On Petition for Review of Final Orders of the Board of Immigration Appeals Pakistani nationals and brothers Syed Kalim Ud Din and Syed Arsalan Ud Din petition for review of a Board of Immigration Appeals decision upholding orders denying them adjustment of status and directing their removal from the United States. The Ud Dins argue that the agency erred in finding them ineligible for adjustment of status based on their earlier filing of frivolous, i.e., deliberately and materially false, asylum applications, see 8 U.S.C. §1158(d)(6), because those applications were untimely and, thus, their concededly false statements could not have been material to a matter properly before the agency for decision. The Ud Dins further fault the agency for alternatively denying them adjustment of status as a matter of discretion. See id. §1255(a). Because both arguments lack merit, we deny the Ud Dins’ petition for their review. Nevertheless, a question arises as to how the Ud Dins’ removal will affect their future ability to apply for reentry to the United States. A permanent and unwaivable bar on reentry applies to any alien who filed a frivolous claim for asylum after receiving notice of that consequence. Otherwise, the alien may be subject to lesser, waivable bars on reentry. Because this court cannot determine on the present record whether the Ud Dins received the notice required to trigger a permanent, unwaivable bar, we grant review as to that single question and remand for the limited purpose of allowing the agency to make an express finding as to notice and, based on that finding, to specify the scope of the reentry bar that will attend the Ud Dins’ removal. PETITION DENIED IN PART, GRANTED IN PART, AND REMANDED. REENA RAGGI, C.J. Pakistani nationals and brothers Syed Kalim Ud Din (“Kalim”) and Syed Arsalan Ud Din (“Arsalan”) petition this court for review of a Board of Immigration Appeals (“BIA”) decision upholding an immigration judge’s (“IJ”) orders denying the Ud Dins adjustment of status and directing their removal from the United States. See In re Syed Kalim Ud Din, Syed Arsalan Ud Din, Nos. A 088 428 002, A 088 428 003 (B.I.A. Oct. 12, 2021), aff’g Nos. A 088 428 002, A 088 428 003 (Immigr. Ct. N.Y.C. Oct. 4, 2018). The agency found the brothers ineligible for adjustment of status based on their earlier filing of frivolous asylum applications, i.e., applications based on knowingly false, material misstatements, see 8 U.S.C. §1158(d)(6); 8 C.F.R. §1208.20 (2008), and, alternatively, denied them adjustment of status as a matter of discretion, see 8 U.S.C. §1255(a). In seeking to avoid removal, the Ud Dins do not dispute the knowing falsity of their asylum applications. Instead, they submit, first, that because their asylum applications were untimely when filed, their false statements could not have been material to a matter properly before the agency for decision. Second, and in any event, the Ud Dins contend that the agency could not find their asylum applications frivolous — a determination that results in their being permanently barred from reentering the United States, see id. §1158(d)(6) — because they did not receive adequate notice of the consequences attending a frivolous application. Third, the Ud Dins argue that the agency, having found them ineligible for adjustment of status based on their earlier frivolous asylum applications, could not alternatively deny them adjustment of status as a matter of discretion. We deny the Ud Dins’ petition to review their first and third challenges to the agency’s decision as those arguments are meritless. We must, however, grant review of the Ud Dins’ second argument because, while the propriety of removing the brothers from the United States is not in doubt, a question arises as to whether, following removal, they are permanently barred from reentering the United States. Such a bar requires a finding not only that the Ud Dins’ asylum applications contained knowingly fabricated material elements, but also that the Ud Dins received adequate notice about the consequences of filing frivolous applications. In general, an alien’s signature on an asylum application form warning of the consequences of filing a frivolous application gives rise to a rebuttable presumption of adequate notice. See 8 C.F.R. §1208.3(c)(2); Niang v. Holder, 762 F.3d 251, 254 (2d Cir. 2014). To the extent the Ud Dins attempted to rebut a notice presumption through their own sworn statements, it is not clear on the present record whether the agency’s adverse credibility findings as to the brothers’ disavowals of filing knowing misstatements also extended to their disavowals of notice. Thus, we grant the petition for review on this single question, and we remand the case to the agency for the limited purpose of allowing it to make an express finding as to notice and, based on that finding, to clarify the scope of the reentry bar attending the Ud Dins’ removal. BACKGROUND I. Asylum Applications In May 2007, the Ud Din brothers lawfully entered the United States from their native Pakistan on nonimmigrant visas valid through November 2007. The Ud Dins overstayed their visas, prompting the Department of Homeland Security (“DHS”), in March 2008, to charge the brothers as removable and to serve them with notices to appear. See 8 U.S.C. §1227(a)(1)(B). In September 2008, the Ud Dins’ retained counsel, Ali Faez Sayyid, filed Form I-589 applications for the brothers to be granted asylum, withholding of removal, and relief under the Convention Against Torture (hereafter, “asylum applications”). Each application told the same story. The brothers professed to be Shia Muslims and members of a political party (the Muttahida Qaumi Movement (“MQM”)) who, on several occasions in 2006 and early 2007, were beaten, shot at, wrongfully arrested, and tortured by religious and political rivals. On one occasion, these rivals purportedly stabbed Arsalan nearly to death. The Ud Dins asserted that if forced to return to Pakistan, they would be killed. Each Ud Din brother signed his I-589 asylum application under oath. On the signature page of each form was printed the following warning in bold font: WARNING: Applicants who are in the United States illegally are subject to removal if their asylum or withholding claims are not granted by an asylum officer or an immigration judge. Any information provided in completing this application may be used as a basis for the institution of, or as evidence in, removal proceedings even if the application is later withdrawn. Applicants determined to have knowingly made a frivolous application for asylum will be permanently ineligible for any benefits under the Immigration and Nationality Act. You may not avoid a frivolous finding simply because someone advised you to provide false information in your asylum application. Admin. R. 293, 1476 (“Frivolousness Warning”) (emphasis added). II. Applications for Adjustment of Status In 2010, before any ruling was rendered on their