OPINION
TRAXLER, Chief Judge:Frank Adoo pleaded guilty to unlawful importation of heroin in violation of 21 U.S.C. § 952(a). At sentencing, the district court concluded that Adoo had not been truthful and therefore was not eligible for sentencing under the “safety valve” exception to the otherwise-applicable statutory minimum sentence. See 18 U.S.C. § 3553(f); U.S.S.G. § 501.2(a). The court sentenced Adoo to 60 months’ imprisonment, the minimum sentence permitted under the statute. Adoo appeals, and we affirm.
I.
Customs officials had intelligence suggesting that Adoo, a native and resident of Ghana and a citizen of the Netherlands, was involved in drug smuggling. Ater learning that Adoo had paid cash for a ticket just a few days before he boarded a flight from Ghana, the officers stopped Adoo when he landed at Baltimore-Washington International Airport on March 27, 2009. Adoo initially told the officers that he was in the United States to visit his nephew “Evans Twum,” the name listed on Adoo’s customs declaration form. When the officers called Twum at the number provided by Adoo, the person answering the phone seemed very nervous and hung up. The officers called back, and the person answering the phone identified himself as Michael Jackson and again hung up. Adoo finally admitted that he had ingested heroin, and he eventually passed pellets containing 998.4 grams of heroin. He was indicted on one count of importing heroin and one count of possession with intent to distribute heroin. Hoping to qualify for sentencing under the safety valve, Adoo met with the government in a proffer session. Adoo told the government that this incident was the first time he had ever smuggled heroin and that he had been paid $10,000 by a man Adoo could identify only as “Kofi.” Adoo did not say who his contact in the United States was to be, and he identified no one in the United States as being involved in the scheme. J.A. 32-33, 130-31. Athough Adoo had provided a phone number for Evans Twum when he was arrested, he refused to implicate Twum in the smuggling. The government showed Adoo his passport, with dozens of stamps showing numerous trips out of Ghana, and told Adoo that the passport appeared to be that of an international drug smuggler. Adoo explained that he traveled to Europe and the United States to buy clothes at outdoor bazaars and department stores. Adoo said he brought the clothes back in his suitcase and then resold the clothes in Ghana. J.A. 31-32, 55. The government informed Adoo at the proffer session that it did not believe he was being truthful and that he did not meet the requirements of the safety valve.
Adoo eventually pleaded guilty to a single count of importing heroin. The plea agreement included a stipulation to facts that the government “would prove beyond a reasonable doubt,” J.A. 23, including a statement that “[intelligence obtained [by Customs officials] showed that Adoo had been involved in heroin smuggling activities. Adoo had traveled to an address in New York utilized by Nigerian heroin smugglers who were apprehended at John F. Kennedy Arport and in Boston.” J.A. 24. The plea agreement noted the government’s opposition to application of the safety valve but preserved Adoo’s right to argue to the district court that he qualified for sentencing under the safety valve and *604to appeal should the court reject his safety-valve argument.
The presentence report (“PSR”) prepared in advance of sentencing stated that Aidoo “appears to meet the criteria set for imposition of a sentence ... without regard to any statutory minimum sentence.” J.A. 104. Applying a three-level acceptance-of-responsibility reduction and the two-level reduction provided for defendants who meet the safety-valve requirements, see U.S.S.G. § 2D1.1(b)(11), the PSR calculated that Aidoo’s advisory sentencing range was 57-71 months.
After receiving the PSR, counsel for Aidoo submitted to the court a letter outlining his view of sentencing. Counsel contended that Aidoo had satisfied all of the safety-valve requirements and noted that the government had not objected to the finding in the PSR that Aidoo was eligible for the safety-valve. In the letter, counsel asserted that several of Aidoo’s international trips had been for the purpose of obtaining medical treatment that was unavailable to Aidoo in Ghana. The day after Aidoo’s letter was filed, the government filed a sentencing memorandum objecting to application of the safety valve because Aidoo had not been truthful and specifying its reasons for believing Aidoo to be ineligible.
