Kareem Richardson, Roy T. Gaul, Marc Taylor, and David Arruda were convicted on multiple counts involving a conspiracy to distribute cocaine. They raise several issues on appeal, most importantly a challenge to the district court’s sentencing finding that the substance they distributed[*49] was both “cocaine base” and “crack.” We affírm.

I. Background

The defendants were arrested after an investigation involving a number of drug purchases by government informant John Thompson. Taylor facilitated Thompson’s purchases of crack cocaine from Gaul in June 1996, and Thompson bought crack directly from Gaul, Richardson, and Arru-da between October 1996 and February 1997. The defendants were indicted for conspiracy to distribute a controlled substance, 21 U.S.C. § 846, and multiple counts of possession of a controlled substance with intent to distribute, id. § 841. Before trial, Taylor pled guilty to conspiracy and two counts of possession. The other defendants went to trial before a jury. Richardson was found guilty of conspiracy and six counts of possession, Gaul of conspiracy and nine counts of possession, and Arruda of conspiracy and one count of possession.

Taylor moved to withdraw his guilty plea, and the district court denied the motion. The court held evidentiary hearings on the nature of the controlled substance, found that the substance was cocaine base and crack, and sentenced the defendants accordingly. Arruda and Taylor received statutory mandatory minimum sentences of ten years imprisonment, Gaul received a statutory mandatory sentence of life imprisonment, and Richardson received a sentence under the Sentencing Guidelines of 161 months imprisonment.

The defendants brought this appeal, raising the following issues: Richardson, Gaul, and Taylor contend that the district court erred in finding that the cocaine was cocaine base and crack; Richardson contends that the court denied him a meaningful opportunity to challenge the government’s sentencing evidence; Taylor contends that the court erred in denying his motion to withdraw his guilty plea and denying him a sentence reduction under the “safety valve”; and Arruda contends that the court erred in its jury instructions on conspiracy.

II. The Finding that the Substance was Cocaine Base and Crack .

In assessing the challenge to the district court’s drug-type finding, we begin by briefly sketching the legal landscape of the cocaine base/crack distinction in the sentencing context, mindful that we have been over this ground many times in recent years. See, e.g., United States v. Charles, 213 F.3d 10, 24-25 (1st Cir.2000); United States v. Ferreras, 192 F.3d 5, 11 (1st Cir.1999); United States v. Martinez, 144 F.3d 189, 190 (1st Cir.1998); United States v. Robinson, 144 F.3d 104, 107-09 (1st Cir.1998).

Both the statute and the Guidelines impose significantly greater penalties for distributing (or manufacturing, dispensing, or possessing with intent to manufacture, distribute, or dispense) a given quantity of “cocaine base” rather than an equivalent quantity of “cocaine” (i.e., cocaine hydrochloride or powder cocaine). See 21 U.S.C. § 841(b)(l)(A)(ii), (iii); U.S.S.G. § 2Dl.l(c). Neither the statute nor the drug-quantity table in the Guidelines that establishes the offense level uses the word “crack.” Section 841(b) does not define “cocaine base,” but we have held that the term, as used in the statute, includes all forms of cocaine base, including but not limited to crack. See United States v. Lopez-Gil, 965 F.2d 1124, 1134 (1st Cir.1992) (opinion on panel rehearing). As used in the Guidelines, however, “cocaine base” has, since a 1993 amendment, a narrower meaning: “ ‘Cocaine base,’ for the purposes of this guideline, means ‘crack.’ ‘Crack’ is the street name for a form of cocaine base, usually prepared by processing cocaine hydrochloride and sodium bicarbonate, and usually appearing in a lumpy, rocklike form.” U.S.S.G. § 2D1.1 Note (D). For Guidelines purposes, then, forms of cocaine base other than crack are treated as cocaine. See U.S.S.G.App. C, Amend. 487 (1993).

[*50] Richardson was sentenced under the Guideline provision for cocaine base; his sentence therefore depended on a finding that the substance attributed to him was crack. Taylor and Gaul received mandatory minimum sentences pursuant to 21 U.S.C. § 841(b)(l)(A)(iii); their sentences therefore depended on a finding that the substance attributed to them was cocaine base, but not on a finding that it was crack.

