
659 F.3d 266 (2011)
John DOE, Petitioner,
v.
ATTORNEY GENERAL OF the UNITED STATES, Respondent.
No. 10-2272.
United States Court of Appeals, Third Circuit.
Argued July 12, 2011.
Filed: September 8, 2011.
*267 Justin Conlon (Argued), Law Offices of Justin Conlon, North Haven, CT, for Petitioner.
John M. McAdams, Jr., Jennifer P. Williams, Lindsay W. Zimliki (Argued), United States Department of Justice, Office of Immigration Litigation, Washington, DC, for Respondent.
Before: RENDELL, SMITH, and FISHER, Circuit Judges.

OPINION
SMITH, Circuit Judge.
Petitioner Igor Rodov has been admitted to the United States as a lawful permanent *268 resident, and he would like to remain here. The government wants to remove him from the country, citing his conviction for aiding and abetting a wire fraud scheme that cost its victims more than $120,000. The Board of Immigration Appeals sided with the government, and Rodov seeks review in this court.

I
Rodov (who identifies himself by name throughout his unsealed court filings, notwithstanding the desire for anonymity suggested by the case caption) was first admitted to the United States in 1998 as a refugee from Belarus, where he had been threatened by anti-Semitism. He became a lawful permanent resident in 2001. In 2007, he returned to the States from a trip abroad, only to discover that he was subject to an arrest warrant arising out of his association with a wire fraud scheme. The government released him into the country, but did not formally "admit" him. Rather, the Department of Homeland Security (DHS) purported to "parole" him into the country, pursuant to 8 U.S.C. § 1182(d)(5)(A), for the purpose of prosecuting him.
The investigation into Rodov's criminal activities eventually resulted in a plea agreement. Rodov waived his right to an indictment; a one-count information filed in the United States District Court for the District of Connecticut charged him with aiding and abetting wire fraud in violation of 18 U.S.C. §§ 2 and 1343. He pled guilty on February 29, 2008. The plea agreement (supplemented by an attached "Stipulation of Offense Conduct") set out the particulars of his crime: Between January and November of 2006, Rodov opened several bank accounts in his own name. A third party (identified only as "John Doe") then proceeded to deposit fraudulently obtained tax refunds in Rodov's accounts. Rodov admitted that he had reason to believe that the funds were of criminal origin, and that he had knowingly and intentionally aided and abetted the wire fraud. Both the information and the stipulation identify a single use of the interstate wires in furtherance of the scheme: On June 16, 2006, John Doe knowingly caused a $6,447 tax refund to be wired into Rodov's Bank of America account. The stipulation goes on to state that "the loss amount attributable to the defendant through his participation in the aforementioned scheme and artifice to defraud was more than $120,000, but less than $200,000." Following entry of Rodov's guilty plea, Judge Burns sentenced him to 12 months' incarceration and three years' supervised release, and ordered him to pay $208,214 in restitution.
DHS thereafter initiated removal proceedings. According to the government, Rodov is an alien seeking admission into the United States, and his conviction of a "crime involving moral turpitude" precludes such admission. See 8 U.S.C. § 1182(a)(2)(A)(i)(I). Rodov responded by asserting that he is not, in fact, an applicant for admission (but is, rather, a lawful permanent resident entitled to admission); that cancellation of his removal is warranted under 8 U.S.C. § 1229b; and that the Convention Against Torture (CAT) bars the government from forcing him to return to Belarus. The government replied that because Rodov has committed a crime involving moral turpitude, 8 U.S.C. § 1101(a)(13)(C)(v) directs that he be treated as an applicant for admission notwithstanding his permanent resident status; that his crime is an "aggravated felony" that renders him ineligible for § 1229b cancellation; and that Rodov cannot meet the requisites for relief under the CAT.
The immigration judge agreed with Rodov. The court first ruled that Rodov's *269 crime is not an aggravated felony, because the information and plea agreement refer only to a single transaction that caused a loss of less than $10,000. See 8 U.S.C. § 1101(a)(43)(M)(i). In a subsequent decision, the judge "note[d]" that Rodov was an arriving alien and concluded that he was removable on account of his conviction. The court nevertheless cancelled Rodov's removal, pursuant to § 1229b(a), after concluding that the balance of various factors weighed in his favor. The court then, "[a]s an aside," stated that if it had needed to reach Rodov's arguments for asylum and relief under the CAT, it would have rejected them.
The Board of Immigration Appeals reversed. It held that the assessment of whether Rodov's felony was aggravated depends not on the single $6,447 transfer but instead on the stipulated total loss of more than $120,000. From this it followed that Rodov had in fact committed an aggravated felony, and thus that his removal could not be cancelled under § 1229b. The Board then stated that Rodov was not eligible for asylum, and concluded that he had not identified any error in the immigration judge's evaluation of his CAT arguments. The BIA thus denied Rodov's alternative grounds for relief and declined to remand the case for further consideration.
Rodov petitioned for our review.

II

A
Upon Rodov's arrival at the border in 2007, DHS purported to parole him for prosecution. The parole statute, 8 U.S.C. § 1182(d)(5)(A), reads (emphasis added):
The Attorney General may, except as provided in subparagraph (B) or in section 1184(f) of this title, in his discretion parole into the United States temporarily under such conditions as he may prescribe only on a case-by-case basis for urgent humanitarian reasons or significant public benefit any alien applying for admission to the United States, but such parole of such alien shall not be regarded as an admission of the alien and when the purposes of such parole shall, in the opinion of the Attorney General, have been served the alien shall forthwith return or be returned to the custody from which he was paroled and thereafter his case shall continue to be dealt with in the same manner as that of any other applicant for admission to the United States.