At the sentencing hearing, the government explained its opposition to application of the safety valve, reiterating the points made in its sentencing memorandum. The government stated that Aidoo’s claim that the March 27 incident was the first time he had smuggled heroin was inconsistent with the information stipulated to in the plea agreement; that the large quantity of heroin Aidoo had ingested (just under a kilogram) suggested that he was an experienced smuggler; that Aidoo had never identified his contact in the United States; and that his international-clothes-buying- and-reselling story was not believable. The government noted that while counsel for Aidoo had stated in his sentencing letter that some of Aidoo’s international trips had been to obtain medical treatment, Aidoo himself had not mentioned any such trips during the proffer session.
Counsel for Aidoo asserted that Aidoo had been completely truthful about the conduct that led to his arrest and was entitled to sentencing under the safety valve. Although counsel presented no evidence to support Aidoo’s story, counsel did represent to the court that counsel had read certain Congressional testimony and various newspaper articles indicating that drug mules ingest, on average, just under a kilogram of drugs. Counsel also noted that Aidoo had medical records in his possession when he was arrested that showed he had received medical treatment in Belgium at least four times. Counsel argued that the stipulation in the plea agreement about Aidoo’s prior activities was not an admission that Aidoo had smuggled previously, but merely reflected his agreement that Aidoo had previously listed an address that at some point was associated with drag smugglers.1 When asked by the district court how Aidoo had paid for all of his international travel, counsel stated he had spoken to the pastor of Aidoo’s church in Ghana and that the church had provided some financial assistance. Counsel argued that the government was free to disbelieve *605Aidoo’s story about his clothes-buying trips, but that the prior trips were not part of a common scheme or plan with the offense of conviction and that Aidoo was not required to explain those trips to qualify for the safety valve.
The district court concluded that Aidoo was not entitled to sentencing under the safety valve because of the “inherent implausibility” of Aidoo’s explanation of his international travel. J.A. 53. The court explained:
[T]hat was not a statement of some kind of wholesale business that he was arranging shipments back on a freighter or a bulk shipment, or that he was buying from factories. It’s just simply implausible that a person can go to a department store in Brussels or some other city, buy some garments, put them in the suitcase, go back to Ghana, and sell them for a price that covers the expenses of the trips.
All the thousands of dollars for international travel and staying in hotels is simply implausible, and, for that reason, I conclude that Mr. Aidoo is not eligible for the safety valve.
J.A. 53. Counsel for Aidoo then explained to the court that Aidoo in his proffer had talked primarily about buying clothes at outdoor bazaars and fairs and had mentioned only one department store. The district court accepted that proffer but explained that it did not change its conclusion: “[T]he signal event [is] that the clothes go into a suitcase and go back to Ghana, so we don’t have anything that could be characterized as a wholesale operation. So even accepting that proffer, my view is the same.” J.A. 55. The district court thus concluded that Aidoo was subject to the five-year mandatory minimum sentence, and the court sentenced him to 60 months’ imprisonment.
II.
A.
The safety-valve statute requires sentencing courts to disregard any statutory mandatory minimum sentence if the defendant establishes that: (1) he does not have more than one criminal history point; (2) he did not use or threaten violence or possess a firearm or other dangerous weapon; (3) the offense did not result in death or serious bodily injury; (4) he was not an organizer, leader, manager, or supervisor of others; and (5) he truthfully provided the government with all evidence and information about the offense and related offenses. See 18 U.S.C. § 3553(f).
Under the statute, the government must be given an opportunity to make a recommendation, but the statute requires the district court to independently determine whether the requirements have been met, including whether the defendant was truthful. See id.; United States v. Ivester, 75 F.3d 182, 185 (4th Cir.1996). In this case, there is no dispute that Aidoo satisfied the first four requirements of § 3553(f). The only question is whether Aidoo satisfied the fifth requirement by “truthfully providing] 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.” 18 U.S.C. § 3553(f)(5).