Turning to practicalities, the government may show by expert chemical analysis that a substance is cocaine base. See Robinson, 144 F.3d at 109. Chemical analysis cannot establish that a substance is crack, however, because crack is chemically identical to other forms of cocaine base, see id. at 108, although it can reveal the presence of sodium bicarbonate, which is usually used in processing crack, see U.S.S.G. § 2D1.1 Note (D). Lay opinion testimony suffices to prove that a substance is crack. See Martinez, 144 F.3d at 190.

The government presented overwhelming evidence that the substance at issue in this case was both cocaine base and crack. DEA chemist Maureen Craig testified at the sentencing hearings that she performed multiple tests on all of the samples and positively identified them as cocaine base. Her testimony was consistent throughout. The defendants’ insinuations notwithstanding, Craig made it clear that she had never found any of the samples to be cocaine hydrochloride. ^[1] ' Although Craig may not have performed all possible tests on every sample — contrary to the defendants’ contention, the record is unclear in this respect — the mere possibility of further tests goes to the weight of the government’s evidence and is no reason to overturn the finding of the district court. See Martinez, 144 F.3d at 190.

Multiple witnesses testified that the substance was crack cocaine. Craig gave her opinion that it was crack based on the appearance of the samples and the presence in some of them of sodium bicarbonate. Government informant John Thompson testified that he purchased crack from the defendants. FBI Agent Dale Dutton testified that the cocaine was “rock-like” and yellowish or off-white in color when seized. (Dutton also testified to his opinion that it was crack, but the government disclaims reliance on that opinion because of Dutton’s inexperience). Boston Police Detective Eduardo Dominguez testified that the samples were crack, based on Dutton’s testimony about its appearance when seized and his own observation that, even after being ground up for laboratory analysis, their consistency was still “gravel-like” and seventy percent was in large enough pieces to sell on the street as crack “gems.” This testimony, “remarking the substance’s distinctive appearance and texture and identifying it as crack, forged the final link in the evidentiary chain.” Martinez, 144 F.3d at 190. The district court was also entitled to consider the “utter absence” of evidence that the substance was anything other than crack cocaine. Robinson, 144 F.3d at 109. The court’s finding that the substance was cocaine base and crack “easily survives clear-error review.” Id.

III. Richardson’s Opportunity to Challenge the Government’s Sentencing Evidence

Richardson was absent from the two sentencing hearings at which Craig, Dut-[*51] ton, and Dominguez testified because his attorney had just had a baby. The district court ordered that Richardson be provided with transcripts of the hearings and delayed the sentencing for over four months after the hearings. Richardson did not seek an additional evidentiary hearing on the identity of the substance or attempt to introduce any sentencing evidence of his own, and he joined in the sentencing memorandum filed by Taylor, Gaul, and Arru-da. The situation at sentencing was just as we have described in a previous case:

The prosecutor pulled no rabbits out of his hat. He merely presented the same information that the defense had previously received and reviewed. The defendant did not move for a further continuance. He did not request an ev-identiary hearing. He did not subpoena any witnesses or offer any evidence. In short, the defendant did not seek in any way to secure a further right of rebuttal.

United States v. Tardiff, 969 F.2d 1283, 1286 (1st Cir.1992).

Richardson now says that he was denied a meaningful opportunity in a new evidentiary hearing to challenge the government’s evidence on the issue of whether the substance was crack cocaine. This argument is unavailing. Richardson waived his right to complain about the absence of such a hearing by failing to ask for one. See id. The district court was entitled to rely on evidence adduced at a proceeding from which Richardson was absent, as long as it gave him an opportunity to respond to that evidence before sentencing. See United States v. Berzon, 941 F.2d 8, 21 (1st Cir.1991). The record makes it clear that Richardson had such an opportunity and never used it.

IV. Taylor’s Motion to Withdraw His Guilty Plea

Taylor changed his plea to guilty shortly before his codefendants went on trial and were found guilty by the jury. About two months thereafter he moved to withdraw the guilty plea. The district court denied the motion and Taylor now asserts that this denial was error.

