
557 F.3d 449 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Robert STEPHENSON, Defendant-Appellant.
No. 06-2574.
United States Court of Appeals, Seventh Circuit.
Argued April 30, 2007.
Decided February 17, 2009.
*451 Lisa M. Noller (argued), Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
Michael J. Petro (argued), Chicago, IL, for Defendant-Appellant.
Before ROVNER, WOOD, and SYKES, Circuit Judges.
ROVNER, Circuit Judge.
Robert Stephenson appeals his sentence for distribution of a controlled substance, objecting to the enhanced penalty he received for distributing crack cocaine. He argues first, that the government failed to prove that he sold crack as opposed to another form of cocaine, second that the enhanced penalties for crack cocaine are unconstitutionally vague, and, finally, that the district court had insufficient evidence to include one kilogram of prior crack distribution as relevant conduct. We affirm on each point.
In 2001, the Drug Enforcement Administration (DEA) targeted Stephenson in its ongoing investigation into crack dealing by members of the Gangster Disciples street gang in Evanston, Illinois. As part of the investigation, the DEA employed a confidential source who had negotiated crack deals with persons in the area before, including Stephenson. The confidential source knew Stephenson as a drug seller who dealt exclusively in crack cocaine.
On July 17, 2001, after two phone calls arranging the terms of the transaction, Stephenson and the confidential agent met in a parking lot of an Evanston YMCA where Stephenson sold the confidential source 36.6 grams of a white chunky substance for $1,100. Both the DEA agent and the confidential source visually identified the substance as crack, and field tests confirmed that the powder contained some form of cocaine.
Approximately two weeks later, the confidential source re-contacted Stephenson and, after several phone calls arranging the deal, the two met again. This time, the confidential source purchased a plastic baggie containing 57.7 grams of a hard, brownish tan chunky substance for $1,550. Again, both the DEA agent and the confidential source identified the substance as crack and field tests indicated that the product contained cocaine.
DEA agents arrested Stephenson on November 5, 2001. In a post-arrest interview, after being Mirandized, Stephenson admitted that he was a crack dealer in the Evanston, Illinois area. He revealed that he began purchasing small amounts of crack in 1996, and eventually began buying four and five ounce quantities. He estimated that he had purchased one kilogram of crack from one particular seller over the course of a five to six year period, ending in 2003. In a second meeting, again after being Mirandized, Stephenson viewed a tape of the August 2 drug sale and confirmed that he appeared in the video selling crack.
On January 13, 2005, Stephenson entered a blind plea to counts one and two of the superseding indictment which charged him with knowingly and intentionally distributing crack cocaine in violation of 21 U.S.C. § 841(a)(1)in excess of five grams in count one and fifty grams in count two. *452 After a May 31, 2005 sentencing hearing, on June 2, 2006, the district court sentenced Stephenson to 180 months on counts one and two, to be served concurrently, a fine of $1,000 and a five year term of supervised release for each count.
Stephenson appealed to this court alleging (1) that the government failed to prove by a preponderance of the evidence that Stephenson possessed crack cocaine as opposed to another form of cocaine; (2) that the enhanced penalties for crack cocaine are unconstitutionally vague; and (3) that the district court erred by including one kilogram of prior crack sales as relevant conduct.
Stephenson's primary strategy in this appeal is to cast doubt on the government's evidence that he sold crack as opposed to another form of cocaine. Although recent judicial and congressional actions have lowered some of the sentences for drug crimes involving crack cocaine, sentences for the sale of crack cocaine are still significantly higher than those for other forms of cocaine, and this distinction obviously fuels Stephenson's appeal.[1] To sentence a defendant under the enhanced penalty, the government must prove by a preponderance of the evidence that the substance at issue is crack, and not some other form of cocaine base. United States v. Branch, 195 F.3d 928, 934 (7th Cir.1999). As we shall see, more than ample evidence supports the government's contention that Stephenson sold crack cocaine, and we review such a factual determination of the type of drugs involved in an offense for clear error only. United States v. Linton, 235 F.3d 328, 329 (7th Cir.2000).
