originally pleaded not guilty to the lone count of the indictment. He later revised his plea. During the change-of-plea colloquy, he confirmed what he had related at the time of the search. At a subsequent stage of the colloquy, he expressed some confusion anent his potential sentencing exposure. The district court patiently explained the dimensions of that exposure. Particularly, the court told the appellant that if the government was able to prove that he had prior drug-related felony convictions, he would be facing a minimum ten-year term of immurement and a maximum penalty of life imprisonment. The appellant assured the court that he understood his situation.
In due course, the court found the appellant's guilty plea to be knowing and voluntary. The court therefore accepted it and invited the appellant, if he so elected, to mount a challenge at the disposition hearing to his prior convictions and the nature of the trafficked substance. The court then commissioned the preparation of the PSI Report.
In its final form, the PSI Report classified the appellant's prior convictions as controlled substance offenses and on that basis characterized him as a career offender within the purview of the federal sentencing guidelines. See USSG § 4B1.1. At the disposition hearing, the appellant did not challenge this taxonomy.
The district court explained that, as a career offender, the appellant's guideline sentencing range (GSR) would be 292 to 365 months in prison. The appellant voiced no objection to this determination. After listening to the arguments of counsel and the appellant's allocution, the court imposed a sentence at the bottom of the GSR (292 months). This timely appeal followed.
In this venue, the appellant begins by arguing that he should be permitted to withdraw his guilty plea because he did not knowingly enter that plea. He claims that he was confused about its consequences throughout the hearing. This argument implicates Federal Rule of Criminal Procedure 11, which sets the template for the acceptance of guilty pleas in federal criminal cases.
Because the appellant raises the issue about the integrity of his plea for the first time on appeal, our review is for plain error. See United States v. Vonn, 535 U.S. 55, 58-59, 122 S.Ct. 1043, 152 L.Ed.2d 90 (2002); United States v. Jiminez, 498 F.3d 82, 85 (1st Cir.2007); United States v. Mercedes Mercedes, 428 F.3d 355, 358 (1st Cir.2005). Plain-error review places a burden on an appellant to show (i) that an error occurred, (ii) which was clear and obvious, (iii) which affected his substantial rights, and (iv) which seriously impaired the fairness, integrity, or public perception of the proceeding. See Johnson v. United States, 520 U.S. 461, 466-67, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997); United States v. Duarte, 246 F.3d 56, 60 (1st Cir.2001).
A party who aspires to demonstrate plain error faces a steep uphill climb, and the appellant cannot scale that pinnacle. To be sure, his basic premise  that a guilty plea must be knowing in order to satisfy the strictures of the Constitution  is impeccable. See Bousley v. United States, 523 U.S. 614, 618, 118 S.Ct. 1604, 140 L.Ed.2d 828 (1998); United States v. Delgado-Hernandez, 420 F.3d 16, 19 (1st Cir.2005). Moreover, to satisfy that standard, the accused must have understood the charges against him and the spectrum of possible penalties to which an admission of guilt will expose him. See Jiminez, 498 F.3d at 85; United States v. Gandia-Maysonet, 227 F.3d 1, 3 (1st Cir. *4 2000). But to recite these general propositions is not to say that they were disregarded in this instance.
The appellant labors mightily to portray his case as falling beyond the pale. His principal plaint is that he started out confused and remained confused as to his sentencing exposure throughout the proceedings below. The district court's attempts at clarification, he adds, did not dispel the haze. Despite the appellant's rhetorical flourishes, however, the record belies his animadversions.
A review of the transcript corroborates that the appellant at one point labored under a misconception about the possible parameters of his sentence: he thought that a five-year mandatory minimum rather than a ten-year mandatory minimum pertained, telling the district court:
Jimenez: So I don't understand why they say ten years as my mandatory minimum. That's what I don't understand. Because I look at the guidelines and it doesn't put me at a ten year minimum.
But that was only a momentary aberration. The transcript shows with conspicuous clarity that the district court promptly corrected this misimpression, advising the appellant that if he did have prior felony drug convictions, as the government represented, "then your mandatory minimum would be ten years, not five years." The court proceeded to explore the margins of the possible sentencing options and to explicate the considerations that bore on sentencing. The completeness and the transparency of this explanation ensured that the appellant, well before the court accepted his changed plea, had come to comprehend the full extent of his sentencing exposure.
The sockdolager is that the appellant proceeded to acknowledge as much. The final aspect of the relevant exchange tells the tale:
Jimenez: I understand what you're saying now, right. For instance, I plead guilty now, so what you're saying [is] a ten year minimum, right? The ten year minimum?