By its plain terms, this enactment grants the Attorney General the authority to parole only an "alien applying for admission to the United States." At the time he sought entry, however, Rodov had already been admitted to the country as a lawful permanent resident. As such, he was presumptively not to be treated as an "alien applying for admission" (meaning that the Attorney General presumptively lacked the statutory authority to parole him), because 8 U.S.C. § 1101(a)(13)(C) provides that "[a]n alien lawfully admitted for permanent residence in the United States shall not be regarded as seeking an admission into the United States for purposes of the immigration laws unless" one of several conditions is met.[1] (We treat as synonymous *270 "alien applying for admission," "alien... seeking an admission," and similar terms.)
Of those conditions, only the fifth is potentially applicable. With exceptions not relevant here, it allows the government to regard a lawful permanent resident as an "alien ... seeking an admission" if he "has committed an offense identified in [8 U.S.C. §] 1182(a)(2)."[2] 8 U.S.C. § 1101(a)(13)(C)(v). Whether or not Rodov could be paroled thus depended on whether he had "committed" an enumerated crime at the time the government sought to parole him. The government must have made its decision on this question at the border, for due process would have prohibited it from stripping a lawful permanent resident of his protected status at that time and only determining that its action was legally permitted at some later date. DHS's representatives were therefore required to determine whether or not there was adequate evidence that Rodov had "committed" his crime when he arrived at his point of entry, well before he had been convicted, or even formally charged.
Rodov argues that DHS cannot have made such a determination without a record of a conviction. Because there was no such record, he says, DHS cannot have validly regarded him as an applicant for admission, and was instead required to admit him into the country without strings attached. The problem with this argument is that subsection (v) does not say "convicted." The choice of the word "committed," rather than "convicted," is significant.[3] Had Congress wished to require a conviction (a term it took some care to define, see 8 U.S.C. § 1101(a)(48)), it would have said so. Note, for instance, that 8 U.S.C. § 1182(a)(2)(A)(i) acknowledges the distinctions between an alien who has been "convicted of" an offense, one "who admits having committed" an offense, and one "who admits committing acts which constitute the essential elements of" an offense. Section 1182(a)(2)(A)(i) also demonstrates that Congress could have chosen a broad but precise phrase like "any alien convicted of, or who admits having committed, or *271 who admits committing acts which constitute the essential elements of," if it had wished to do so. It instead selected "committed," a distinct term in need of construction.
It seems likely that Congress had in mind situations akin to that which is now before the court when it wrote the statute. A permanent resident who has been convicted of one of the enumerated crimes has probably already lost his "lawful" status as a consequence (the criminal grounds for inadmissibility listed in § 1182(a)(2) parallel the criminal grounds for deportability under § 1227(a)(2)(A)), so a statute permitting the state to regard him accordingly would be redundant. In addition, subsection (iii)covering aliens who have "engaged in illegal activity after having departed the United States"parallels subsection (v) and clearly does not require a conviction. The choice of "committed" is of a piece with the choice of "engaged in." Seen in this light, the statute's text indicates that the government is not required to show a conviction.
The question then becomes: What sort of showing must be made before the government may conclude, for purposes of a parole determination, that an alien has "committed" a crime, and, accordingly, regard him as an applicant for admission? The word "committed" does not contain or imply a burden of proof: "to commit" means only "to perpetrate"; a "commission" is "the act of doing or perpetrating." Black's Law Dictionary (9th ed.2009). The word describes only historical events, and does not say anything about what evidence exists or what a third party knows.
The balance of the statute does not specify either who bears the burden of proof, or how heavy that burden is. The Immigration and Nationality Act contains a section concerning burdens of proof at removal proceedings, 8 U.S.C. § 1229a(c), but it is not helpful. Subsection (c)(2)(B) provides that an alien claiming lawful permanent resident status has the burden of proving, "by clear and convincing evidence, that [he] is lawfully present in the United States pursuant to a prior admission," but there is no dispute that Rodov fit that description at the time he attempted to reenter the country. Subsection (c)(2)(A) provides that an applicant must establish, "clearly and beyond doubt," that he is entitled to admission, but this does not apply to the predicate question of whether the alien is an applicant. While we suppose that it could be argued that one of these subsections should apply here, absent an explicit textual basis we will not require a person to prove that he has not committed an offense in order to ensure that he is treated in a manner consistent with his lawful permanent resident statusparticularly since the preamble to § 1101(a)(13)(C) indicates that a permanent resident is presumptively to be regarded as such.
Another subpart of the burden-of-proof statute, § 1229a(c)(3)(A), directs that "the Service has the burden of establishing by clear and convincing evidence that, in the case of an alien who has been admitted to the United States, the alien is deportable." This section too is not by its text applicable here: the question is not whether Rodov is deportable, but whether he should have been treated as an "alien who has been admitted to the United States" when he sought to enter the country. Subsection (c)(3)(B) lists several documents that the government may use to prove that an alien has been convicted of a crime, but as explained above we do not think that the statute requires that a conviction be proved.