asylum applications, the Ud Dins married United States citizens. Attorney Sayyid then pursued another route to help the brothers avoid removal: he prepared and filed I-130 forms for each brother’s spouse to petition for her husband to remain in the United States. The petition for Kalim was granted in 2010; the petition for Arsalan was granted in 2011. In 2010, Sayyid also prepared and filed an I-485 form for Kalim to register as a permanent resident or to adjust his status. This request was denied in July 2011 based on pending removal proceedings. Dissatisfied with Sayyid’s efforts on their behalf, in 2012, the Ud Dins replaced him with attorney Robert Murtha, Jr., who prepared and filed a Form I-485 application for Arsalan and re-submitted such an application for Kalim. In 2013, Murtha asked the immigration court to terminate the brothers’ removal proceedings and to remand their cases to the United States Citizenship and Immigration Services (“USCIS”) for consideration of their Form I-485 applications. DHS opposed this request, and, in June 2014, the immigration court held a hearing on the Ud Dins’ consolidated removal proceedings. At that hearing, DHS raised questions about the veracity of the Ud Dins’ asylum applications. Directed to respond, Murtha submitted a letter in December 2014, which stated that the Ud Dins’ asylum applications had been “prepared and filed” by attorney Sayyid, who “concocted” their contents. Id. at 952, 959. Murtha acknowledged that the brothers were “never” MQM members and did not know much about that movement. Id. While acknowledging that the brothers had signed their asylum applications, Murtha explained that they “had not — could not — read [them] for lack of English.” Id. Accompanying Murtha’s letter were sworn affidavits from the Ud Dins admitting that their asylum applications had been fabricated. They confirmed Sayyid’s preparation and filing of the applications and their own inabilities to read English. Each brother professed that Sayyid had told him, “No problem — just sign. I’ll take care of everything.” Id. at 953, 960. The Ud Dins reported that their May 2007 trip to the United States was the most recent of several that they had made to this country. Far from looking to escape religious and political persecution, their purpose in remaining in the United States was to secure “a better future.” Id. In March 2015, DHS formally opposed the Ud Dins’ motion to remand their cases to the USCIS. Disputing the brothers’ professed ignorance of false statements in their asylum applications, DHS submitted an affirmation from attorney Sayyid stating that he had “reviewed/explained and read the contents” of the filed applications and attachments “to the [Ud Dins] in ‘Urdu,’” which is “the language they fully understand.” Id. at 459. DHS also noted that although the Ud Dins claimed that Sayyid had provided ineffective assistance of counsel in submitting their asylum applications, they had not notified Sayyid of their complaints or filed disciplinary actions against him as required by Matter of Lozada, 19 I. & N. Dec. 637 (B.I.A. 1988). See Debeatham v. Holder, 602 F.3d 481, 484-85 (2d Cir. 2010) (approving Lozada requirements). In August 2015, attorney Murtha provided the immigration court with evidence that the Ud Dins had recently filed complaints about Sayyid with the California and Virginia Bars, of which Sayyid was a member.1 The Ud Dins also submitted affidavits reiterating that Sayyid had fabricated their asylum applications and denying that Sayyid had explained their applications to them in Urdu. Thereafter, and for reasons not apparent on the record, removal proceedings against the Ud Dins lay dormant until 2018. III. Resumed Proceedings Before the IJ By April 2018, when the Ud Dins’ removal proceedings resumed before a new IJ, the brothers had withdrawn their asylum applications with prejudice and were seeking only adjustment of status. DHS acknowledged that the Ud Dins were prima facie eligible for adjustment based on their wives’ approved Form I-130 applications. Nevertheless, DHS opposed adjustment, in relevant part because the Ud Dins had “submitted…fraudulent application[s]” for asylum. Admin. R. 132. The IJ stated his understanding that the Ud Dins’ signatures on their Form I-589 asylum applications gave rise to a “ rebuttable presumption” that the Ud Dins had knowledge of the applications’ contents. Id. at 133. The IJ also confirmed with the parties that the immigration court had not itself given the Ud Dins “oral or written frivolous advisals.” Id. at 155. The case was then continued until August. A. The Hearing At a hearing conducted in August 2018, the Ud Dins each testified through an Urdu interpreter. Their testimony was not always consistent. At certain points, Kalim appeared to acknowledge that, before his asylum application was filed, attorney Sayyid had told him that it would be based on Kalim’s alleged membership in MQM. At other times, Kalim claimed it was only years later — when he filed for relief from removal based on his marriage to a United States citizen — that he came to understand the falsity of his asylum application. While acknowledging that Sayyid had communicated with him in Urdu, Kalim denied that Sayyid ever reviewed the application with him in that language before filing it. Arsalan similarly testified that Sayyid had not reviewed his asylum application with him in Urdu before he signed it. Instead, Sayyid had asked Arsalan to sign the asylum application with “quite a few blank papers,” telling Arsalan that he would “get some affidavits made.” Id. at 224-25. Arsalan claimed that he learned of the falsehoods in his asylum application only when attorney Murtha brought them to his attention years later. At another point in his testimony, however, Arsalan acknowledged that Sayyid had told him that his asylum application would be filed “with regard to MQM.” Id. at 224. Arsalan testified that “when the application was being filed,” Sayyid gave him and his brother “certain books to read about” MQM and the Shia religion so they might speak knowledgeably on those topics. Id. at 227-28. B. The IJ’s Decision In an oral ruling on October 4, 2018, the IJ denied the Ud Dins’ requests for adjustment of status and ordered them removed to Pakistan. In so ruling, the IJ identified two issues: (1) whether the Ud Dins had “filed a frivolous asylum application,” and (2) if not, “whether this court should exercise discretion granting [them] adjustment of status.” Id. at 66-67. The IJ answered the first question in the affirmative and, in the alternative, answered the second question in the negative. 