The defendant bears the burden of “proving] that the prerequisites for application of the safety valve provision, including truthful disclosure, have been met.” United States v. Beltran-Ortiz, 91 F.3d 665, 669 (4th Cir.1996); accord United States v. Alvarado-Rivera, 412 F.3d 942, 947 (8th Cir.2005) (en banc); United States v. Marquez, 280 F.3d 19, 23 (1st Cir.2002); United States v. Gambino, 106 F.3d 1105, 1110 (2d Cir.1997); United States v. Ra*606mirez, 94 F.3d 1095, 1101 (7th Cir.1996). And because the burden is on the defendant, the government has no obligation to present evidence of the defendant’s failure to satisfy the requirements of the safety valve. See United States v. Sanchez, 475 F.3d 978, 980 (8th Cir.2007) (“The United States has no burden to refute a defendant’s assertion that his information is truthful if his proffer is inadequate.”); Marquez, 280 F.3d at 24-25 (“Were we to ... insist upon extrinsic evidence, district courts would be bound to accept even the most arrant nonsense from a defendant’s mouth so long as the government could not directly contradict it by independent proof. A rule to that effect would turn the burden of persuasion inside out.”).
B.
On appeal, Aidoo argues that the district court erred by concluding he was not entitled to sentencing under the safety valve. While Aidoo acknowledges that the burden of proving compliance with the statute belongs to him, he argues that he did prove his compliance and that the government therefore was obligated to come forward with evidence showing that he had not been truthful or that his disclosure was less than complete. Because the government did not present such evidence, Aidoo contends that the district court had no basis for refusing to apply the safety valve.
In support of his claim that the government was required to disprove his story, Aidoo relies primarily on United States v. Miranda-Santiago, 96 F.3d 517 (1st Cir.1996). In Miranda-Santiago, the First Circuit held that the government could not defeat the application of the safety valve “simply by saying, We don’t believe the defendant,’ and doing nothing more.” Id. at 529. The court made it clear, however, that any obligation on the part of the government arises only if the defendant has established the credibility of his story:
The defendant plainly has the burden of proving, by a preponderance of the evidence, entitlement to relief under section 3553(f). However, where a defendant in her submissions credibly demonstrates that she has provided the government with all the information she reasonably was expected to possess, in order to defeat her claim, the government must at least come forward with some sound reason to suggest otherwise.
Id. at 529 n. 25 (emphasis added; citation omitted). Since Miranda-Santiago was decided, the First Circuit has repeatedly emphasized the narrowness of that holding. For example, in Marquez, the First Circuit rejected the defendant’s claim that Miranda-Santiago required the government to present evidence showing that his disclosure was untruthful or incomplete. See Marquez, 280 F.3d at 24. The Marquez court reiterated the established rule that “a sentencing court may reject a safety valve proffer based on its reasoned assessment of the defendant’s credibility in light of the facts — and that the court may do so without the benefit of independent rebuttal evidence.” Id. As to the defendant’s understanding of Miranda-Santiago, the court explained that
Miranda-Santiago stands merely for the proposition that when the record, taken as a whole, will not support a finding that the defendant has failed to provide a truthful and complete proffer, the government’s lack of confidence in the proffer is insufficient, in and of itself, to justify a denial of access to the safety valve.
Id.; see also United States v. Padilla-Colon, 578 F.3d 23, 31 (1st Cir.2009) (reaffirming the Marquez court’s understanding of Miranda-Santiago); United States *607v. White, 119 F.3d 70, 74 (1st Cir.1997) (“Miranda-Santiago in no sense suggests that the sentencing court cannot arrive at an independent determination regarding a criminal defendant’s truthfulness, based on the evidence before it. Rather, we there held merely that it was clear error to conclude that the defendant had been untruthful, based solely on a PSR which directly contradicted the district court’s determination.”).