Given our sophisticated crime laboratories, it might seem an easy task to determine whether a particular drug is crack or another form of cocaine base, but no chemical test can distinguish between crack and cocaine base. Crack is merely one form of cocaine basea form that arises as the end result of one method of turning the salt form of cocaine, cocaine hydrochloride (powder cocaine), back into a base form. See United States v. Edwards, 397 F.3d 570, 574 (7th Cir.2005). Drug dealers alter the form of naturally occurring cocaine to offer drug users their preferred method of ingesting the chemical. Crack can be smoked, but not snorted or injected; powder *453 cocaine can be snorted, but not smoked. Id. at 490-91.[2] Other methods of converting cocaine hydrochloride into a base form produce cocaine base that is not crack. See United States v. Booker, 70 F.3d 488, 491 (7th Cir.1995). For example, freebase cocaine, popular in the 1970s, is another form of cocaine base, although one that has lost popularity due to its volatile and dangerous production methods. Id. This circuit has rejected rigid definitions of crack, noting that to employ such a rigid definition would invite those in the drug trade to make minor changes in structure, processing, or packaging to avoid the increased penalties for selling crack cocaine. United States v. Abdul, 122 F.3d 477, 479 (1997). Instead of applying a rigid definition, this circuit has held that a sentencing judge must determine whether a defendant sold "crack," as those who buy and sell in the market generally understand the term. Id. The experts in this field are those who spend their lives and livelihoods enmeshed with the drugsusers, dealers, and law enforcement officers who specialize in narcotics crimes. United States v. Kelly, 519 F.3d 355, 364 (7th Cir.2008); United States v. Bradley, 165 F.3d 594, 596 (7th Cir.1999) ("those who smoke, buy, or sell this stuff are the real experts on what is crack.")
In this case the "experts" all agreed that Stephenson sold crack and not some other form of cocaine to the confidential source. The confidential source, a former crack buyer and addict, readily identified the substance as crack, and also noted that he had never bought any drug other than crack from Stephenson.[3] In fact, the confidential source refused the DEA's request that he ask Stephenson for "crack, cooked or hard" because, as the he explained, Stephenson was a crack dealer and only sold crack. Presumably the confidential source was concerned that such an obvious reference to crack would blow his cover as a government agent.
The DEA agent who testified at Stephenson's sentencing hearing qualified as another expert in the field. At the time that he testified, DEA Special Agent Steve Moran had worked for the DEA for approximately eight years and had seen hundreds of samples of crack cocaine. See United States v. Gray, 410 F.3d 338, 347 (7th Cir.2005) (agent who had been with the DEA for seven years and previously had worked for five years as a narcotics canine officer was qualified as expert in identifying drugs). He testified that the price, appearance, packaging, and manner of transaction were consistent with crack cocaine.
The defendant himself identified his wares as "crack." After his arrest, and after officers read Stephenson his Miranda rights, the defendant agreed to speak to the investigating officers and admitted that he was a "crack cocaine dealer in Evanston, Illinois," and described several aspects of his crack business. Stephenson never told the agents that he sold cocaine or cocaine base. In his second post-arrest interview, after viewing a video of one of his transactions, Stephenson again admitted that he sold crack, referring to the drugs as "crack," or "cooked" or "hard"slang terms for crack cocaine.
At Stephenson's plea hearing, the government set forth its rendition of what the evidence would show if presented at trial. In that recitation, the government indicated *454 that Stephenson had sold crack cocaine on two separate occasions. It used the word "crack cocaine" no fewer than six times in its presentation of the evidence, after which time, the court engaged in the following colloquy with the defendant:
THE COURT: Mr. Stephenson, have you heard the statement of the prosecutor?
STEPHENSON: Yes, sir.
THE COURT: Is her statement correct?
STEPHENSON: Yes, sir.
THE COURT: Do you disagree with any part of the statement?
STEPHENSON: No, sir.
THE COURT: Do you wish to add to any part of the statement?
STEPHENSON: No, sir.
* * *
THE COURT: If you could just tell me in your own words what it was on each of these two occasions, on July 19, 2001, what was it that you did that was illegal, in your own words, not in legalese, just what it was.
STEPHENSON: Sold the guy cocaine base.
THE COURT: Okay. And when you sold himwhen you sold him the drugs, did you know it was crack cocaine? Did you know it was cocaine?
STEPHENSON: Yes.