1. Frivolousness Finding Observing that DHS bore the burden to demonstrate that an asylum application is “frivolous,” id. at 68, the IJ identified four factors that needed to be satisfied: (1) notice to the alien of the consequences of filing a frivolous application; (2) a specific finding by the Immigration Judge or the Board that the alien knowingly filed a frivolous application; (3) sufficient evidence in the record to support the finding that a material element of the asylum application was deliberately fabricated; and (4) an indication that the alien has been afforded sufficient opportunity to account for any discrepancies or implausible aspects of the claim. Matter of Y-L-, 24 I. & N. Dec. 151, 155 (B.I.A. 2007). The IJ determined that factors (3) and (4) were not at issue because the Ud Dins conceded that the basis for “both asylum applications was deliberately fabricated” and they had been able to explain these falsehoods in testimony before the IJ. Admin. R. 68-69. Turning to factor (1), the IJ construed this court’s decision in Niang v. Holder, 762 F.3d 251, to hold that “the written warning contained in the form I-589 application…[p]rovide[s] adequate notice sufficient to satisfy” that factor. Admin. R. 69 (internal quotation marks omitted) (citing Pavlov v. Holder, 697 F.3d 616 (7th Cir. 2012), for same proposition). Because the Ud Dins admitted signing their Form I-589s, which contained the Frivolousness Warning, the IJ concluded that they “had notice[] of the consequences of filing a frivolous application.” Id. As to factor (2), i.e., whether the Ud Dins knowingly filed frivolous asylum applications, the IJ discredited the Ud Dins’ testimony denying such knowledge and “g[a]ve weight to” attorney Sayyid’s affirmation that he had reviewed the completed Form I-589s with the brothers in Urdu before they signed them. Id. at 71. Having thus found the Ud Dins to have knowingly made frivolous applications for asylum and to have received notice of the consequences of doing so, the IJ concluded that they were “statutorily ineligible for adjustment of status.” Id. at 74 (citing 8 U.S.C. §1158(d)(6)). 2. Discretionary Determination The IJ further ruled that, even if the Ud Dins had been eligible for adjustment of status, he would exercise his discretion to deny such relief. He explained that although the Ud Dins had “established significant equities in the United States in the form of businesses, family ties, [and] children,” these circumstances were “significantly outweighed by the fact that both respondents knowingly perpetrated a fraud upon the immigration court.” Id. (reasoning that “[w]hen false or fake claims are perpetrated on this court, it adulterates the importance and necessity of protection law here in the United States which is namely to protect those who need it most, asylees and refugees”). IV. BIA Dismisses the Appeal On appeal to the BIA, the Ud Dins challenged the IJ’s frivolousness finding, arguing, as relevant here, that (1) the notice requirement had not been satisfied because they had not understood the Frivolousness Warning on their asylum applications; and, in any event, (2) their applications could not have been frivolous as a matter of law because they were untimely. In response, DHS both disputed the Ud Dins’ frivolousness arguments and submitted that the brothers’ failure to challenge the IJ’s alternative, discretionary denial of adjustment of status rendered harmless any error in the IJ’s frivolousness analysis. In a non-precedential decision dated October 12, 2021, the BIA dismissed the Ud Dins’ appeal, “adopt[ing] and affirm[ing] the entirety of the Immigration Judge’s decision for the reasons stated therein.” Id. at 2. Specifically citing Niang v. Holder, 762 F.3d at 254, the BIA held that the IJ “reasonably determined that the respondents received the required notice of the consequences of filing a frivolous asylum application based on the express written warnings contained in the I-589 application.” Admin. R. 3. As for the argument that the frivolousness bar was inapplicable as a matter of law to untimely asylum applications, the BIA ruled it “foreclosed” by agency precedent. Id. (citing Matter of M-S-B-, 26 I. & N. Dec. 872 (B.I.A. 2016); Matter of X-M-C-, 25 I. & N. Dec. 322 (B.I.A. 2010)). Finally, the BIA ruled that the IJ had “properly denied adjustment as a matter of discretion, in the alternative,” based on “the seriousness of the misrepresentations made, which outweighed the equities presented by the [Ud Dins], including family and business ties in the United States.” Id. The Ud Dins timely petitioned this court for review. DISCUSSION Because the Ud Dins “petition[] for review of a BIA decision that affirms an IJ decision without rejecting any part of its reasoning, this court properly considers both decisions in deciding whether to grant the requested review.” Likai Gao v. Barr, 968 F.3d 137, 144 (2d Cir. 2020); see Scarlett v. Barr, 957 F.3d 316, 326 (2d Cir. 2020) (“To the extent the BIA adopts the IJ’s reasoning in denying relief, we review the two decisions in tandem.” (internal quotation marks omitted)). “We review the agency’s factual findings…under the substantial evidence standard, treating them as ‘conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary.’” Xiu Xia Lin v. Mukasey, 534 F.3d 162, 165 (2d Cir. 2008) (quoting 8 U.S.C. §1252(b)(4)(B)); accord Quintanilla-Mejia v. Garland, 3 F.4th 569, 583 (2d Cir. 2021). At the same time, “we review de novo all questions of law, including the application of law to facts.” Scarlett v. Barr, 957 F.3d at 326; accord Ojo v. Garland, 25 F.4th 152, 159 (2d Cir. 2022). Thus, we review de novo the legal “question of eligibility for adjustment of status.” Cruz-Miguel v. Holder, 650 F.3d 189, 193 (2d Cir. 2011); accord Crocock v. Holder, 670 F.3d 400, 402-03 (2d Cir. 2012). The Ud Dins bore the burden of proving their entitlement to adjustment of status. See 8 U.S.C. §1229a(c)(4)(A) (“An alien applying for relief or protection from removal has the burden of proof to establish that the alien…satisfies the applicable eligibility requirements; and…with respect to any form of relief that is granted in the exercise of discretion, that the alien merits a favorable exercise of discretion.”); Crocock v. Holder, 670 F.3d at 403 (explaining that, in seeking adjustment of status, alien bears “burden of demonstrating admissibility”). Nevertheless, when adjustment is denied based on an alien’s previous filing of a frivolous asylum application, “the preponderance of the evidence must support an Immigration Judge’s finding that the respondent knowingly and deliberately fabricated material elements of the claim.” Matter of Y-L-, 24 I. & N. Dec. at 157; see Mei Juan Zheng v. Mukasey, 514 F.3d 176, 180 (2d Cir. 2008) (noting same). Following these principles here, we deny the Ud Dins’ petition for review of the agency’s decision to deny them adjustment of status as a matter of discretion. Respondent submits that such a conclusion makes it unnecessary to review the agency’s decision that the Ud Dins’ earlier filing of frivolous asylum applications made them ineligible for adjustment of status. We disagree because a denial based on frivolousness results in a lifetime, unwaivable bar on reentry, whereas a discretionary denial results in a lesser, waivable