Since any obligation on the part of the government under Miranda-Santiago arises only after the defendant has carried his burden of proof, Aidoo’s various arguments that the government was required to present evidence disproving his story are thus dependent on his assertion that he carried his burden of proof and established at the sentencing hearing that he provided a truthful and complete disclosure of all relevant information. The record, however, does not support this assertion.
Counsel for Aidoo insisted at sentencing that Aidoo had truthfully told the government everything he knew about the incident leading to his arrest. A defendant’s “bare assertion that he was truthful,” however, is insufficient to “satisfy his burden to prove by a preponderance of the evidence that he provided a full and honest disclosure.” United States v. Montes, 381 F.3d 631, 637 (7th Cir.2004). The defendant’s burden under the safety valve is a true burden of proof that rests, at all times, on the defendant. To carry his burden, the defendant must persuade the district court that he has made full, truthful disclosure of information required by the safety valve. See Ramirez, 94 F.3d at 1100 (“The court’s conclusion in favor of the defendant necessarily depends upon the defendant’s persuasive ability to demonstrate to the court that he is eligible for the reduced sentence.”); United States v. Montanez, 82 F.3d 520, 523 (1st Cir.1996) (“It is up to the defendant to persuade the district court that he has truthfully provided the required information and evidence to the government.” (internal quotation marks omitted)). At least in cases like this one, where the government opposes application of the safety valve, a defendant cannot carry his burden of proof without presenting some kind of evidence. See United States v. Cervantes, 519 F.3d 1254, 1258 (10th Cir.2008) (“Absent a favorable recommendation from the government, a defendant needs to put on evidence at the sentencing hearing to meet his burden of showing that he truthfully and fully disclosed everything he knew and to rebut government claims to the contrary.”); United States v. Martinez, 301 F.3d 860, 866 (7th Cir.2002) (explaining that a defendant “cannot meet this burden if the government challenged the truthfulness, accuracy, or completeness of his statements and he produced nothing to persuade the district court that his disclosures were truthful and complete”).2
Aidoo, however, did not testify at the sentencing hearing, and he presented no other evidence showing that he had provided the government with complete and truthful disclosure. To be sure, counsel for Aidoo talked about evidence — the medical records showing Aidoo received treatment in Europe, and the newspaper articles and Congressional testimony indicating that it is not unusual for drug *608smugglers to ingest up to a kilogram of narcotics. The documents, however, were not presented to the district court, and the government did not stipulate to any of the information proffered by counsel for Aidoo. Nonetheless, even if we treat counsel’s statements about the documents as evidence, they do little to further Aidoo’s claim. The medical records explain only a few of the “dozens and dozens” of international trips shown on Aidoo’s passport, J.A. 32, and the ability of some smugglers to ingest a kilo of narcotics says nothing about the likelihood that a first-time “body packer,” as Aidoo claimed to be, could ingest such a large quantity. This evidence, at best, may be consistent with Aidoo’s story, but the evidence falls far short of proving that Aidoo provided full and truthful disclosure. Given the weakness of the evidentiary record — a record that Aidoo was obligated to establish — we cannot say that the district court clearly erred by concluding that Aidoo was not eligible for sentencing under the safety valve. See United States v. Wilson, 114 F.3d 429, 432 (4th Cir.1997) (explaining that the district court’s determination of whether a defendant has satisfied the safety valve criteria is a question of fact reviewed for clear error); see also United States v. Adu, 82 F.3d 119, 125 (6th Cir.1996) (“Where the government challenges a defendant’s claim of complete and timely disclosure and the defendant does not produce evidence that demonstrates such disclosure, a district court’s denial of a motion under § 3553(f) and § 5C1.2(5) is not clearly erroneous.”).
This case, therefore, is quite unlike Miranda-Santiago, where the only inference that could be drawn from the record was that the defendant had provided a truthful and complete proffer. Because Aidoo failed to create a record that affirmatively establishes that he provided complete and truthful disclosure to the government, we reject Aidoo’s arguments that, under Miranda-Santiago, the government was required to present evidence showing that he had not been truthful or that his disclosure was less than complete.