There is a hole in the Immigration and Nationality Act: it requires an immigration officer to determine whether an *272 arriving lawful permanent resident has committed a crime, but omits mention of how the officer is to do so. Obviously, some burden of proof must be met, and we think it necessary to prescribe one as a matter of federal common law. "A federal court has the power `to declare, as a matter of common law or "judicial legislation," rules which may be necessary to fill in interstitially or otherwise effectuate the statutory patterns enacted in the large by Congress.'" Cunningham v. R.R. Ret. Bd., 392 F.3d 567, 575 (3d Cir.2004) (quoting United States v. Little Lake Misere Land Co., 412 U.S. 580, 593, 93 S.Ct. 2389, 37 L.Ed.2d 187 (1973)). To our knowledge, no other federal court of appeals has addressed this question, so we are left to infer the correct rule from the statute's purposes, understood in light of general legal principles. One such principle, suggested above, is that a party is not ordinarily required to prove a negative: we do not think that an alien should have to present evidence that he has not committed a crime in order to avert adverse government action. The burden thus must be on the government. But how heavy is it? Here we are informed by the legislatively and administratively prescribed procedure. The initial decision whether to treat a permanent resident as an alien seeking admission is made by an immigration officer working at the alien's point of arrival in the country. See 8 C.F.R. § 1235.3(b)(5)(ii). There is no hearing, and no neutral arbiter who can be entrusted to assess whether the available evidence is sufficient to satisfy a "preponderance" or "clear and convincing" standard. An elevated standard would also invite a comparison of the government's evidence against that proffered by the alien-defendant; but a person who has not been charged, and who may not even be aware that he is the subject of a criminal investigation, will not have had the opportunity to retain counsel or develop a defense. And one of the purposes of the provision allowing an arriving permanent resident to be treated as an applicant for admission appears to have been to permit the government to invoke procedures like § 1182(d)(5) paroleincluding parole for purposes of prosecution. Requiring that the government develop evidence sufficient to win its case before it can take the step of paroling a person for prosecution would make little sense.
At the same time, revoking a person's lawful-resident status entails restraints on the rights and privileges that he had previously enjoyed. General due process principles therefore counsel that something more than an immigration officer's say-so must be required. With that in mind, we think the proper standard to employ here is probable cause to believe that the alien has committed one of the crimes identified in 8 U.S.C. § 1182(a)(2). Ordinary procedures, familiar to anyone with a passing knowledge of criminal law and procedure, should be followed in determining whether probable cause exists: Where a warrant has issued for the alien's arrest on suspicion of the commission of one of the enumerated crimes, probable cause will be presumed. Where such a warrant has not issued, treatment of the arriving alien as an applicant for admission rather than as a permanent resident will be contingent on a judge's (or a magistrate's) assessment of the proffered basis for believing probable cause to exist. And, of course, if it becomes apparent at some later point that probable cause no longer exists, the government may no longer "regard[]" the lawful permanent resident as an applicant for admission. Cf., e.g., Cannon v. Macon Cnty., 1 F.3d 1558, 1563 (11th Cir.1993) (holding that a detainee has a constitutional right to be released from confinement "after it was or should have *273 been known that [he] was entitled to release").
It follows from this holding that, at the time Rodov sought re-entry into the United States, the government possessed sufficient evidence to establish that he had "committed" the crime of aiding and abetting wire fraud for purposes of § 1182(a)(13)(C)(v). There was by that time an outstanding warrant for Rodov's arrest, and he has never challenged its validitythus implicitly conceding that probable cause existed.[4] Accordingly, DHS was permitted to regard him as an applicant for admission, to parole him for purposes of prosecution, and to seek his removal as an inadmissible alien (rather than as a deportable permanent resident).
Although we have reached the result sought by the government, we believe it necessary to consider the position that the Attorney General has advanced in his briefing and at oral argument. According to the government, there is no need for us to concern ourselves with the burden-of-proof question, because DHS was permitted to parole Rodov into the country for prosecution irrespective of whether he is an alien seeking admission or a lawful permanent resident. And because the decision to parole an alien is, according to the Attorney General, committed to his essentially unreviewable discretion, we lack jurisdiction to review his decision. If this were true, counsel's infelicitous description of parole as a legal "black hole" from which there is no prospect of escape except through an act of executive grace would be fairly accuratethough it might also be subject to serious due process challenge. But for reasons suggested above, the government's position is quite obviously contrary to the plain language of the statutes that are in play here. Section 1182(d)(5)(A) grants discretion to order parole only of "alien[s] applying for admission to the United States," and § 1101(a)(13)(C) provides that a lawful permanent resident "shall not be regarded as seeking an admission" unless one of several conditions (including commission of a designated offense) is met. The Attorney General is not empowered to finally decide whether any of those six prerequisites is satisfied. Whether one of them has been established is a legal question subject to our review in the same manner as other analogous determinationsfor instance, if Rodov had contested the issue, we would have assessed the probable cause question just as though this were a criminal appeal. Because the statutes do not grant the Attorney General discretion regarding parole unless and until one of the conditions enumerated in § 1101(a)(13)(C) is satisfied, his claim that we are without jurisdiction to review this predicate issue rings hollow.
*274 The government cites two BIA decisions, In re Badalamenti, 19 I. & N. Dec. 623, 626 (B.I.A.1988), and In re Accardi, 14 I. & N. Dec. 367, 368-69 (B.I.A.1973), for the proposition that parole is not limited to applicants for admission. Although the BIA's interpretation of a statute within its enforcement jurisdiction is entitled to Chevron deference, see En Hui Huang v. Att'y Gen., 620 F.3d 372, 379 (3d Cir.2010), that rule of interpretation does not apply unless the statute is ambiguous. Roth v. Norfalco LLC, 651 F.3d 367 (3d Cir.2011) (citing Chevron U.S.A., Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 844, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984)). Whatever the merits of the BIA's interpretation as regards Messrs. Badalamenti and Accardi (neither was a citizen or lawful permanent resident; both had been brought to the country involuntarily for the specific purpose of prosecution), it unambiguously does not have any application to a person in Rodov's position, whose rights as a permanent resident had vested subject only to a limited set of conditions. The Attorney General's effort to dodge the burden-of-proof issue is thus futile, and counsel's conspicuous decision not to address it (despite the fact that Rodov raised it in his opening brief, at 43-46) has left us with access to only one side of the argument. Suffice it to say that the government has not been helpful.