bar. We also decline to review the Ud Dins’ claim that their applications could not be frivolous as a matter of law because they were untimely. But because we cannot discern from the present record whether the IJ made factual findings sufficient to support the notice requirement for frivolousness, we grant the petition for the limited purpose of remanding this case to the agency for an explicit ruling on this single point. I. Discretionary Denial of Adjustment of Status In challenging the agency’s decision to deny them adjustment of status as a matter of discretion, the Ud Dins confront two preliminary hurdles: exhaustion and waiver. These merit only brief discussion because, even if the Ud Dins clear these hurdles, their argument that the IJ lacked authority to make a discretionary ruling in the alternative is meritless, and their challenge to the exercise of that discretion is beyond this court’s jurisdiction to review. A. Exhaustion and Waiver Respondent submits that the Ud Dins’ failure to challenge the IJ’s discretionary denial of adjustment of status on appeal to the BIA precludes review of that determination in this court. The argument finds support in 8 U.S.C. §1252(d)(1), which states that “[a] court may review a final order of removal only if…the alien has exhausted all administrative remedies available to the alien as of right.” As the Supreme Court has recently made clear, this exhaustion requirement is “not jurisdictional” but, instead, a “quintessential claim-processing rule.” Santos-Zacaria v. Garland, 143 S. Ct. 1103, 1110, 1112 (2023). “A claim-processing rule may be mandatory in the sense that a court must enforce the rule if a party properly raises it,” Fort Bend County v. Davis, 139 S. Ct. 1843, 1849 (2019) (internal quotation marks and brackets omitted), and we have generally treated §1252(d)(1)’s issue exhaustion requirement as “mandatory,” Lianping Li v. Lynch, 839 F.3d 144, 148-49 (2d Cir. 2016); see Brito v. Mukasey, 521 F.3d 160, 164 (2d Cir. 2008) (applying rule to deny petition to review adverse adjustment of status determination); see also Lin Zhong v. DOJ, 480 F.3d 104, 107 (2d Cir. 2007).2 An exception obtains, however, where the BIA nonetheless addressed an issue not raised on appeal. See Ojo v. Garland, 25 F.4th at 160. That is this case. The BIA not only rejected the Ud Dins’ specific challenges to the denial of their adjustment applications based on their previous filing of frivolous asylum claims, but also addressed and upheld the IJ’s decision alternatively to “den[y] adjustment as a matter of discretion.” Admin. R. 3. The Ud Dins, however, also did not challenge the agency’s discretionary denial of adjustment in their counseled opening brief to this court; rather, they questioned that alternative ground for decision only in their reply brief. We generally deem such a belated argument waived. See, e.g., JP Morgan Chase Bank v. Altos Hornos de Mex., S.A. de C.V., 412 F.3d 418, 428 (2d Cir. 2005) (“[A]rguments not made in an appellant’s opening brief are waived even if the appellant…raised them in a reply brief.”). While we “have discretion” to review waived arguments “if manifest injustice would otherwise result,” id., the Ud Dins fail to demonstrate that such injustice would result here. No matter because, even if we were to exercise our discretion in favor of the Ud Dins, their challenges to the agency’s discretionary denial are either meritless or unreviewable. B. Agency Authority To Deny Adjustment of Status as a Matter of Discretion in the Alternative to Finding the Ud Dins Ineligible for Such Relief The Ud Dins argue that once the IJ found them statutorily ineligible for adjustment of status based on their filing of frivolous asylum applications, the IJ had “no authority” alternatively to deny them such relief as a matter of discretion. Reply Br. 3. In support, they cite 8 U.S.C. §1158(d)(6), which states as follows: If the Attorney General determines that an alien has knowingly made a frivolous application for asylum and the alien has received the notice under paragraph (4)(A), the alien shall be permanently ineligible for any benefits under this chapter, effective as of the date of a final determination on such application. Id. (emphasis added). We are not persuaded. While the word “shall” when used in laws and regulations generally expresses a mandate, see WEBSTER’S THIRD NEW INT’L DICTIONARY 2085 (Philip Babcock Gove ed. 1986); Maine Cmty. Health Options v. United States, 140 S. Ct. 1308, 1320 (2020) (“The first sign that the statute imposed an obligation is its mandatory language: ‘shall.’”), §1158(d)(6)’s mandate pertains to an alien’s ineligibility for benefits, not to an agency’s jurisdiction to adjudicate a benefits claim, whether as a matter of eligibility or discretion. See generally Gonzalez v. Thaler, 565 U.S. 134, 146 (2012) (noting that “statute’s reference to ‘shall’ alone does not render statutory deadline jurisdictional” (internal quotation marks omitted)). That conclusion is reinforced by Supreme Court precedent instructing that, “when Congress does not rank a statutory limitation on coverage as jurisdictional, courts should treat the restriction as nonjurisdictional.” Arbaugh v. Y & H Corp., 546 U.S. 500, 516 (2006). Thus, before construing a statutory limitation as jurisdictional, we look for a “clear statement” in text signaling that legislative intent. Santos-Zacaria v. Garland, 143 S. Ct. at 1112. Section 1158(d)(6) contains no such clear statement. It “neither speaks in jurisdictional terms nor refers in any way to the jurisdiction of the courts.” Donnelly v. Controlled Application Rev. & Resol. Program Unit, 37 F.4th 44, 54 (2d Cir. 2022) (internal quotation marks omitted). The omission is especially telling because, in other portions of §1158, Congress did expressly confer or withhold jurisdiction. See 8 U.S.C. §1158(a)(3), (b)(3)(C); Santos-Zacaria v. Garland, 143 S. Ct. at 1113 (noting “more clearly jurisdictional language in related statutory provisions”). While we thus need not look beyond statutory text and context to reject the Ud Dins’ jurisdictional challenge, we note that the conclusion also finds support in a provision of the law’s implementing regulation. That regulation, 8 C.F.R. §1240.12(c), specifically authorizes IJs “to issue orders in the alternative or in combination.” Id.; see also Matter of X-M-C-, 25 I. & N. Dec. at 325 n.2 (suggesting — albeit in dictum — that, after making frivolousness finding rendering alien ineligible for benefits, IJ might consider “making an alternative finding that, even if the application is not frivolous, the applicant has not met the burden of proof” because “[a]lternate findings can promote the efficient resolution of cases” (emphasis in original)). At oral argument, counsel for the Ud Dins acknowledged finding no authority to the contrary. Indeed, cases coming before this court frequently present alternative findings of ineligibility for adjustment of status and denial of