Our conclusion that the government had no obligation to present evidence rebutting Aidoo’s proffer leaves little room for Aidoo to challenge the district court’s rejection of the safety valve. At the sentencing hearing, the government, in accordance with its statutory right to make a recommendation, see 18 U.S.C. § 3553(f), pointed out the shortcomings of Aidoo’s proffer, such as his refusal to implicate Evans Twum or to otherwise identify his contact in the United States, and suggested that Aidoo’s clothes-buying story was not believable. See Ramirez, 94 F.3d at 1102 (“The government may respond to the defendant’s statements by challenging them for their lack of candor or completeness or by calling to the court’s attention the omission of evidence that the defendant should know and has not turned over to the government.”). The district court was entitled to consider those arguments when making its independent determination of whether the defendant had satisfied the statutory requirements. See United States v. Gales, 603 F.3d 49, 54 (D.C.Cir.2010) (explaining that even though the government did not present evidence contradicting the defendant’s story, the district court was entitled to consider the government’s assertion that the defendant’s story was not credible); United States v. Ponce, 358 F.3d 466, 468-69 (7th Cir.2004) (“A district court has the discretion ... to consider the government’s statements regarding contradictions and omissions in a defendant’s offer of information....”). The district court was likewise entitled to draw on its common sense and real-world experience to conclude that buying clothes at retail in *609the United States and Europe — in suitcase-sized lots — for resale in Ghana was unlikely to be a money-making venture, particularly given the airfare and hotel costs associated with international travel. See Gales, 603 F.3d at 54 (district court is entitled to draw reasonable inferences when determining the credibility of defendant’s proffer); Marquez, 280 F.3d at 24 (“[A] sentencing court may reject a safety valve proffer based on its reasoned assessment of the defendant’s credibility in light of the facts.... ”); Beltran-Ortiz, 91 F.3d at 669 n. 4 (“[District courts remain free to reject a defendant’s claim of full disclosure for credibility reasons....”); Montanez, 82 F.3d at 523 (“The government is perfectly free to point out the suspicious omissions at sentencing, and the district court is entitled to make a common sense judgment....”); cf. United States v. Perry, 747 F.2d 1165, 1169 (7th Cir.1984) (“Judges in the federal system, whether they are in the trial or appellate system, do not operate in a vacuum, shielded from knowledge of drug operations in the real world....”).
Aidoo, however, contends that the district court’s disbelief of the clothes-buying story cannot justify the court’s refusal to apply the safety valve. The safety valve requires disclosure of information “concerning the offense or offenses that were part of the same course of conduct or of a common scheme or plan.” 18 U.S.C. § 3553(f)(5). Adoo argues that because the government failed to connect any prior drug-smuggling by Adoo to the offense of conviction, he was not obligated under the safety valve to explain his prior travels. And because he was not required to disclose information about his prior travels, Adoo contends that the court’s disbelief of his clothes-buying story does not preclude application of the safety valve. See, e.g., United States v. Miller, 179 F.3d 961, 967-68 (5th Cir.1999) (concluding that the defendant was entitled to application of safety valve despite his lies about prior conduct, because the prior conduct was not relevant conduct about which disclosure is required). We disagree.
As an initial matter, we note that even if the prior smuggling alluded to in the plea agreement was not sufficiently connected to the offense of conviction, that does not mean that Adoo’s explanation of his international travel cannot be subject to scrutiny under the safety valve. Section 3553(f)(5) requires broad disclosure from the defendant; it is a tell-all provision that requires the defendant to “truthfully supply details of his own culpability.” United States v. Real-Hernandez, 90 F.3d 356, 361 (9th Cir.1996); accord Montes, 381 F.3d at 636 (The “plainly broad language [of § 3553(f)(5) ] suggests that any and all information that the defendant possesses concerning the offense must be provided to the Government.” (internal quotation marks omitted)). As noted above, Adoo offered the clothes-buying story to bolster his claim that the incident leading to his arrest was his first venture into smuggling. Whether the incident was Adoo’s first time smuggling is the kind of detail about the offense of conviction that must be disclosed under the safety valve. See United States v. Gonzalez-Montoya, 161 F.3d 643, 652 (10th Cir.1998) (“Under § 3353(f)(5), a defendant must affirmatively volunteer all he knows [about the offense of conviction], including facts beyond the basic elements of the crime.”). The story that Adoo offered up to bolster his claim on this point should likewise be treated as part of the disclosure required by the safety valve.