B
Rodov next argues that the government should be equitably estopped from treating him as an arriving alien, even if the statutes permit it. Although labeled "estoppel," this claim is really in the nature of a due process complaint. See Rodov Br. 54 ("The petitioner submits that [the equitable estoppel] requirements should not be applied in the case at bar because the nature of his due process/equitable estoppel claim does not relate to an affirmative misrepresentation made by the Government, as is often done, but instead relates to procedural manipulation by the Government to make removal of the petitioner easier."). In support, Rodov cites Doggett v. United States, 505 U.S. 647, 656, 112 S.Ct. 2686, 120 L.Ed.2d 520 (1992), and United States v. Marion, 404 U.S. 307, 324, 92 S.Ct. 455, 30 L.Ed.2d 468 (1971), for the notion that the government cannot manipulate procedure to gain a tactical advantage in litigation. In both of those cases, the government conceded that intentional, bad-faith, and prejudicial delays in moving forward with a prosecution would implicate constitutional guarantees. Neither case is directly applicable here (Rodov's argument concerns not delays but the statutorily-authorized decision to treat him as an applicant for admission), and Rodov has not presented a compelling case for the fairly extravagant interpretation of their holdings that he wishes us to adopt. At least in the absence of an argument more substantial than those with which we are today presented, we cannot conclude that the Attorney General's invocation of statutorily-authorized procedural devices violates the Due Process Clause.

III
Having concluded that Rodov was properly regarded as an applicant for admission, we now turn to the merits of the BIA's order that he be removed from the country as an inadmissible alien. The primary question here is whether the crime to which Rodov pled guilty is an "aggravated felony" for purposes of the immigration laws. If so, Rodov is ineligible to have his removal cancelled, and the BIA's reversal of the immigration judge's cancellation order must be affirmed. Because Rodov's offense (aiding and abetting wire fraud) clearly "involves fraud or deceit," it qualifies as an "aggravated felony" if "the *275 loss to the victim or victims exceeds $10,000." 8 U.S.C. § 1101(a)(43)(M)(i).
The usual approach to deciding whether a crime is an aggravated felony is to look only at the elements and nature of the offense in question, without considering the particular facts underlying the conviction. See Leocal v. Ashcroft, 543 U.S. 1, 7, 125 S.Ct. 377, 160 L.Ed.2d 271 (2004). But "where, as here, `a statute criminalizes different kinds of conduct, some of which would constitute [aggravated felonies] while others would not, the court must apply a modified categorical approach by which a court may look beyond the statutory elements to determine'" whether the alien was actually convicted of an aggravated felony. Restrepo v. Att'y Gen., 617 F.3d 787, 791 (3d Cir.2010) (quoting United States v. Stinson, 592 F.3d 460, 462 (3d Cir.2010)) (alteration in original); Nijhawan v. Holder, ___ U.S. ___, 129 S.Ct. 2294, 2302, 174 L.Ed.2d 22 (2009). The wire fraud statute, 18 U.S.C. § 1343, makes no distinctions on the basis of the amount of loss, so we must look to the specific facts of this case to determine whether the relevant loss amount exceeds the $10,000 threshold. Rodov argues that his crime does not clear this bar, because the plea agreement specifically identifies as the basis for his conviction only a single specific transaction in the amount of $6,447. The government responds by pointing out that the plea agreement stipulated that Rodov was personally responsible for causing a loss of more than $120,000.
We agree in principle with Rodov's assertion that a court assessing whether a felony is aggravated must limit itself to consideration of "the loss `tethered' to the alien's specific offense of conviction." Rodov Br. 29-30 (citing Alaka v. Att'y Gen., 456 F.3d 88, 105-07 (3d Cir.2006); Nijhawan, 129 S.Ct. at 2303). Indeed, that rule is dictated by Alaka, a case in which the petitioning alien had pled guilty to one of three counts of aiding and abetting bank fraud. Although the overall scheme caused a total of $47,969 in losses, the guilty plea identified just a single act with respect to which the loss was only $4,716.68. See 456 F.3d at 92, 107. Focusing on the particular contents of the plea agreement (rather than the indictment or the sentence), we held that "it was legal error for the IJ to consider the amount of intended loss for all of the charges rather than the single count for which she was convicted." Id. at 106.
We then noted the possible existence of an "exception to the strict emphasis on the plea agreement," id. at 108, arising out of the Tenth Circuit's opinion in Khalayleh v. INS, 287 F.3d 978 (10th Cir.2002). That case involved a resident alien who had pled guilty to one count of a four-count indictment alleging the use of four insufficient-funds checks to defraud a bank. The specific count to which he pled guilty involved a check in the amount of $9,308, but the total actual loss resulting from the four checks exceeded $24,000. The Tenth Circuit acknowledged that if each of the counts had been a distinct crime, the petitioner would have been able to argue that only the one giving rise to the guilty plea was relevant to the determination of whether his felony was aggravated. Id. at 980. The court concluded, however, that:
Count Two of the indictment did not allege a discrete fraud involving only the $9,308 check. It alleged a scheme to defraud that encompassed a number of checks.... The "offense" of conviction was the entire scheme charged in Count Two of the indictment. Hence, the "loss" to be measured is the loss resulting from that scheme.
Id. Because it was the overall scheme that mattered, and not the individual check, the *276 court counted the entire $24,000 loss amount and concluded that the crime in question was an aggravated felony. Id.
While the Alaka panel described the Tenth Circuit's approach, we did not express an opinion on its merits. We did not address the question whether Alaka's crimes were all part of a common scheme, though we did state that our holding was "not affected by the District Court's conclusion, for sentencing purposes, that Alaka's conduct as to the dismissed charges was `part of a common scheme or plan as the offense of conviction.'" 456 F.3d at 108.