(TR. 1/13/05, pp. 23-24).
Stephenson also informed the probation department that all of the information contained in the superceding indictmentincluding the charge that the he "sold cocaine base in the form of crack cocaine" was true and accurate. (R. 53 at p. 6).
We need not linger too long over Stephenson's choice of words that he "sold the guy cocaine base." All crack cocaine is cocaine base, but not all cocaine base is crack. See Edwards, 397 F.3d at 571. In the context of the discussion, particularly in light of the immediately preceding colloquy referencing only crack cocaine, both the court and Stephenson clearly were referring to that subset of cocaine base known as crack.
From start to finish, all of the players involved in this transaction understood that Stephenson was selling crack cocaine. Nevertheless, Stephenson insists that his situation resembles that of Carl Edwards, whose case we remanded for re-sentencing when the district court sentenced Edwards to the mandatory minimum for crack cocaine after finding that he possessed non-crack forms of cocaine base. Edwards, 397 F.3d 570. We reversed the district court in that case because of an error in its legal conclusionthat is, we reiterated our prior holdings that the enhanced penalties described in 21 U.S.C. § 841(b) apply only to crack cocaine and not to other forms of cocaine base. Id. at 577. We left undisturbed the district court's factual finding that Edwards possessed non-crack forms of cocaine. Id. Although, as it turns out, Edwards was one of Stephenson's suppliers, the factual finding that Edwards possessed non-crack cocaine for the offense of conviction in that particular case has no bearing on the factual findings in this case that Stephenson possessed crack. Edwards, unlike Stephenson, denied from the get-go that he sold crack as opposed to powder cocaine. Id. at 572. Edward's drug experts testified that the drug in question had neither the physical form nor color generally associated with crack. Id. at 573. The government's drug expert testified that the substance was indeed crack, but he based this conclusion not on scientific tests or expert examination but on the definition in the Sentencing Guidelines, which reads: "`Cocaine base,' for the purposes of this guideline, means `crack.'" *455 Id. at 572. Because the government's expert relied exclusively on the legal definition of "cocaine base" rather than scientific evidence, the district court rejected his conclusion that the substances Edwards possessed were crack. Id. at 572-73. Stephenson's case presented none of this confusion. The evidence from all of the experts, including from Stephenson himself, indicated that Stephenson sold crack cocaine.
In sentencing the defendant, the district court noted that "the government has proven that the Defendant was dealing crack cocaine, as that term has been defined in the precedent, by any standard of proof known in law, including proof beyond a reasonable doubt." (R. 53 at p. 2). The district court reviewed all of the potential evidence in the caseall of the evidence we have outlined herein concluding that Stephenson sold crack cocaine. Id. at 5. Particularly, the district court relied on the testimony of the confidential source and the DEA agent, the physical description of the drug, and the admissions Stephenson made after the police read him his Miranda, rights. Id. All of this, the court noted, was sufficient to establish beyond a reasonable doubt that Stephenson sold crack cocaine. Id. The district court also noted that although all of that evidence sufficiently established that Stephenson sold crack cocaine, Stephenson's agreement with the statements at the plea hearing and with those in the pre-sentencing report added additional support for the conclusion. Id. at 6. This was not a close case; the district court correctly concluded that Robert Stephenson was selling crack cocaine.
We turn next to an argument Stephenson makes for the first time on this appealthat the definitions of "cocaine base" is so vague that the enhanced penalties for crack cocaine run afoul of the due process guarantees of the Fifth Amendment. Because Stephenson did not raise this argument below, we review it for plain error only. United States v. Cusimano, 148 F.3d 824, 828 (7th Cir.1998).
Stephenson incorrectly labels this question a matter of first impression. We have held definitively, on more than one occasion, that the sentencing provisions for cocaine and cocaine base are not ambiguous and that the enhanced penalties in 21 U.S.C. § 851 for "cocaine base" apply to crack cocaine. See Edwards, 397 F.3d at 574-75; Booker, 70 F.3d at 494.[4] Despite these clear holdings, we address Stephenson's argument once more.