such relief as a matter of discretion. See, e.g., Guo Qi Wang v. Holder, 583 F.3d 86, 89-90 (2d Cir. 2009); Ling Yang v. Mukasey, 514 F.3d 278, 279 (2d Cir. 2008). Moreover, the Supreme Court recently stated that if an IJ “decides that denial [of adjustment of status] would be appropriate regardless of eligibility, the judge need not address eligibility at all.” Patel v. Garland, 142 S. Ct. 1614, 1619 (2022). If an IJ has jurisdiction to deny relief as a matter of discretion regardless of eligibility, he also has jurisdiction to deny relief as a matter of discretion in the alternative to denying relief based on ineligibility. Thus, the Ud Dins’ challenge to the agency’s authority to deny adjustment of status as a matter of discretion as an alternative to denying such relief based on ineligibility is without merit. C. Lack of Judicial Authority To Review Discretionary Denial of Adjustment of Status The Ud Dins argue that even if the IJ was authorized to make a discretionary determination in the alternative, his discretionary denial decision warrants review. That argument is defeated by 8 U.S.C. §1252(a)(2)(B)(i), which states that “no court shall have jurisdiction to review…any judgment regarding the granting of relief under section…1255 of this title,” i.e., the section dealing with adjustment of status determinations. See Cruz-Miguel v. Holder, 650 F.3d at 193 (“Federal courts lack jurisdiction to review a discretionary denial of adjustment of status.”). While an exception obtains for “constitutional claims or questions of law” informing an adjustment of status decision, 8 U.S.C. §1252(a)(2)(D), that provision “does not preserve review of questions of fact,” Patel v. Garland, 142 S. Ct. at 1619. In seeking to come within this exception, the Ud Dins argue that the IJ’s discretionary denial decision is “so intertwined with his [legally erroneous] frivolous bar ruling” that it cannot be separated from it. Reply Br. 3. They are wrong. Even assuming — without deciding — that §1252(a)(2)(B)(i) does not deprive this court of jurisdiction to review a discretionary denial of adjustment of status that “is based on the same grounds as [a legally challenged] eligibility determination,” Ling Yang v. Mukasey, 514 F.3d at 279 (recognizing possibility), that is not this case. Here, the agency’s ineligibility and discretionary denial decisions are both based on a finding that the Ud Dins knowingly submitted materially false asylum applications. That, however, is a factual finding for which the Ud Dins do not — and cannot — seek review in this court. See Patel v. Garland, 142 S. Ct. at 1619. To the extent that, in this petition for review, the Ud Dins argue that the agency’s notice finding was infected by legal error — a point we discuss further infra — that challenge is simply irrelevant to the agency’s discretionary denial decision. Thus, the Ud Dins’ challenge to the agency’s discretionary denial decision, far from being “intertwined” with their legal challenge to the agency’s ineligibility determination, is distinct from it. In these circumstances, accepting the Ud Dins’ contrary argument would approve judicial review of agency fact findings, even in the absence of any claim that those findings were a product of legal error. “Such legal alchemy would defeat” the jurisdictional distinctions that Congress has drawn. Guyadin v. Gonzales, 449 F.3d 465, 468 (2d Cir. 2006). Accordingly, we deny the Ud Dins’ petition to review the discretionary denial part of their challenge to removal. II. Ineligibility Based on Frivolousness Determination The Ud Dins submit that the IJ erred in finding that their filing of frivolous asylum applications made them ineligible for adjustment of status pursuant to 8 U.S.C. §1158(d)(6). As previously noted, §1158(d)(6) makes an alien “permanently ineligible” for adjustment of status if the Attorney General determines that the alien both “knowingly made a frivolous application for asylum” and received the required notice under §1158(d)(4)(A). The Ud Dins argue (1) that their “asylum applications cannot be frivolous as a matter of law, because they were filed out of time, and therefore any fabricated elements would not be ‘material’ to their claims.” Petitioners’ Br. 14. They further argue (2) that, in any event, the agency applied the wrong legal standard in determining that they received the notice of consequences required to support a frivolousness determination. Respondent submits that we need not address these arguments because the agency’s alternative discretionary denial of adjustment of status is “independently dispositive” of the brothers’ removability. Respondent’s Br. 18; see Oral Arg. Tr. 16:3-5 (“[T]he Court never has to get to the frivolousness argument because [the Ud Dins' petition for review] falls on the discretionary argument.”). We are not persuaded by this mootness argument. At the same time, however, we deny review of the Ud Dins’ timeliness challenge, which is meritless. But we must grant review of their notice challenge and remand to the agency so that it can answer the question of notice consistent with legal standards stated in this opinion. A. Mootness As respondent correctly observes, our decision not to review the agency’s discretionary denial of adjustment of status leaves intact the orders directing the Ud Dins’ removal from the United States. That, however, does not render moot the brothers’ challenge to the agency’s frivolousness determination. That is because severe consequences attend removal following a frivolousness determination that would not otherwise apply. Specifically, a finding that the Ud Dins “knowingly” filed a “frivolous application for asylum” after “receiv[ing]…notice” of the consequences makes the brothers “permanently ineligible” for readmission to the United States with no possibility for waiver of that bar. 8 U.S.C. §1158(d)(6) (quoted fully supra at 15); see Yuanliang Liu v. DOJ, 455 F.3d 106, 112 (2d Cir. 2006) (stating that frivolousness finding “permanently forecloses the petitioner from all benefits under the immigration laws of this country”). By contrast, removal in the absence of such a finding results in a lesser 10-year bar on readmission, see 8 U.S.C. §1182(a)(9)(B)(i)(II), which can be waived for aliens, like the Ud Dins, who are married to United States citizens, upon a showing of “extreme hardship,” id. §1182(a)(9)(B)(v). Even if the Ud Dins, having been denied discretionary adjustment of status based on their knowing filing of false asylum applications (even without notice of consequences), might be generally “inadmissible” under 8 U.S.C. §1182(a)(6)(C)(i), because that bar is also waivable, see id. §1182(i)(1), it too is less severe than that erected by §1158(d)(6). In sum, because the Ud Dins face more severe consequences upon removal based on the IJ’s frivolousness finding, the brothers’ challenges to that finding are not moot. That conclusion finds implicit support in Yuanliang Liu v. DOJ, 455 F.3d at 108, in