OPINION
SMITH, Circuit Judge.Petitioner Igor Rodov has been admitted to the United States as a lawful perma*268nent 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 *269crime 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 synony*270mous “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. § 11S2(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 *271who 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 *272arriving 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 *273been 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.
*274The 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.
Ill
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 *275loss 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, 557 U.S. 29, 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 *276court 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 ease does not require us to consider whether KhalayleKs 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 pri- or 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“[decisions,” 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.
Y
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.
. 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 ToroRomero 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 *270applying 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.
. 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).
. The legislative history does not explain the choice. See S.Rep. No. 82-1137, at 4 (1952).
. 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.