"[T]he void-for-vagueness doctrine requires that a penal statute define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement." Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 75 L.Ed.2d 903 (1983). A statute may operate in an unconstitutionally vague manner if it: "(1) does not provide a person of ordinary intelligence a reasonable opportunity to know what is prohibited, or (2) fails to provide explicit standards to prevent arbitrary and discriminatory enforcement *456 by those enforcing the statute." United States v. Lim, 444 F.3d 910, 915 (7th Cir.2006). Unless a vagueness challenge threatens a First Amendment interest, a court must examine the challenge on an "as-applied" basis  that is, whether the statute is unconstitutionally vague in light of the facts of the case at hand. Id.
In this case, the evidence clearly indicates Stephenson sold crack cocaine. Stephenson admitted that he was a crack cocaine dealer in Evanston. Both the physical presentation of the drug and the expert opinions of the confidential source and the DEA agent supported this identification. If indeed some cocaine base samples might lie in a gray area where they are unidentifiable as either crack or non-crack cocaine base, these were not. There was nothing confusing or ambivalent about the physical description of the crack, the method of packaging, the price, the language by which the experts, buyers and sellers referred to the substance, the manner in which Stephenson sold it, or the fact that Stephenson admitted to being a crack dealer in Evanston. We have long held that the statute is not ambiguous and that conclusion is all the more clear when applied to the facts of this case. Stephenson's due process rights have not been impeded by a vague definition of cocaine base.
Stephenson's last effort to reduce his sentence takes aim at the relevant conduct the district court considered in increasing his sentence. Upon his arrest, Stephenson not only admitted to selling the crack at issue in the indictment, but also admitted that during the course of his employ as a crack cocaine dealer in Evanston from 1996 to 2003, he had purchased approximately one kilogram of crack. The district court, whose finding we review only for clear error (see United States v. Delatorre, 406 F.3d 863, 866 (7th Cir. 2005)), credited Stephenson's claim that he had purchased one kilogram of crack cocaine. Stephenson argues that the activity was too remote in time, and the admission too imprecise in details and thus unreliable to support an increase for relevant conduct.
A court may increase a defendant's sentence for uncharged and unconvicted relevant conduct provided that the conduct constitutes part of the "same course of conduct or common scheme or plan as the offense of conviction." U.S.S.G. § 1B1.3(a)(2). See also United States v. White, 519 F.3d 342, 347 (7th Cir.2008). A court may not treat other drug transactions, in and of themselves, as events common to the plan or scheme. United States v. McGowan, 478 F.3d 800, 803 (7th Cir. 2007). Rather the assessment must include specific findings about the "similarity, regularity and temporal proximity of the offenses." White, 519 F.3d at 348. This court requires that the district court explicitly state which findings demonstrate the necessary relation to the convicted offense. United States v. Panaigua-Verdugo, 537 F.3d 722, 726 (7th Cir.2008). The court can do so expressly (the preferred method) or by reference to the facts and reasoning of the presentence investigation report. Id. In this case, the district court did bothreferencing specific provisions of the investigation reports and sentencing transcripts, and concluding that the multiple sales amounting to a total of approximately one kilogram of crack cocaine were part of the same course of conduct as they were connected by a common purpose, a similar modus operandi, and involved common victims. (R. at 53, p. 7). In this case Stephenson sold the same drug (crack), in the same locale (Evanston, Illinois), using the same one or few suppliers, continuously throughout a common time frame (1996-2003).
*457 Contrary to Stephenson's argument, the relevant conduct was not too remote in time. Stephenson admitted to selling approximately one kilogram of crack between 1996 and 2003. The court convicted Stephenson for crack sales which occurred smack in the middle of that time framein 2001. Delatorre, 406 F.3d at 867 (offenses and his offense of conviction were part of the same course of conduct even despite the near three-year gap between them). Furthermore, the evidence demonstrated that Stephenson's drug trafficking was more or less steady over the period of time in question, showing a continuous pattern of drug trafficking. See White, 519 F.3d at 348; United States v. Farmer, 543 F.3d 363, 373 (7th Cir.2008) ("Where the defendant's convicted offense was merely the latest drug sale in an unbroken series of deals regularly made, that is sufficient to find the defendant's prior drug transactions were part of the same course of conduct as the offense of conviction.")