This case does not require us to consider whether Khalayleh's approach is the law of this circuit. Rodov did not plead guilty to a single discrete act of accepting a $6,447 transfer. He admitted to aiding and abetting the entire scheme. In the section of his plea agreement discussing the nature and elements of his offense, Rodov admitted to knowingly and intentionally aiding and abetting a plan to obtain money via fraudulent pretenses, using the interstate wires. That section makes no mention of any specific transaction: it refers to the entire scheme as the underlying crime which Rodov admitted to aiding and abetting. Furthermore, the "Stipulation of Offense Conduct" specifies that Rodov aided and abetted the fraud by "opening several bank accounts in his personal name with local banking institutions," into which John Doe caused a number of fraudulent tax refunds to be deposited. And, of course, the stipulation also indicates that Rodov's conduct caused between $120,000 and $200,000 in losses. Taking these terms of the plea agreement together, it is plain that Rodov was convicted of aiding and abetting the entire fraudulent scheme. His admitted participation was not limited to one $6,447 deposit; that transaction appears to the court to have been included in the plea agreement to establish the "use of the interstate wires" element of the underlying offense. Because Rodov pled guilty not to a single fraudulent transaction but to aiding and abetting the whole of a large-scale criminal endeavor, there is no need to decide whether conduct outside the specific offense of conviction can be pertinent to the aggravated felony determination. Rodov was in fact convicted of committing all of the relevant conduct. The BIA's conclusion that his crime constituted an aggravated felony was correct.

IV
Rodov's final argument to the immigration judge was that he is entitled to asylum, withholding of removal, and protection under the Convention Against Torture. Because the immigration judge (erroneously, as it turns out) granted his request for cancellation of removal on other grounds, there was no need for him to address the CAT questions. The court nevertheless stated "as an aside" that, "if it were to consider the respondent's application for asylum it would deny that application," as well as the request for withholding of removal under the CAT. The BIA correctly reversed the immigration judge's cancellation of Rodov's removal on the basis of his conviction of an aggravated felony, and then went on to reject his contentions under the CAT. On appeal to this court, Rodov argues that the BIA should have remanded his case to the immigration judge for a decision on his CAT arguments.
Given the immigration judge's prior statements, Rodov's CAT requests are likely to go unfulfilled. However, we must conclude that proper procedure requires us to remand the case to the immigration judge. The BIA's jurisdiction is limited to *277 "[d]ecisions," see 8 C.F.R. § 1003.1(b), and the immigration judge explicitly did not decide the CAT questions, see App. 162, 339-40. Thus the BIA lacked jurisdiction to address Rodov's CAT arguments, and the case must be remanded so that the immigration judge can address them in the first instance.

V
For the reasons set forth above, we will deny the petition for review in part, affirming the BIA's decision in all respects except with regard to Rodov's CAT claims. We will grant the petition with respect to the BIA's statements concerning the CAT, vacating those statements insofar as they constitute an order. We will remand the case to the immigration court for the limited purpose of deciding the CAT questions.
RENDELL, Circuit Judgeconcurring in part and dissenting in part.

I.
I agree with the majority's rulings on most of the issues in this appeal, including its decision to affirm the BIA's denial of Rodov's application for asylum and withholding of removal, and to remand the case to the immigration judge to decide whether Rodov is entitled to protection under the Convention Against Torture. In particular, I agree with the majority's analysis of the statutory provisions governing the timing of the immigration officials' determination of whether a returning lawful permanent resident ("LPR") has "committed" an offense. However, I cannot agree with the majority's view as to what that determination should be based on. The majority concludes that, for the purposes of 8 U.S.C. § 1101(a)(13)(C)(v), the mere existence of an arrest warrant was sufficient to establish that Rodov had "committed" the relevant offense. In so concluding, the majority disregards the true meaning of the term, "committed," and improperly lowers the bar regarding the evidence needed for officials at the point of entry to find that Rodov "committed" a crime.[1] This is a significant issue of first impression and an important one for returning LPRs. While probable cause for an arrest warrant may be sufficient to show the likelihood of commission, it does not provide any proof whatsoever that the alien has indeed committed an offense. I think that more is required to establish commission under 8 U.S.C. § 1101(a)(13)(C)(v) than probable cause to believe an alien has committed an offense. Therefore, I respectfully dissent in part from the majority's opinion.
Given this, I would reason through the analysis as follows. First, it was improper for the Government to regard Rodov as an applicant for admission at the time he sought reentry because, at that point, there was no evidence whatsoeverand no admission by Rodovthat he had "committed" an offense listed in § 1182(a)(2). Thus, under § 1101(a)(13)(C), Rodov, an "alien lawfully admitted for permanent residence," should not have been regarded as an "applicant for admission" when he reentered the United States in 2007, and should not have been paroled. If Rodov was not seeking admission, then, under 8 U.S.C. § 1227, he should have been permitted to enter as an LPR.
In order to remove him from the country, the Government would have to show that he was deportable for a reason other than "inadmissib[ility] at the time of entry *278 or of adjustment of status." 8 U.S.C. § 1227(a)(1). After Rodov was convicted of aiding and abetting wire fraud in January 2009, the DHS could have issued a Notice to Appear ("NTA") charging him as an LPR who was deportable under INA § 237(a)(2)(A)(iii), 8 U.S.C. § 1227(a)(2)(A)(iii), which provides that "[a]ny alien convicted of an aggravated felony at any time after admission is deportable." The DHS did properly find that, because Rodov's crime constituted an aggravated felony under 8 U.S.C. § 1101(a)(43)(M)(i), he was not statutorily eligible for cancellation of removal. Accordingly, were DHS to bring deportation proceedings against him, it would most likely determine him to be deportable. However, he cannot be excluded as inadmissible.