Multiple factors are relevant to whether a defendant has met his burden of establishing a “fair and just reason,” Fed. R.Crim.P. 32(e), to withdraw his guilty plea, “the most significant of which is whether the plea was knowing, voluntary and intelligent within the meaning of Rule 11,” United States v. Cotal-Crespo, 47 F.3d 1, 3 (1st Cir.1995). Other factors include: (1) the plausibility of the proffered reason for withdrawing the plea; (2) the timing of the motion to withdraw; (3) whether the defendant asserted his innocence; and (4) whether the plea was pursuant to a plea agreement. See United States v. Aker, 181 F.3d 167, 170 (1st Cir.1999). Before allowing a defendant to withdraw his plea the court must also consider the potential prejudice to the government. See United States v. Marrero-Rivera, 124 F.3d 342, 347 (1st Cir.1997).

Taylor contends that his plea was involuntary because he did not understand the consequences of pleading guilty. A defendant’s knowledge of the consequences of his plea is one of Rule ll’s “core concerns.” Cotal-Crespo, 47 F.3d at 4. Although his argument is difficult to understand, Taylor apparently argues that the district court misled him about the consequences of his plea by telling him that he could face an enhanced sentence under the Guidelines if the substance he possessed was found to be cocaine base, when in fact an increased sentence required an additional finding that the substance was crack, and hence an additional evidentiary burden for the government. This contention misapprehends the nature of Taylor’s sentence. He did not receive an increased Guidelines sentence based on a finding that the substance was crack. Instead, he received a ten-year mandatory minimum sentence for distributing more than 50 grams of cocaine base, see 21 U.S.C. § 841(b)(l)(A)(iii), and, as we have[*52] explained above, that sentence did not require a finding that the cocaine base was in crack form. ^[2]

The transcript of the change of plea hearing reveals that although there was some initial confusion about these matters, the district court made sure that Taylor understood the sentence he was facing before finally accepting the guilty plea:

[THE COURT:] But, do you understand that if I find 50 or more grams of cocaine base, that that’s the kind of guideline — not the kind. That is the guideline and the statutory provision that’s the bottom for the sentence? That’s the minimum that you’re going to do is 10 years?

[TAYLOR:] Yes, sir.

[THE COURT:] So you’re pleading guilty and leaving it to me to make the determination whether or not we’re dealing with 50 grams or more of cocaine base here?

[TAYLOR:] Yes, sir.

This was a correct statement of the consequences of the guilty plea, and we cannot say that the court erred in finding that Taylor understood those consequences. See Cotal-Crespo, 47 F.3d at 7 (cocaine conspiracy defendants understood consequences of plea when court advised them that, inter alia, they faced ten-year mandatory minimum); cf. United States v. Gray, 63 F.3d 57, 60 (1st Cir.1995) (cocaine conspiracy defendant did not understand consequences and should have been allowed to withdraw plea when court erroneously suggested that ten years was maximum, not minimum, sentence).

Other factors also weigh in favor of the court’s decision to deny Taylor’s motion to withdraw his plea. The court supportably found that Taylor’s proffered reason for seeking withdrawal was implausible, stemming more from garden-variety second thoughts and unhappiness with the court’s finding that the substance was over 50 grams of cocaine base — which led inexorably to the ten-year mandatory minimum — than from any lack of understanding at the time of the plea. ^[3] Although the court did not consider the timing of the request to be significant, the fact that it was made after the trial of Taylor’s codefendants means that if withdrawal were allowed the government would face the prejudice of an additional trial. There was a plea agreement, but Taylor does not contend that the government breached it in any way. Finally, and significantly, Taylor has never asserted his innocence. The court did not abuse its discretion in concluding that Taylor did not establish a fair and just reason to withdraw his plea.

Y. Denial of Taylor’s Request for a “Safety Valve” Reduction

Taylor sought relief from his mandatory minimum sentence in the “safety valve” provision. See 18 U.S.C. § 3553(f); U.S.S.G. § 5C1.2. The district court’s denial of that request was grounded in the fifth of the five safety valve criteria:

[*53] not later than the time of the sentencing hearing, the defendant has truthfully provided to the Government all information and evidence the defendant has concerning the offense or offenses that were part of the same course of conduct or of a common scheme or plan, but the fact that the defendant has no relevant or useful other information to provide or that the Government is already aware of the information shall not preclude a determination by the court that the defendant has complied with this requirement.