The Court: I have to inform you that you could be facing a ten year mandatory minimum. Now whether you are or not subject to the ten year mandatory minimum, I don't know. I'm telling you that's a possibility.
Shortly thereafter, the following colloquy occurred:
The Court: And do you also understand . . . that if your guilty plea is accepted, you could face a penalty of at least ten years and up to life in prison, followed by a period of supervised release of at least eight years and up to life, a fine of up to $4 million, and a special assessment of at least $100. Do you understand that you could receive sentences up to that amount?
Jimenez: Yes.
A defendant's acknowledgment, during a change-of-plea proceeding, that he understands a lucid explanation of his potential sentencing exposure is powerful evidence of the knowing nature of his guilty plea. See Jiminez, 498 F.3d at 86.
Given the tenor of the discourse here, this case finds a close analog in United States v. Isom, 85 F.3d 831 (1st Cir.1996), in which the defendant pleaded to drug-related charges and thereafter sought to withdraw his plea on the ground that he had misunderstood the extent of the possible penalties. See id. at 833-34. After examining the transcript of the change-of-plea colloquy, we rejected Isom's appeal, noting that the lower court had thoroughly explored whether he understood his situation. See id. at 836. Similarly, the lower court in this case took pains to ascertain *5 that the appellant understood the dimensions of his sentencing exposure.
We summarize succinctly. While the appellant started with an inaccurate impression of what his minimum sentence could be, the district court set him straight. At and after that point, the appellant repeatedly reassured the court that he understood his potential sentencing exposure. The record bears out that he did.
The bottom line, then, is that we can discern no error, plain or otherwise, with respect to the Rule 11 colloquy. It follows, as night follows day, that there is no reason to allow withdrawal of the appellant's guilty plea. See Mercedes Mercedes, 428 F.3d at 359 (explaining that the fact that a defendant receives a harsher sentence than the one he anticipated is not a basis for setting aside a plea).
The appellant next contends that his sentence should be vacated on the ground that the two prior convictions that the sentencing court used as predicates for his career offender designation were inadequately substantiated. We examine this contention.
In order to qualify as a career offender, a defendant, among other things, must have at least two prior felony convictions for crimes of violence or controlled substance offenses. USSG § 4B1.1(a). This latter category is restricted to drug offenses that involve something more than simple possession; manufacture, import, export, distribution, or dispensation of a controlled substance qualifies, as does possession with intent to do any of the foregoing. Id. § 4B1.2(b).
In this case the government, in advance of the change-of-plea hearing, filed an information pursuant to 21 U.S.C. § 851(a)(1).[1] That information described three prior felony convictions for narcotics offenses and suggested that these prior convictions warranted sentencing the appellant to an enhanced prison term of no less than ten years, see 21 U.S.C. § 841(b)(1)(B)(iii). Later, the PSI Report characterized two of those convictions as controlled substance offenses within the purview of the sentencing guidelines and used that characterization as a basis for classifying the appellant as a career offender. See USSG § 4B1.1. Thus, we train the lens of our inquiry on those two convictions.[2]
Both convictions occurred in New York. The first was for possession of a controlled substance in the third degree; it arose under N.Y. Penal Law § 220.16, a statute that criminalizes, inter alia, knowing and unlawful possession of a stimulant weighing one gram or more with intent to sell the same. The second, arising under N.Y. Penal Law § 220.39, was for the unlawful sale of a controlled substance in the third degree. After the appellant chose not to dispute either the PSI Report's account or its characterization of these convictions at the disposition hearing,[3] the district court *6 classified him as a career offender, established a GSR of 292 to 365 months, and imposed a 292-month incarcerative term.
Before us, the appellant posits that the district court erred when it relied on the PSI Report for proof of these prior convictions. He notes that the PSI Report supports one conviction by purporting to summarize a police report about the underlying crime and provides no documentation at all for the other charge. This skimpy substantiation, he maintains, falls short of the evidentiary bar established by the Supreme Court in Shepard v. United States, 544 U.S. 13, 20, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005). Shepard holds that in determining whether a prior conviction resulting from a guilty plea is a proper predicate conviction for purposes of the Armed Career Criminal Act, 18 U.S.C. § 922, a sentencing court's inquiry should be "confined to records of the convicting court." Shepard, 544 U.S. at 23, 125 S.Ct. 1254. These were said to include "the terms of the charging document, the terms of a plea agreement or transcript of colloquy between judge and defendant in which the factual basis for the plea was confirmed by the defendant, or . . . some comparable judicial record of this information." Id. at 26, 125 S.Ct. 1254; see Conteh v. Gonzales, 461 F.3d 45, 53 (1st Cir. 2006) (discussing Shepard).