For the reasons set forth below, however, I disagree with respect to the majority's holding as to the threshold issue it addresses, namely, whether officials at the point of entry had a sufficient basis for concluding that he had committed an offense under 8 U.S.C. § 1101(a)(13)(C)(v). I suggest that they did not.

II.
As the majority explains, 8 U.S.C. § 1101(a)(13)(C)(v) states that a returning LPR who has "committed" a crime identified in § 1182(a)(2), including a crime involving moral turpitude, should be considered an applicant for admission and thus subject to the various grounds of inadmissibility included in 8 U.S.C. § 1182. Under the majority's reading, the determination that a returning LPR has "committed" a crime of moral turpitude can be based on the entry officials' knowledge that there is an outstanding arrest warrant charging him with such a crime. Because of the lack of existing caselaw on this issue, the majority establishes this as a "matter of federal common law." (Maj. Op. 272). See Cunningham v. R.R. Ret. Bd., 392 F.3d 567, 575 (3d Cir.2004) ("A federal court has the power to declare, as a matter of common law or judicial legislation, rules which may be necessary to fill in interstitially or otherwise effectuate the statutory patterns enacted in large by Congress.") (internal citation and quotation marks omitted) (quoted in Maj. Op. 272). In sua sponte setting forth a rule as to the sufficiency of the evidence for a finding that someone has "committed" a crime under subsection (v), the majority does little more than ruminate on what standard it thinks is the most fair. As the majority itself acknowledges, its reading of subsection (v) assigns the immigration officer stationed at an LPR's point of arrival responsibility for determining whether the alien should be stripped of his LPR status and treated as an applicant for admission, or should be admitted and processed as an LPR.[2] The lack of due process in such a system,[3] the majority asserts, calls for a lower burden of proof in determining whether an LPR has "committed" a crime. Not too low, however, because "[g]eneral due process principles ... counsel that something more than an immigration officer's say-so *279 must be required." (Maj. Op. 272). Striking a compromise between two extremesa conviction requirement, on the one hand, and an immigration officer's independent assessment, on the otherthe majority settles on probable cause as the appropriate standard.[4]
Neither the majority, nor the BIA in the opinion from which Rodov has appealed, offers support for the conclusion that the existence of an arrest warrant, presumably based on probable cause, is sufficient to establish "commission" of a crime for the purposes of subsection (v). While the majority is correct that other Courts of Appeals have not addressed this exact question, I do not think that the absence of precise authority on the question merits our formulation of a new, substantive rule of federal common law. See Carley v. Wheeled Coach, 991 F.2d 1117, 1128-29 (3d Cir.1993) (noting the "well-established principle that rules of federal common law should be narrowly drawn and imposed only in rare circumstances where there is a `significant conflict' between a federal interest and the application of state law"); Texas Indus., Inc. v. Radcliff Materials, Inc., 451 U.S. 630, 641, 101 S.Ct. 2061, 68 L.Ed.2d 500 (1981) ("Absent some congressional authorization to formulate substantive rules of decision, federal common law exists only in such narrow areas as those concerned with the rights and obligations of the United States, interstate and international disputes implicating the conflicting rights of States or our relations with foreign nations, and admiralty cases.").
Not only is the promulgation of such a rule uncalled for, it is actually in conflict with relevant authority as to what is necessary to prove "commission" of an offense. Existing caselaw supports the view that more than just probable cause is needed to find that an alien or LPR has "committed" an offense. See De Vega v. Gonzales, 503 F.3d 45, 47 (1st Cir.2007) ("The relevant category for this case covers LPRs who have `committed an offense identified in section 1182(a)(2),' meaning those LPRs who have been convicted of, `or who admit[] having committed, or who admit[] committing acts which constitute the essential elements of,' a crime involving moral turpitude.") (internal citations omitted).[5]
*280 The majority correctly draws attention to the choice of the word "committed," instead of "convicted," in subsection (v); clearly, "commission" of an offense includes a broader category of acts than only "conviction." However, as De Vega suggests, it is reasonable to read § 1101(a)(13)(C)(v)'s language"committed an offense identified in section 1182(a)(2)"as encompassing the behavior specifically identified in § 1182(a)(2)(A)(i)(I): conviction of, admission of committing, or admission of committing essential elements of, a crime involving moral turpitude. See De Vega, 503 F.3d at 47. It makes sense to use "committed" rather than "convicted" in order to include offenses for which aliens have not been convicted, but which they have admitted to committing.
The use, and interpretation in the caselaw, of the word "committed" in sentencing statutes also supports this reading. When sentencing statutes use the word "committed," we are to consider not only the elements of the offense but also underlying facts and conduct to see if they establish, by a preponderance of the evidence, that defendant committed an offense, even if he was not convicted for that offense. In United States v. Mi Kyung Byun, 539 F.3d 982 (9th Cir.2008), for example, the court was called on to interpret 18 U.S.C. § 2423, which criminalizes transportation of minors with intent to engage in criminal sexual activity, focusing on the phrase, "when committed against a minor." Id. at 985 (quoting 18 U.S.C. § 2423) (emphasis added). The Ninth Circuit explained that the "use of the word `committed,' rather than `convicted' persuasively indicates that, in determining whether the victim of Byun's crime was a minor, we may consider not only the elements of the crime of which Byun was convicted but her actual conduct." Id. at 991. See also Taylor v. United States, 495 U.S. 575, 600, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990) (noting that the use of "convicted" instead of "committed" in 18 U.S.C. § 924, which provides a sentencing enhancement for a defendant convicted of unlawful possession who has three prior convictions for violent felonies, indicates that Congress intended the sentencing court to look to the crimes for which defendant was convicted, "not to the facts underlying the prior convictions.").