Moreover, even if we were to accept Adoo’s view that his international travels were not connected to the offense of conviction and that his clothes-buying *610story was not part of the disclosure required by the safety valve, we would still find no error in the district court’s consideration of the plausibility of Aidoo’s clothes-buying story. As Aidoo notes, a defendant’s lies about an unrelated matter or later-corrected lies about the offense do not automatically foreclose application of the safety valve. See United States v. Brownlee, 204 F.3d 1302, 1304 (11th Cir.2000); Miller, 179 F.3d at 967-68. Nonetheless, while the lies may not be disqualifying, neither are they irrelevant. The district court is obligated to determine for itself whether the defendant has truthfully provided the government with all the relevant information that he knows, and the court is free to consider any lies the defendant may have told when evaluating the defendant’s truthfulness. See United States v. Nuzzo, 385 F.3d 109, 119 n. 25 (2d Cir.2004) (“While a district court may find the fifth criterion of the safety valve satisfied despite prior lies and omissions, neither a district court nor this Court is precluded from considering those prior lies and omissions in determining whether the defendant has met his burden of proving that the information provided as of sentencing is complete and truthful.”); Brownlee, 204 F.3d at 1305 (“[T]he evidence of [the defendant’s prior] lies becomes part of the total mix of evidence for the district court to consider in evaluating the completeness and truthfulness of the defendant’s proffer.” (internal quotation marks omitted)). In this case, as noted above, it was proper for the district court to use its own common sense to find Aidoo’s clothes-buying story implausible. Upon finding the story implausible, the district court committed no error by basing its rejection of the safety valve on the fact that Aidoo lied during his proffer session. See United States v. Guerra-Cabrera, 477 F.3d 1021, 1025 (8th Cir.2007) (“The district court was ... entitled to infer untruthfulness from the implausibility of appellants’ accounts.”); United States v. Fletcher, 74 F.3d 49, 56 (4th Cir.1996) (affirming denial of safety valve in case where district court found that defendant lied by fabricating an alibi at trial: “[I]t is not illogical to assume that the judge similarly determined that [the defendant] failed to comply with the fifth condition” of § 3553(f)).
III.
We turn now to Aidoo’s remaining challenges to the district court’s rejection of his safety-valve claim.
A.
In the course of its ruling, the district court stated that “if Mr. Aidoo was an experienced heroin smuggler, then he was required to advise the government of that fact and explain his experience, how many times he has done this, who he did it for, his modus operandi.” J.A. 52. Aidoo argues that this description of the disclosure obligation effectively requires disclosure of every criminal act the defendant has ever committed. While a defendant seeking a substantial-assistance reduction in his sentence might be required to make that kind of wide-ranging disclosure, see U.S.S.G. § 5K1.1(a)(2), the safety valve’s disclosure requirement is limited to information about the offense of conviction and any other crimes that constitute relevant conduct, see 18 U.S.C. § 3553(f). Aidoo thus contends that the district court measured his compliance against a standard of disclosure higher than that imposed by the safety valve. We disagree.