18 U.S.C. § 3558(f)(5); U.S.S.G. § 5C1.2(5). The defendant bears the burden of showing his entitlement to a safety valve reduction. See United States v. Cadavid, 192 F.3d 230, 239 (1st Cir.1999). We review the district court’s safety valve findings for clear error. See United States v. Woods, 210 F.3d 70, 76 (1st Cir.2000).

A defendant is not required to make the necessary disclosure in any particular way. See United States v. Montanez, 82 F.3d 520, 522 (1st Cir.1996). What counts is the substance of the disclosure. The defendant must, by “an affirmative act of cooperation with the government,” United States v. Wrenn, 66 F.3d 1, 3 (1st Cir.1995), truthfully provide all the information he possesses concerning the crime.

There is no evidence in the record that Taylor made the requisite disclosure. At the sentencing hearing, the prosecutor represented to the court that there had been only an aborted proffer session, at which Taylor gave an account that the government regarded as “absurd.” Taylor’s attorney, on the other hand, said that the proffer session “broke down because Mr. Taylor said that he was not going to talk about anybody’s activity other than his own and that he did not know the people that were involved because they were much younger than he.” Under either version, Taylor never truthfully told the government all he knew about the conspiracy.

Taylor nevertheless argued to the district court that he met the safety valve criteria because apart from the aborted interview, “the Government never requested [him] to come in and give a truthful proffer.” The district court was correct to reject that argument. Taylor was given a proffer session and failed to divulge all the information he possessed concerning the crime. Because the court did not clearly err in finding that Taylor had not proved his entitlement to the safety valve reduction, Taylor was properly sentenced to the mandatory minimum of ten years.

VI. Arruda’s Challenge to the Jury Instructions

Arruda objected to one sentence in the district court’s jury instructions on the requirements for proving a defendant’s involvement in. a conspiracy: “Proof that a defendant willfully joined in the agreement may be based on evidence of that defendant’s own actions or words.” That sentence was similar to, but differed in one noteworthy respect from, a portion of Instruction 4.03 of the Pattern Criminal Jury Instructions for the District Courts of the First Circuit (1998) ^[4] : “Proof that [defendant] willfully joined in the agreement must be based upon evidence of his/her own words and/or actions.” (emphasis added).

The quoted language from the pattern instruction, though not found verbatim in any of our cases, is a correct statement of the law. A conspiracy conviction requires that a defendant’s “membership in the conspiracy be proved on the basis of his own words and actions (not on the basis of mere association or knowledge of wrongdoing).” United States v. Cintolo, 818 F.2d 980, 1003 (1st Cir.1987); see also, e.g., United States v. Torres, 965 F.2d 303, 308 (7th Cir.1992) (“As a matter of substantive law, membership in a conspiracy[*54] depends on the accused’s own acts and words.”). Arruda argues that by using the word “may” instead of “must,” the district court erroneously implied that other types of evidence, such as his association with the conspirators or his knowledge of their wrongdoing, could be sufficient to prove that he willfully joined the conspiracy.

“Jury instructions must be gauged in the context of the charge as a whole, not in isolation.” United States v. Robbio, 186 F.3d 37, 42 (1st Cir.1999) (internal quotation marks omitted). Although the word “may” creates an arguable ambiguity, the court’s instructions did not affirmatively suggest that proof of Arruda’s joining the conspiracy could be based on mere association or knowledge of wrongdoing. Other portions of the instructions effectively made the point that Arruda’s guilt could only be established by his own words or actions. The court told the jury that “mere association” does not establish membership in a conspiracy, that the defendant must have willfully joined the conspiracy, and that the government had to prove both intent to agree and intent to commit the underlying crime. Most significantly, the court also stated that

no defendant may be found guilty for the acts of others unless you find that that defendant himself engaged in criminal acts.... The fundamental question is whether or not through acts and statements of his own, reflected both in those acts and statements and in the other evidence in this case, the defendant has been shown beyond a reasonable doubt to have engaged in the crime that is alleged.

Those additional instructions cured the possible ambiguity of the word “may.” The charge as a whole correctly informed the jury that a guilty verdict against Arru-da on the conspiracy charge had to rest on evidence of his own actions or words.

Affirmed.