In United States v. Charlesworth, 217 F.3d 1155, 1159-60 (9th Cir.2000), the Ninth Circuit addressed the question of whether a sentencing judge properly denied the four-level reduction in U.S.S.G. § 2P1.1, which provides penalties for escape and instigating or assisting escape from a prison, based on evidence that a defendant "committed" a felony. The Ninth Circuit, noting that the term "committed" should be given its plain meaning, explained that the "use of the word `committed'... suggests that neither a conviction for a felony nor even an indictment is required." Id. at 1159. Rather, the court noted that proof of "uncharged facts or conduct" that have been established by a preponderance of the evidence "is sufficient to establish that the defendant committed a felony in order to preclude the reduction of the sentence under § 2P1.1(b)(3)." Id. See also United States v. Strachan, 968 F.2d 1161, 1162-63 (11th Cir.1992) (noting that, because the sentencing guidelines do not define "committed," it must be given its ordinary meaning, *281 and holding that a district court can deny the reduction under § 2P1.1(b)(3) "if a preponderance of the evidence demonstrates that the defendant committed a disqualifying offense, even if there has been no formal conviction."); United States v. Durham, 178 F.3d 796, 799 (6th Cir.1999) (assuming, without directly addressing the question, that § 2P1.1(b)(3) requires neither a conviction nor an indictment in order to preclude application of the reduction).
While, in interpreting "committed" in the immigration statute, we do not have the same preponderance standard in place, the treatment of the word "committed" in the sentencing context is still instructive. It suggests that, if we give the word "committed" its plain meaning,[6] it describes facts or conduct. Perhaps those facts need not be established by a preponderance of evidence in all statutory contexts, but, at the time a person can be regarded as having "committed" a crime, there must be some evidence that the crime has taken place. The majority equates the type of proof to "historical events." (Maj. Op. 271). I agree. Yet, probable cause for an arrest does not constitute proof of historical events or the fact of commission.[7]
Even assuming it is appropriate to fashion federal common law here, I am still skeptical of the majority's analysis. To begin with, the definition of "probable cause" itself casts doubt on the majority's interpretation. Probable cause to arrest is present "when the facts and circumstances within the arresting officer's knowledge [at the time of the arrest] are sufficient in themselves to warrant a reasonable person to believe that an offense has been or is being committed by the person to be arrested." Merkle v. Upper Dublin Sch. Dist., 211 F.3d 782, 788, 789 (3d Cir.2000) (citation omitted) (internal quotation marks omitted). Probable cause to arrest establishes that an officer believes that an offense has been committed; it is not proof that that the offense has actually been committed. Importantly, the statute does not state that the determination is whether the LPR "may have" committed or even "probably" committed the offense. The required finding is that he did commit the offense. The existence of probable cause (assuming the warrant was so supported) is not proof that the crime was actually committed.[8]
In addition, it seems antithetical to the "general due process principles" cited by the majority itself that a determination of an alien's or LPR's status using a lowered burden of proof for commission occurs without any legal process whatsoever. As noted above, even the majority acknowledges the absence of process and counsel, and the significance of the restraints resulting from the determination. If the absence of the availability of process at the point of entry means anything at all, it means that more definitive proofevidence as to commission, admission, *282 or convictionis required for an immigration official to conclude that someone has "committed" a crime. The majority misunderstands what a heightened standardone requiring, for example, conviction or admissionwould mean in practice. It would not necessitate "a comparison," presumably conducted by the immigration official at the point of entry, "of the government's evidence against that proffered by the alien-defendant." (Maj. Op. 272). To the contrary, the immigration official could only deem an LPR to be "seeking admission," and thus subject to being paroled when he has some evidence that the LPR actually committed a listed offense.
Here, there were no statements by the petitioner, nor any facts known to the airport official that could be considered evidence that the petitioner had committed the crime charged. Surely, the mere presence of an arrest warrant is not enough.

III.
Ultimately, as noted above, I would reach the same result as the majority herethat Rodov cannot remain in the country unless he can prove his CAT claimbut I would reach this result on the basis that he is deportable under 8 U.S.C. § 1227(a)(2)(A)(iii) because he was convicted of committing an aggravated felony. I disagree with the majority's conclusion that he was an applicant for admission upon reentry to the U.S. who was later deemed inadmissible when he was convicted of a crime of moral turpitude, because probable cause to believe he committed a crime of moral turpitude does not provide sufficient proof of "commission" so as to fulfill 8 U.S.C. § 1101(a)(13)(C)(v) and strip him of his LPR status.
NOTES
[1]  In the instant proceeding, DHS seeks Rodov's removal because he is inadmissible another action that the government is not ordinarily empowered to take against a lawfully admitted permanent resident. See Toro-Romero v. Ashcroft, 382 F.3d 930, 936 (9th Cir.2004) (noting the distinction between aliens who are inadmissible under 8 U.S.C. § 1182, and those who are admitted but deportable pursuant to 8 U.S.C. § 1227). Thus the entirety of this proceeding is premised on the notion that Rodov has been an "alien applying for admission" since his last, fateful attempt to enter the country.

Our dissenting colleague agrees that we should deny the petition seeking cancellation of removal, but we do not fully understand her reasoning. Assuming arguendo that she is correct and that the immigration official at the border possessed insufficient evidence to conclude that Rodov had "committed" his offense at the time he sought reentry, then he should have been freely admitted rather than paroled. To remove him after his conviction, DHS would have been required to initiate deportation proceedings, which it has not done. All we have is an inadmissibility proceeding, which is invalid in toto if Rodov is an admitted lawful permanent resident. Thus if she is correct about the construction of the word "committed," we think our colleague ought to argue that the entire removal proceeding should be declared voidat which point DHS could immediately seek Rodov's deportation in a separate removal action.