At the disposition hearing, the appellant never lodged an objection to the inclusion of either of these prior convictions in the PSI Report. By the same token, he did not object to the district court's designation of him as a career offender. These omissions are all the more striking because, at multiple times during the Rule 11 hearing, the district court expressly invited the appellant to take the opportunity provided by the disposition hearing to challenge any supposed mischaracterization of his prior criminal record or any overly ambitious attempt to invoke career offender status.
For example, at one point in the Rule 11 proceeding, the following colloquy occurred:
Jimenez: Okay. So right now I'm just pleading guilty right now to this charge here?
The Court: Correct.
Jimenez: I'm not signing no paper that says I'm doing ten years or nothing like that yet?
The Court: That's right.
Jimenez: I'm just pleading guilty to this right now.
The Court: That's correct. That's correct.
Jimenez: Then the next time I come to court, we'll discuss that time situation after that?
The Court: That's right. The determination as to whether you have three prior convictions or not would be made later.
Jimenez: Okay. So right now, I just want to get it straight, because I don't want to have no mix-up. I'm pleading guilty to five grams or more of a controlled substance. That's what I'm pleading guilty to?
The Court: Correct.
Jimenez: My past history will be discussed later on to determine my sentencing?
The Court: That's right.

*7 Jimenez: All right.
Later, the following exchange occurred:
The Court: And as I said earlier, whether you do or do not [face penalties of at least ten years and up to life in prison], I guess remains to be seen until these issues, . . . namely, whether you have three prior convictions, whether the substance that you possessed was cocaine base or crack cocaine. Do you understand that?
Jimenez: Yes.
The Court: But you understand that if those issues are resolved against you, that as things stand, that you could be looking at a mandatory minimum of ten years?
Jimenez: And if they're resolved the way I'm saying, it . . . could bring me down to a five year minimum, right?
The inevitable conclusion from this history is that the appellant  having been expressly invited to object on the ground that his predicate convictions did not qualify him for career offender status and having eschewed the opportunity  waived that objection. See United States v. Olano, 507 U.S. 725, 733, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (describing waiver as the "intentional relinquishment or abandonment of a known right") (quoting Johnson v. Zerbst, 304 U.S. 458, 464, 58 S.Ct. 1019, 82 L.Ed. 1461 (1938)); United States v. Rodriguez, 311 F.3d 435, 437 (1st Cir. 2002) (finding a waiver where defendant initially objected to prior convictions but later withdrew his objection). We use the term "waiver" advisedly. A waiver is unlike a forfeiture, for the consequence of a waiver is that the objection in question is unreviewable. See Rodriguez, 311 F.3d at 437; United States v. Mitchell, 85 F.3d 800, 807 (1st Cir.1996). Not even plain-error review is available to a party who has waived a claim of error. So it is here.
We add a coda. Even if this claim of Shepard error were properly before us, we would reject it. Where, as here, the characterization of an offense contained in a presentence report is not disputed before the sentencing court, the report itself is competent evidence of the fact stated and, thus, is sufficient proof of that fact. See United States v. Pelletier, 469 F.3d 194, 202-03 (1st Cir.2006) (explaining that "in the absence of any objection, a statement in a presentence report is sufficient to prove the fact proposed"); United States v. Cordero, 42 F.3d 697, 701 (1st Cir.1994) (upholding reliance on description in PSI Report for proof of predicate conviction).[4] That is the situation here. Shepard is, therefore, inapposite.
The fact that the government sufficiently proved the two prior convictions does not necessarily end our inquiry. In some circumstances, the question would remain whether the underlying offenses qualify as controlled substance offenses within the meaning of the applicable sentencing guideline. See USSG § 4B1.2(b). Here, however, the appellant has made no argument, either in the lower court or in this court, that his prior convictions, if properly substantiated, do not qualify as convictions for controlled substance offenses. He has, therefore, effectively conceded this point. See United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990) (warning that a party "has an obligation to spell out its arguments squarely and distinctly, or else forever hold its peace") (internal quotation marks omitted).