which an alien facing removal sought review of both the IJ’s (1) adverse credibility determination, and (2) frivolousness finding. This court denied the petition as to (1), but granted it as to (2), vacating and remanding the IJ’s frivolousness finding. See id. at 118. Our sister circuits have also granted petitions to review frivolousness findings at the same time that they have denied review of other issues informing removal. See, e.g., Ning Wang v. Lynch, 845 F.3d 299, 300 (7th Cir. 2017) (denying petition “with regard to the denial of [petitioner's] applications for immigration relief” but granting petition “with regard to the finding of frivolousness”); Limbeya v. Holder, 764 F.3d 894, 896 (8th Cir. 2014) (leaving intact removal order but “remand[ing] for further proceedings on the issue of frivolousness”); Mingkid v. U.S. Att’y Gen., 468 F.3d 763, 768-69 (11th Cir. 2006) (rejecting mootness argument because vacating frivolousness finding “incontrovertibly leaves [petitioners] in better position than they would be in without our relief”); Farah v. Ashcroft, 348 F.3d 1153, 1154 (9th Cir. 2003) (affirming “order of removal but vacat[ing] the order of permanent ineligibility for immigration benefits”). Thus, we proceed to address the Ud Dins’ challenges to the IJ’s frivolousness finding. B. Finding Untimely Asylum Applications Frivolous Subject to certain exceptions not invoked here, an application for asylum in the United States generally must be “filed within 1 year” of an alien’s arrival in this country. 8 U.S.C. §1158(a)(2)(B). The Ud Dins arrived in the United States in May 2007 and did not file for asylum until September 2008. Thus, although the IJ did not specifically find their asylum applications untimely, respondent does not dispute the Ud Dins’ contention that they were. The Ud Dins argue that because their applications were untimely, the misstatements they contained were not material and, consequently, the applications could not have been frivolous. The implementing regulation for §1158(d)(6) provides: [A]n applicant is subject to [§1158(d)(6)] only if a final order by an immigration judge or the Board of Immigration Appeals specifically finds that the alien knowingly filed a frivolous asylum application. For purposes of this section, an asylum application is frivolous if any of its material elements is deliberately fabricated. Such finding shall only be made if the immigration judge or the Board is satisfied that the applicant, during the course of the proceedings, has had sufficient opportunity to account for any discrepancies or implausible aspects of the claim. For purposes of this section, a finding that an alien filed a frivolous asylum application shall not preclude the alien from seeking withholding of removal. 8 C.F.R. §1208.20 (2008) (emphasis added). The regulation does not define what constitutes a “material” element of an asylum application. In an analogous immigration context, the Supreme Court has instructed that a “misrepresentation is material if it has a natural tendency to influence, or was capable of influencing, the decision of the decisionmaking body to which it was addressed.” Kungys v. United States, 485 U.S. 759, 770 (1988) (internal quotation marks omitted) (discussing material misrepresentation supporting denaturalization). Nor does the regulation or the statutory text say whether an untimely asylum application can be found frivolous.3 In urging a negative answer to that question, the Ud Dins rely on Luciana v. Attorney General of the United States, in which the Third Circuit concluded, as a matter of law, that an alien’s false statements could not be “material” to an asylum application that was untimely filed. 502 F.3d 273, 280 (3d Cir. 2007). That court reasoned that when an asylum application “ha[s] to be rejected as time-barred,” “[e]vidence going to the merits of the application,” even if knowingly false, is “not material” because it is of “no consequence, no matter how persuasive or compelling it might have been.” Id. The court cited no supporting authority for its conclusion, pointing instead to “the bare force of logic,” and its desire to ensure a “just” outcome. Id. at 283.4 Every other court of appeals to have considered the question, however, has reached a different conclusion. See Ghazali v. Holder, 585 F.3d 289, 291-94 (6th Cir. 2009) (specifically rejecting Luciana’s reasoning); Mingkid v. U.S. Att’y Gen., 468 F.3d at 767-68 [11th Cir.] (concluding that “nothing, jurisdictional or otherwise,…divests an immigration judge of the authority to enter a ruling of frivolousness on” untimely asylum application); Ignatova v. Gonzales, 430 F.3d 1209, 1214 (8th Cir. 2005) (refusing to disturb agency’s finding of untimeliness, while continuing to consider frivolousness finding). We join them today. Beginning with text, we note that §1158(a)(2)(B) does not signal — much less clearly signal — that its time limit for filing asylum applications is jurisdictional so as to require IJs presented with asylum applications to address timeliness before frivolousness. See Ghazali v. Holder, 585 F.3d at 292 (rejecting jurisdictional characterization of §1158(a)(2)(B)); see supra at 15-16 (citing precedent instructing that absent Congress’s clear statement that statutory rule is jurisdictional, courts should construe rule as nonjurisdictional). As Judge Sutton, writing for the panel in Ghazali, observed, §1158(d)(6) “does not contain an inflexible order of battle — to the effect that immigration judges must address the statutory bars first and, once they do, may no longer make a frivolousness finding if a statutory [time] bar applies.” 585 F.3d at 291-92. Indeed, for courts to impose such an order would contravene the “long since settled” rule “that a reviewing court is generally not free to impose additional judge-made procedural requirements on agencies that Congress has not prescribed and the Constitution does not compel.” Garland v. Ming Dai, 141 S. Ct. 1669, 1677 (2021) (internal quotation marks omitted). Doing so would be particularly inapt here, where the agency itself has held that “the only action required to trigger a frivolousness inquiry is the filing of an asylum application,” Matter of X-M-C-, 25 I. & N. Dec. at 324; and where regulations specifically authorize, and precedent and practice approve, IJs “issu[ing] orders in the alternative or in combination,” 8 C.F.R. §1240.12(c); see supra at 16 (discussing approving precedent). In Mei Juan Zheng v. Mukasey, 514 F.3d at 181-82, this court considered whether a frivolousness finding under §1158(d)(6) could be made even as to a withdrawn asylum application. Rather than answering that question, this court remanded and “invite[d] the BIA to consider” it first. Id. at 181. When it did so in Matter of X-M-C-, the BIA answered that a frivolousness finding under §1158(d)(6) could be made even as to a withdrawn asylum application. See 25 I. & N. Dec. at 322. We have since held the BIA’s interpretation of §1158(d)(6) reasonable and accorded it Chevron deference. See Mei Juan Zheng v. Holder, 672 F.3d 178, 183-85 (2d Cir. 2012) (citing Chevron, U.S.A., Inc. v. Nat. Res. Def. Council, Inc., 467 U.S. 837 (1984)). In doing so, we implicitly rejected Luciana’s reasoning as to materiality.5 Following Mei Juan Zheng v. Holder, we here conclude that just as an IJ can find a withdrawn asylum application to have been frivolous, so too can he find an untimely application to have been frivolous. In both circumstances, what matters is that the alien filed an asylum application with the agency; that is “the only action required to trigger a frivolousness inquiry.” Matter of X-M-C-, 25 I. & N. Dec. at 324; see Ghazali v. Holder, 585 F.3d at 292-93 (making same point); accord Matter of M-S-B-, 26 I. & N. Dec. at 877-79 (rejecting Luciana and relying on “persua[sive]” reasoning in Ghazali to conclude in dictum that “ neither the materiality requirement under 8 C.F.R. §1208.20 nor the time-bar provision under [8 U.S.C. §1158(a)(2)(B)] precludes an Immigration Judge from making a frivolousness finding in cases involving time-barred applications for asylum, including cases in which the fabrications relate to the merits”).6 Any different conclusion risks the perverse result of treating untimely asylum applicants better than timely applicants when both have filed frivolous asylum applications. As Judge Sutton explained in Ghazali, Why should [petitioner], who filed an untimely frivolous application, be treated better than an applicant who filed a timely frivolous application? Under [petitioner]‘s theory, [the former] would be free to file another application while the other applicant would not be, even though the only difference between them is that the second applicant followed the Act’s timeliness requirements. If [petitioner] is right, no good deed goes unpunished. If he is wrong, as we think he is, he gets his just deserts — at least relative to those who file timely, but fabricated, applications. Ghazali v. Holder, 585 F.3d at 294-95 (emphasis in original); see also Matter of X-M-C-, 25 I. & N. Dec. at 325-26 (making same point in context of withdrawn application); accord Mei Juan Zheng v. Holder, 672 F.3d at 185 (same); cf. Bittner v. United States, 143 S. Ct. 713, 723-24 (2023) (declining to interpret statute such that “those who willfully violate the law may face lower penalties than those who violate the law nonwillfully” (emphases in original)). Here, the IJ found that the Ud Dins knew that attorney Sayyid had filed signed asylum applications on their behalf containing false claims of persecution. Such claims would naturally tend to influence an IJ in deciding whether to grant asylum and, thus, are properly deemed material. See 8 U.S.C. §1158(b)(1)(A) (stating alien eligible for asylum if “refugee”); id. §1101(a)(42)(A) (defining “refugee,” in part, as one who has suffered “persecution or [has] a well-founded fear of persecution on account of…religion…or political opinion”). In sum, text, context, and precedent all support the conclusion that any filed asylum application containing knowingly false, material statements can be deemed frivolous, regardless of whether the application was timely filed. C. Notice of Consequences The Ud Dins argue that the IJ erred as a matter of law in finding that they received the notice of consequences required for a frivolousness determination, thereby rendering them ineligible for adjustment of status. See 8 U.S.C. §1158(d)(4)(A) (mandating that, at time alien files asylum application, “the Attorney General shall…advise the alien…of the consequences, under paragraph (6), of knowingly filing a frivolous application for asylum”); id. §1158(d)(6) (quoted supra at 15). In finding adequate notice, the IJ relied on Niang v. Holder, in which this court held that the Frivolousness Warning printed on Form I-589 asylum applications was sufficient to provide the requisite notice. See 762 F.3d at 254. Sister circuits agree. See Khaytekov v. Garland, 26 F.4th 751, 758-60 (6th Cir. 2022), cert. denied, 143 S. Ct. 1061 (2023); Ndibu v. Lynch, 823 F.3d 229, 234-35 (4th Cir. 2016); Ruga v. U.S. Att’y Gen., 757 F.3d 1193, 1196-97 (11th Cir. 2014); Pavlov v. Holder, 697 F.3d at 618 [7th Cir.]; Cheema v. Holder, 693 F.3d 1045, 1049 (9th Cir. 2012); Ribas v. Mukasey, 545 F.3d 922, 929-30 (10th Cir. 2008). Respondent argues that the IJ would have been correct in concluding from Niang that the Ud Dins’ signatures on their Form I-589 applications were “conclusive of notice” and thus “dispositive” evidence that the notice requirement was satisfied. Oral Arg. Tr. 11:18-23, 19:2-3. If that is indeed how the IJ (and BIA) construed Niang — a point on which the record is not clear — that would be error. Thus, a remand is necessary to ensure that the notice determination required for a finding of frivolousness is made in accordance with applicable law. While in Niang, the petitioner’s signature on his Form I-589 was held sufficient to demonstrate notice, the opinion is careful to note that, in that case, petitioner did not assert “that he did not receive or was unable to understand the warning that appears on the signature page of his asylum application form.” Niang v. Holder, 762 F.3d at 254 n.1. This qualification signals that an alien’s signature on a Form I-589 gives rise to a presumption of notice. Such an interpretation comports with 8 C.F.R. §1208.3(c)(2), which states that an applicant’s signature on a Form I-589 “establishes a presumption that the applicant is aware of the contents of the application.” While the BIA has described the presumption as a “strong” one, it recognizes that it can be “rebutted.” Matter of Valdez, 27 I. & N. Dec. 496, 499 (B.I.A. 2018). Indeed, implicit in the term “presumption” is the possibility for rebuttal. See, e.g., Flemming v. Matteson, 26 F.4th 1136, 1140 (9th Cir. 2022) (observing that “all presumptions[] can be rebutted”); Illinois Tool Works, Inc. v. Grip-Pak, Inc., 906 F.2d 679, 682 (Fed. Cir. 1990) (recognizing “all presumptions[to be] rebuttable”); Gurley v. Wilson, 239 F.2d 957, 959 (D.C. Cir. 1956) (“After all, presumptions are rebuttable.”); 9 WIGMORE ON EVIDENCE §2491, at 305 (James H. Chadbourn rev. 1981) (explaining that “presumption…invoke[s] a rule of law compelling the jury to reach the conclusion in the absence of evidence to the contrary from the opponent” (emphasis in original)).7 Accordingly, if an alien plausibly claims and presents credible evidence that he was unable to understand the printed Frivolousness Warning on his signed asylum application, the presumption of understanding established by his signature may not be determinative of notice. Further inquiry is necessary. See Zhi Wei Pang v. Bureau of Citizenship & Immigr. Servs., 448 F.3d 102, 105-06 (2d Cir. 2006) (holding that when alien “challenges the accuracy of the contents of his I-589 application that was signed under penalty of perjury, the IJ must evaluate the petitioner’s