The district court made this statement in the course of considering the government’s claim that Aidoo was an experienced smuggler, and the statement is an accurate description of the disclosure that *611would be required if Aidoo were an experienced member of a drug-smuggling conspiracy. See, e.g., United States v. Romo, 81 F.3d 84, 85 (8th Cir.1996) (“To satisfy § 3553(f)(5), Romo was required to disclose all the information he possessed about his involvement in the crime and his chain of distribution, including the identities and participation of others.”); Ivester, 75 F.3d at 184 (“[S]atisfaction of § 3553(f)(5) requires a defendant to disclose all he knows concerning both his involvement and that of any co-conspirators.”). Moreover, even if the court’s statement could somehow be viewed as an indication that the court had an impermissibly broad view of the disclosure required when there is no conspiracy, any such error would be harmless, given our conclusion that the issue upon which the district court based its rejection of the safety valve — Aidoo’s explanation for his international travels — was properly considered by the court, whether or not those travels were sufficiently connected to the offense of conviction.
B.
The PSR included a determination by the probation officer that Aidoo “appealed] to meet the criteria” for sentencing under the safety valve. J.A. 104. The Federal Rules of Criminal Procedure require objections to the PSR to be filed within fourteen days of receipt of the PSR, see Fed.R.Crim.P. 32(f)(1); neither the government nor Aidoo filed any formal objections to the PSR. Six days before sentencing, however, the government filed its sentencing memorandum objecting to application of the safety valve.
On appeal, Aidoo contends that the district court erred by entertaining the government’s untimely objection to the PSR’s safety-valve determination. Aidoo did not raise the timeliness of the government’s objection below, and we therefore review the claim for plain error only. To obtain relief under plain-error review, Aidoo must first establish that “the district court erred, that the error was plain, and that it affected his substantial rights.” United States v. Robinson, 627 F.3d 941, 954 (4th Cir.2010) (internal quotation marks and alterations omitted). “Even when this burden is met, we have discretion whether to recognize the error, and should not do so unless the error seriously affects the fairness, integrity or public reputation of judicial proceedings.” United States v. Hargrove, 625 F.3d 170, 184 (4th Cir.2010) (internal quotation marks omitted), cert. denied, — U.S. ——, 132 S.Ct. 292, 181 L.Ed.2d 177 (2011).
As an initial matter, it is not entirely clear that the time limits of Rule 32(f)(1) constrain the government’s ability to challenge a defendant’s eligibility for safety-valve sentencing. The safety-valve statute requires the district court to give the government an opportunity to express its views about the applicability of the statute, see 18 U.S.C. § 3553(f) (court must “impose a sentence ... without regard to any statutory minimum sentence, if the court finds at sentencing, after the Government has been afforded the opportunity to make a recommendation,” that defendant satisfied the statutory requirements (emphasis added)), and it is not apparent to us that the court’s statutory obligation to seek out the government’s views should be affected by the government’s failure to timely object to a PSR’s safety-valve recommendation.
In any event, assuming the time limits of Rule 32(f)(1) apply, we note that the district court under Rule 32 has the authority to change the time limits for good cause. See Fed.R.Crim.P. 32(b)(2). Given Aidoo’s failure to question the timeliness of the government’s objection, the *612district court’s decision to hear the government’s objection may be treated as an implicit finding of the existence of good cause. See United States v. Archuleta, 128 F.3d 1446, 1452 n. 12 (10th Cir.1997) (“[N]o explicit finding of good cause is necessary” when defendant failed to contemporaneously object to consideration of government’s untimely objection to recommendation in PSR.). It seems to us that, if nothing else, the government’s right under the statute to express its views on the applicability of the safety valve would constitute good cause to modify the time limits and treat the government’s sentencing memorandum as timely filed. Aidoo, however, does not even attempt to argue against the existence of good cause, and he therefore has failed to establish that the district court erred, much less plainly erred, by hearing the government’s views on his safety-valve eligibility.