We turn next to the appellant's residual claims of sentencing error. The first of these is his asseveration that the *8 district court transgressed his constitutional rights by sentencing him on the basis that he had possessed crack cocaine. To bolster this asseveration, he notes that he pleaded guilty only to possessing generic cocaine base, and that the government presented no scientific evidence addressing the composition of the cocaine base that was seized from his dwelling. This issue was not raised below and, thus, engenders plain-error review. See Duarte, 246 F.3d at 60.
There was no plain error here. Although the sentencing guidelines make numerous distinctions that depend upon the type of drug involved in the offense of conviction, there is no such distinction between crack cocaine and cocaine base under the career offender guideline. That is critically important because the appellant was not sentenced as a garden-variety drug-trafficker but as a career offender. Since his offense level, calculated without reference to the career offender provisions, was less than his offense level calculated in accordance with those provisions,[5] the latter trumped the former. See USGG § 4B1.1(b) (directing that "if the offense level for a career offender from the [career offender] table . . . is greater than the offense level otherwise applicable, the offense level from the [career offender] table . . . shall apply").
The career offender provisions do not distinguish between crack cocaine and other forms of cocaine base. See id. Consequently, regardless of whether the appellant possessed 39.22 grams of crack cocaine or 39.22 grams of some other form of cocaine base, his GSR as a career offender would have been the same.
To say more on this point would be supererogatory. In the circumstances at hand, the sentencing court's treatment of the seized contraband as crack cocaine could not have constituted plain error. See Duarte, 246 F.3d at 61-62 (explaining that the plain error doctrine requires that the alleged error must have affected the appellant's substantial rights).
In a last-ditch effort to secure vacation of his sentence, the appellant asserts that the 100:1 crack-to-powder ratio embedded within the sentencing guidelines is unreasonable and unjust.[6] Even while voicing this assertion, he acknowledges in his brief that a recent decision of this court decides the issue adversely to him. See United States v. Pho, 433 F.3d 53, 54, 61-65 (1st Cir.2006). He nonetheless exhorts us to reconsider the question.
The legal landscape anent the crack/powder disparity changed significantly on December 10, 2007, when the Supreme Court held that a district court can deviate from a properly calculated guideline sentencing range on the basis of that disparity. See Kimbrough v. United States, ___ U.S. ___, 128 S.Ct. 558, ___, ___, slip op. at 21, ___ L.Ed.2d ___ (2007).
Although the appellant sought this exact legal peripeteia, its arrival does not benefit him at all. As we have explained, the *9 crack/powder dichotomy is irrelevant to the career offender sentence actually imposed in this case. Consequently, the decision in Kimbrough  though doubtless important for some cases  is of only academic interest here.
That ends this aspect of the matter. A federal appellate court, reviewing a criminal conviction, has no business answering purely academic questions. See United States v. Padilla, 415 F.3d 211, 225 (1st Cir.2005) (en banc) (Boudin, C.J., concurring); United States v. Pighetti, 898 F.2d 3, 5 n. 2 (1st Cir.1990). That rule governs here.
We need go no further. For the reasons elucidated above, we uphold the appellant's conviction and sentence.
Affirmed.
NOTES
[1]  That statute provides in pertinent part:

No person who stands convicted of an offense under [the federal drug-trafficking laws] shall be sentenced to increased punishment by reason of one or more prior convictions, unless before trial, or before entry of a plea of guilty, the United States attorney files an information with the court (and serves a copy of such information on the person or counsel for the person) stating in writing the previous convictions to be relied upon. . . .
21 U.S.C. § 851(a)(1).
[2]  The record reflects that the appellant had yet a third conviction  this one for criminal possession of a controlled substance in the fourth degree, in violation of N.Y. Penal Law § 220.09. We need not consider this third conviction in connection with this appeal.
[3]  Without limiting the generality of the foregoing, it is worthy of special note that the appellant has made no argument that either of these convictions is for an offense that falls outside the contemplation of the career offender provisions.
[4]  The absence of any timeous challenge to the PSI Report distinguishes the case at hand from our recent decision in United States v. Brown, 510 F.3d 57, 73-75 (1st Cir.2007).
[5]  The appellant's base offense level as a career offender was 37, regardless of the type of drug involved in the offense of conviction. See USSG § 4B1.1(b). Absent career offender status, his base offense level would have been calculated under section 2D1.1(c) of the guidelines; even if the district court treated his offense as involving crack cocaine, the base offense level under that guideline would not have exceeded 32.
[6]  In the interim since the briefs in this appeal were submitted, amendments to the sentencing guidelines were ratified by Congress, becoming effective as of November 1, 2007. Even more recently, the Sentencing Commission has made those amendments retroactive (as of March 3, 2008).