Moreover, the details of his transactions contained sufficient specificity to establish evidence of a same course of conduct. During his post-arrest interview, Stephenson recited details of his crack transactions that included names of suppliers, quantities purchased, approximate transaction dates and amounts, and aggregate quantities. (R. at 40, Ex. 11-26-B, p. 2-3). Stephenson's earlier conduct hit all the trigger points for relevancysignificant similarity, regularity, and temporal proximity as well as common victims, accomplices, purpose, or modus operandi. See Farmer, 543 F.3d at 373.
Finally, the district court rejected Stephenson's claim that he exaggerated the amount of his sales to curry favor and inflate his value as a potential government source. The district court did not err by considering Stephenson's admission as evidence of his relevant conduct. See United States v. Wilson, 502 F.3d 718, 722 (7th Cir.2007) (basing finding of relevant conduct of selling 1.6 kilograms of cocaine on defendant's admission); United States v. Warneke, 310 F.3d 542, 550 (7th Cir.2002) (noting that "an admission of relevant conduct in a plea agreement is even better than a jury's finding beyond a reasonable doubt"); United States v. Beith, 407 F.3d 881, 887 (7th Cir.2005) (approving district court's consideration of relevant conduct to which the defendant admitted when determining which offense guideline most appropriately reflected the scope of the criminal activity). There was no evidence to suggest that Stephenson was exaggerating his drug dealing activities.
In sum, we conclude that the district court did not err in determining that Stephenson was guilty of distributing crack cocaine; the definition of crack cocaine is not unconstitutionally vague, and the district court appropriately considered relevant conduct in calculating Stephenson's sentence. The judgment of the district court is AFFIRMED.
NOTES
[1]  For example, effective November 1, 2007, the Sentencing Commission altered the guidelines suggestions for crack sentencing by reducing the base offense level associated with each quantity of crack by two levels. See Amendments to the Sentencing Guidelines for United States Courts, 72 Fed.Reg. 28571-28572 (2007). See also Kimbrough v. United States, ___ U.S. ___, 128 S.Ct. 558, 569, 169 L.Ed.2d 481 (2007). The Sentencing Commission took such action after its multiple attempts to persuade Congress to reduce or eliminate the crack/powder disparity were rejected. Furthermore, last year the Supreme Court held that the advisory nature of the Sentencing Guidelines applies to crack sentencing cases such that it would not be an abuse of discretion for a district court to conclude that the crack/powder disparity yields a sentence greater than necessary to achieve the goals of the statute at issue. Kimbrough, 128 S.Ct. at 575. It is questionable whether the changes announced in Kimbrough affect Stephenson, as he appears to have put all his eggs in the "I sold cocaine and not crack" basket. But see United States v. Padilla, 520 F.3d 766, 774 (7th Cir.2008) ("[defendant] did contest before the district court and again on appeal whether the drugs in question were crack. We can presume that [the defendant's] primary purpose in disputing the drug type was to avoid the harsh effects of the crack sentencing disparity, since no other logical inference exists. In so doing, [the defendant] preserved the issue, however obliquely, of whether the district court could consider the 100:1 sentencing disparity in sentencing."). In any event, at no time while this appeal has been pending did Stephenson make any argument regarding Kimbrough or the reasonableness of his sentence in this court, and thus the argument is waived.
[2]  For a more comprehensive explanation of the differences between the various forms of cocaine, see Booker, 70 F.3d at 490-91.
[3]  For ease of use, we will refer to the confidential source as "he" although this may or may not reflect the actual gender of the confidential source.
[4]  Although some circuits have concluded that the enhanced penalty applies in different manners, see Edwards, 397 F.3d at 575-76 (chronicling division among circuits), in this circuit it has long been clear that the enhanced penalty applies only to crack cocaine, as that term is understood by those who use and sell the drug. Id.; Booker, 70 F.3d at 494. The Supreme Court thus far has not concluded that certiorari is warranted to resolve these differences. See, e.g., United States v. Brisbane, 367 F.3d 910 (D.C.Cir. 2004) cert. denied, 543 U.S. 938, 125 S.Ct. 342, 160 L.Ed.2d 245 (2004); Booker, 70 F.3d at 494, cert. denied, 517 U.S. 1111, 116 S.Ct. 1334, 134 L.Ed.2d 484 (1996).