[2]  There can be no dispute that the crime for which Rodov was under investigation (and of which he was later convicted) is one of those identified in § 1182(a)(2). That section specifies, inter alia, "crimes involving moral turpitude" as one of several criminal grounds for a declaration of inadmissibility, and fraud is universally recognized as being such a crime. See, e.g., Jordan v. De George, 341 U.S. 223, 232, 71 S.Ct. 703, 95 L.Ed. 886 (1951) ("Whatever else the phrase `crime involving moral turpitude' may mean in peripheral cases, the decided cases make it plain that crimes in which fraud was an ingredient have always been regarded as involving moral turpitude."); Ghani v. Holder, 557 F.3d 836, 840 (7th Cir.2009).
[3]  The legislative history does not explain the choice. See S.Rep. No. 82-1137, at 4 (1952).
[4]  Contra our colleague's suggestion, an unchallenged and presumptively valid arrest warrant certainly does imply the existence of "some evidence that the crime has taken place." Post, at 281 (emphasis removed). A warrant issues only when a "neutral and detached magistrate" is satisfied that probable cause exists, Johnson v. United States, 333 U.S. 10, 14, 68 S.Ct. 367, 92 L.Ed. 436 (1948), which means that he has been shown evidence "sufficient to warrant a prudent man in believing that the petitioner had committed or was committing an offense." Beck v. Ohio, 379 U.S. 89, 91, 85 S.Ct. 223, 13 L.Ed.2d 142 (1964). See also, e.g., Schneyder v. Smith, 653 F.3d 313, 323 (3d Cir.2011) ("For probable cause to exist, the evidence available must provide police or the warrant-issuing magistrate with reasonable grounds to believe that the person to be arrested is guilty of a crime."). Although the immigration official who paroled Rodov into the country probably did not have before him all of the evidence with which the government established probable cause to believe that he had aided and abetted wire fraud, the arrest warrant was more than a sufficient proxy.
[1]  The BIA failed entirely to grapple with this issue, concluding without analysis that, because Rodov later pled guilty to a fraud offense, he had "committed" that offense at the time he sought admission to the United States.
[2]  See Maj. Op. 272 (acknowledging that an immigration officer's determination at the point of entry that an LPR has committed a crime of moral turpitude "revok[es] ... [that] person's lawful-resident status," and, thus, "entails restraints on the rights and privileges that he had previously enjoyed.").
[3]  As the majority points out, when an immigration officer determines an alien's admissibility status at the point of entry, "[t]here is no hearing, and no neutral arbiter who can be entrusted to assess whether the available evidence is sufficient to satisfy a `preponderance' or `clear and convincing' standard." (Maj. Op. 272).
[4]  See Maj. Op. 272 ("With [general due process principles] in mind, we think the proper standard to employ here is probable cause to believe that the alien has committed one of the crimes identified in 8 U.S.C. § 1182(a)(2).").
[5]  In other cases where LPRs have been regarded as "seeking admission" and found inadmissible due to having committed crimes of moral turpitude, they had been convicted of a crime or did not challenge the "seeking admission" designation. See, e.g., Alaka v. Att'y Gen., 456 F.3d 88, 92 (3d Cir.2006) (at the time she reentered, petitioner had been convicted in the U.S. for aiding and abetting bank fraud); Nadal-Ginard v. Holder, 558 F.3d 61, 66 (1st Cir.2009) (at the time of attempted reentry, petitioner had been convicted of four counts of larceny); Singh v. U.S. Dep't of Homeland Sec., 526 F.3d 72, 76 n. 5 (2d Cir.2008) (the court noted that Singh, who was found to be inadmissible for committing a crime of moral turpitude, "was convicted of his offense after he had applied for admission," but, because he "does not rely on this fact as a possible ground for challenging the inadmissibility ruling ... any argument to that effect is waived, and we do not address it."). But see Oduko v. Immigration & Naturalization Serv., 276 Fed.Appx. 21 (2d Cir. 2008). In Oduko, an unpublished opinion, the Second Circuit ruled that petitioner could properly be regarded as having "committed" a crime of moral turpitude when, at the time of his attempted reentry, he had been indicted, but not convicted, of criminal possession of stolen property. Id. at 23-24. The Second Circuit explained, briefly: "Here, the BIA's interpretation of § 101(a)(13)(C) is reasonable as Congress selected the term `committed' rather than the term `convicted.' ... Because Oduko committed the offense involving moral turpitude prior to his attempted reentry, he came under the exception in INA § 101(a)(13)(C) and was properly treated as an arriving alien." Id. at 24 (internal citations omitted). However, this authority does not bind us and, even if it did, the circumstances are distinguishable because indictment for a crime requires a higher level of proof than the mere issuance of an arrest warrant.
[6]  See United States v. Thomas, 315 F.3d 190, 196 (3d Cir.2002) ("[T]he `plain meaning' is our starting point. We do not lightly disregard the statutory language.") (citing Immigration & Naturalization Serv. v. Elias-Zacarias, 502 U.S. 478, 482, 112 S.Ct. 812, 117 L.Ed.2d 38 (1992)).
[7]  See also Black's Law Dictionary, Entry on "Commission" (9th ed.2009) (defining "commission" as "[t]he act of doing or perpetrating (as a crime).").
[8]  While the majority suggests that the Government should not have to develop evidence before paroling a person, (Maj. Op. 272), the statute requires the Government to make a determination, and that determination must have an adequate basis in fact. Surely they could ask him about the warrant or get copy of it and follow up with some investigation before imposing restraints on him.