Moreover, even if Aidoo could satisfy the first three prongs of the plain-error standard, the claimed error in this case is not sufficiently serious to require us to exercise our discretion to correct it. See Robinson, 627 F.3d at 959 (“Plain error review exists to correct only the most grievous of unnoticed errors.”). As previously discussed, the district court was statutorily required to make an independent determination of Aidoo’s eligibility, and Aidoo bore the burden of proving to the district court that he had satisfied the requirements of § 3553(f). Neither the court’s obligation to independently determine Aidoo’s eligibility nor Aidoo’s obligation to prove his eligibility was affected or relieved by the unobjected-to recommendation in the PSR. See United States v. McLean, 951 F.2d 1300, 1302-03 (D.C.Cir.1991) (A defendant seeking an acceptance-of-responsibility reduction “must be prepared to carry his burden of convincing the court by a preponderance of the evidence that he is entitled to it. The favorable recommendation of the probation officer does not relieve him of the burden. Neither does the government’s failure to object.” (citation omitted)); United States v. White, 875 F.2d 427, 431 (4th Cir.1989) (district court’s decision to give acceptance-of-responsibility reduction “is not controlled by the presentence report recommendation, nor is the district court required to apply it simply because the government did not specifically object to its proposed application”).
Accordingly, whether or not the government formally objected, Aidoo was obligated by the operation of § 3553(f) itself to come to court prepared to prove his entitlement to safety-valve sentencing by convincing the district court that he had provided complete, truthful disclosure to the government. While Aidoo now contends that he would have been “better positioned” to respond to the government’s views if the government had filed a timely, formal objection to the PSR, the government’s opposition to safety-valve sentencing was known throughout the proceedings. The government informed Aidoo at the end of the proffer session that it did not believe he qualified under the statute, the plea agreement spelled out the government’s opposition to safety-valve sentencing, and the government reiterated that opposition in its sentencing memorandum filed six days before sentencing. Aidoo did not argue below that he needed additional time to gather evidence to counter the government’s position or otherwise suggest that he was surprised by the government’s opposition to application of the safety valve. And even on appeal, Aidoo identifies no argument that he would have made or evidence that he would have presented to support his claim of truthful disclosure if the government had filed a formal objection to the PSR that was timely under Rule 32(f)(1).
*613Under these circumstances, we cannot conclude that the fairness, integrity or public reputation of judicial proceedings was seriously affected by the district court’s decision to consider the government’s views notwithstanding the government’s failure to file a timely formal objection to the PSR’s safety-valve recommendation. See Hargrove, 625 F.3d at 184. Aidoo has thus failed to carry his burden under plain-error review of establishing that he is entitled to relief for the asserted Rule 32 error. See United States v. Byers, 649 F.3d 197, 213 (4th Cir.2011) (“Plain error review is strictly circumscribed, and meeting all four prongs is difficult, as it should be.” (internal quotation marks and alteration omitted)), cert. denied, — U.S. -, 132 S.Ct. 468, 181 L.Ed.2d 305 (2011).
IV.
To summarize, we reject Aidoo’s claims that the district court applied the wrong legal standard and that the government’s failure to timely object to the PSR should have precluded the court’s consideration of the government’s objection to application of the safety valve. We likewise reject Aidoo’s challenges to the district court’s denial of relief under § 3553(f). Aidoo bore the burden of proving that he had provided truthful and complete disclosure to the government, but he presented no evidence compelling such a conclusion. The district court committed no error when concluding that Aidoo’s international-clothes-buying story was false, and that conclusion provided a proper basis for the court’s rejection of Aidoo’s claim that he was entitled to sentencing under the safety valve. Accordingly, we hereby affirm Aidoo’s sentence.
AFFIRMED
. We note that counsel’s statement seems to suggest that on previous trips to the United States, Aidoo listed on his customs declaration form an address in New York that was used by Nigerian drug smugglers, while the stipulation in the plea agreement indicates that Aidoo actually visited the address associated with the drug smugglers. The precise details of Aidoo’s connection to the New York address, however, are not relevant to our decision.
. Given the nature of sentencing proceedings, the evidence supporting a defendant's claim of truthful disclosure need not be as formal as might be required in a trial. See United States v. Cervantes, 519 F.3d 1254, 1258 (10th Cir. 2008) (noting that defendant’s evidence “may include proffer documents, stipulated facts, or, in all likelihood, testimony from the defendant or a representative of the government subject to cross-examination”).