explanations and determine whether the presumption of 8 C.F.R. §208.3(c)(2) has been rebutted”); Matter of Y-L-, 24 I. & N. Dec. at 157 (stating that frivolousness finding must be supported by preponderance of evidence). Indeed, this court has stated as much summarily. See Kanagaratnam v. Gonzales, 240 F. App’x 896, 898 (2d Cir. 2007) (citing Pang in stating that, when alien offers plausible explanation for lack of knowledge, “the IJ must evaluate this explanation and determine whether it rebuts the presumption, under 8 C.F.R. §1208.3(c)(2), that the applicant was aware of the contents of the application when it was filed”); see also Gui Cun Liu v. Ashcroft, 372 F.3d 529, 534 (3d Cir. 2004) (Alito, J.) (remanding petition in part because IJ “did not explain why…presumption had not been successfully rebutted by other evidence”); Matter of Valdez, 27 I. & N. Dec. at 499 (“When an alien challenges the accuracy of the contents of a signed application, the Immigration Judge must evaluate the alien’s explanations and consider the facts of the particular case to determine whether he or she has rebutted the presumption of knowledge of the document’s contents.”). Here, the Ud Dins admit signing their Form I-589 asylum applications. Thus, it was entirely appropriate for the IJ to presume that they were aware of and understood the Frivolousness Warnings contained therein. See 8 C.F.R. §1208.3(c)(2). Indeed, if the Ud Dins had not come forward with any evidence to rebut this presumption, the IJ would have been entitled to conclude that the brothers’ signatures established the requisite notice of the consequences of their knowingly false filings. See Niang v. Holder, 762 F.3d at 254-55. But, as we detailed in the Background section of this opinion, the Ud Dins did come forward with evidence that challenged the presumption of notice established by their signatures on their Form I-589 applications, specifically, their sworn affidavits and testimony maintaining that the forms had never been translated for them. In response, DHS offered an affirmation from attorney Sayyid, stating that he had “read the contents and the attachments” of the Ud Dins’ Form I-589 applications to the brothers in Urdu. Admin. R. 459. The IJ generally discredited the Ud Dins in favor of Sayyid. See id. at 71 (“The court will give weight to [Sayyid's] affidavit.”). As to notice, a concern arises because the record indicates that the IJ made this adverse credibility determination in the context of finding that the Ud Dins had knowingly filed false asylum applications. That finding is not at issue here.8 What cannot confidently be determined on the present record is whether the IJ’s adverse credibility determination also pertained to Sayyid’s reading the Form I-589s’ Frivolousness Warnings to the Ud Dins. An affirmative answer is not obvious because the knowing and material falsehoods stated in the forms are distinct from the warning given therein. Might Sayyid have read the former to the Ud Dins because it was information that he had added to the forms on the brothers’ behalf, but not have read the latter, which required no information to be supplied by the brothers or their attorney? We do not know. Sayyid was not available for examination at the brothers’ hearing. More to the point, we do not know how the IJ answered the question. Thus, we will not assume that the IJ’s adverse credibility finding, made in expressly determining knowing falsehood, was also intended to support an unexplained finding of notice, particularly where respondent here mistakenly maintains that it would have been permissible for the IJ to have construed Niang to hold the Ud Dins’ signatures on their asylum applications determinative of notice. See supra at 27; see also Mufied v. Mukasey, 508 F.3d 88, 91 (2d Cir. 2007) (declining to assume that IJ made findings “sub silentio merely because she considered evidence relevant to that question for another purpose”). That conclusion is reinforced by the severity of the consequences attending a frivolousness determination. See Limbeya v. Holder, 764 F.3d at 901 (stating that “clear explanation from agency is particularly important” when making frivolousness determination because of attending “serious consequences” (internal quotation marks omitted)); see also Yuanliang Liu v. DOJ, 455 F.3d at 117. Accordingly, we grant the Ud Dins’ petition for review only as it pertains to the notice requirement for frivolousness, and we remand the case to the agency for further proceedings limited to that issue. If the IJ, in his original ruling, in fact found the Form I-589 Frivolousness Warning to have been read to the Ud Dins in Urdu so that they did understand it and, on that basis, found the notice requirement for a frivolousness finding satisfied, he can clarify that on remand. On the other hand, if the IJ misread our decision in Niang to warrant finding notice based simply on the Ud Dins’ signatures on their Form I-589s, without need to consider the claim that they had not received translations of — and so did not understand — anything in those forms, then the IJ should reconsider the notice requirement consistent with this opinion and, based on his finding, determine whether the Ud Dins, upon removal, are permanently barred from reentering the United States. See, e.g., Mufied v. Mukasey, 508 F.3d at 91-92 (stating that remand to agency generally warranted for additional factfinding). CONCLUSION To summarize, we conclude as follows, (1) The agency’s finding that the Ud Dins were ineligible for adjustment of status did not deprive it of the authority alternatively to deny the Ud Dins adjustment of status as a matter of discretion. (2) The Ud Dins’ challenge to the agency’s frivolousness finding is not moot because a determination that they are ineligible for adjustment of status on that basis triggers a stricter reentry bar following removal than if adjustment is denied as a matter of discretion. (3) The agency may make a frivolousness finding as to an untimely filed asylum application. (4) An alien’s signature on an asylum application gives rise to a rebuttable presumption that the notice requirement for frivolousness has been satisfied. Accordingly, (1) We DENY the Ud Dins’ petition for review of their removal orders insofar as they challenge the agency’s (a) discretionary decision to deny their applications for adjustment of status, and (b) frivolousness determination as to their untimely filed asylum applications. (2) We GRANT the Ud Dins’ petition for review of their removal orders insofar as they challenge the agency’s finding that they received the notice required to hold them ineligible for adjustment of status based on the filing of frivolous asylum applications. (3) We REMAND for the limited purpose of allowing the agency to make an express finding as to notice consistent with principles stated in this opinion and, based on that finding, to specify the scope of the reentry bar that will attend the Ud Dins’ removal.
