Mlaith Abdelqadar, a citizen of Jordan, has been ordered removed from the United States following his conviction for purchasing food stamps from welfare recipients. Food stamps — in Illinois, “WIC stamps” issued under the state’s program for women, infants, and children — may be used only to secure designated goods, such as bread and milk. Replacing the stamps with cash enables recipients to buy goods they prefer to the state’s list. Economists may approve; Illinois does not. Intermediaries in this black-market trade buy at a discount and make a profit by turning the stamps in at face value (or selling them to crooked grocers, who redeem them with the state). Fraud is a necessary component of the scheme; unless the purchaser deceives the state about how he acquired the stamps, it will not reimburse the holder. Immigration officials treated the offense of which Abdelqadar has been convicted, 720 ILCS 5/17B-5, as a species of fraud, and because crimes of deceit are the classic exemplars of moral turpitude, see Jordan v. DeGeorge, 341 U.S. 223, 71 S.Ct. 703, 95 L.Ed. 886 (1951), the immigration judge and Board of Immigration Appeals concluded that he is removable under 8 U.S.C. § 1227(a)(2)(A)® and (ii).

Section 1227(a)(2)(A)® provides:

Any alien who (I) is convicted of a crime involving moral turpitude committed within five years ... after the date of admission, and (II) is convicted of a crime for which a sentence of one year or longer may be imposed, is deportable.

Subsection (ii) adds:

Any alien who at any time after admission is convicted of two or more crimes involving moral turpitude, not arising out of a single scheme of criminal misconduct, regardless of whether confined therefor and regardless of whether the convictions were in a single trial, is de-portable.

Abdelqadar has been convicted of violating 720 ILCS 5/17B-5 twice, but he contends that these represent a single “scheme of misconduct” and that subsection (i) therefore provides the only ground of removal. Although Illinois authorizes a sentence of one year or longer for this offense, Ab-delqadar insists that the statute does not define a “crime of moral turpitude.” Moreover, he contends that his conviction came more than five years after the date of his admission to the United States. Logically the first question is whether the crime of which he has been convicted is one of “moral turpitude”, for if it is not then neither subsection (i) nor subsection (ii) authorizes removal.

We start with that issue, which like the others is strictly legal and thus within the jurisdiction granted by 8 U.S.C. § 1252, as amended by § 106 of the REAL ID Act of 2005, Pub.L. 109-13, 119 Stat. 231, 310-11. Abdelqadar failed to exhaust his administrative remedies on this subject when he omitted from his arguments to the Board any contention that violations of 720 ILCS 5/17B-5 are not crimes of moral turpitude, but the agency forfeited the benefit of this omission by briefing the issue on the merits without observing that Abdelqadar had failed to present his contentions to the Board. The agency’s assertion at oral argument that failure to preserve an issue deprives us of subject-matter jurisdiction, so that we must ignore[*671] the agency’s own forfeiture, lacks any visible means of support. Our jurisdiction is supplied by the alien’s timely petition for review of the agency’s final decision. Courts have jurisdiction over cases and controversies, not particular legal issues that affect the outcome. We cannot imagine any reason why an agency should be forbidden, on jurisdictional grounds, to excuse an alien’s failure to exhaust a particular issue. See Mathews v. Eldridge, 424 U.S. 319, 328, 96 S.Ct. 893, 47 L.Ed.2d 18 (1976) (a final, decision by the agency is essential to jurisdiction, but failure to exhaust particular issues may be waived by the agency); Weinberger v. Salfi, 422 U.S. 749, 766-67, 95 S.Ct. 2457, 45 L.Ed.2d 522 (1975) (same).

Neither § 1227 nor any other provision of the immigration laws defines “crime of moral turpitude,” so the agency has some latitude in supplying a definition. See INS v. Aguirre-Aguirre, 526 U.S. 415, 119 S.Ct. 1439, 143 L.Ed.2d 590 (1999); INS v. Cardoza-Fonseca, 480 U.S. 421, 107 S.Ct. 1207, 94 L.Ed.2d 434 (1987); Gattem v. Gonzales, 412 F.3d 758, 763-65 (7th Cir.2005). As in Wei Cong Mei v. Ashcroft, 393 F.3d 737 (7th Cir.2004), we need not pin down just how much leeway the agency possesses, because the Board’s approach does not come near the outer bounds. Crimes entailing deceit or false statement are within the core of the common-law understanding of “moral turpitude.” Any purchase of food stamps for cash entails misrepresentation to the state about how the holder came by the stamps. Nothing else makes this economic crime profitable.

The best one can say for Abdelqadar’s position is that the- statute does not include fraud as an element. Here is the text of § 5/17B-5:

A person who knowingly (i) uses, acquires, possesses, or transfers Illinois Department of Public Health or Department of Human Services Special Supplemental Food Program for Women, Infants and Children (WIC) Food Instruments or authorizations to participate in the Illinois Department of Public Health or Department of Human Services Special Supplemental Food Program for Women, Infants and Children (WIC) in any manner not authorized by law or the rules of the Illinois Department of Public Health or Department of Human Services or (ii) alters, uses, acquires, possesses, or transfers altered Illinois Department of Public Health or Department of Human Services Special Supplemental Food Program for Women, Infants and Children (WIC) Food Instruments or authorizations to participate in the Illinois Department of Public Health or Department of Human Services Special Supplemental Food Program for Women, Infants and Children (WIC) is guilty of a violation of this Article and shall be punished as provided in Section 17B-20.

A welfare recipient could violate this statute by knowingly using food stamps to buy liquor from a dishonest merchant, because this would be a “manner not authorized by law or the rules”, without making any misrepresentation (though ,the merchant would do so later to redeem the stamps for cash). An “aggravated felony”- — a ground for removal given in § 1227(a)(2)(A)(iii)— usually must be identified based on the elements of the offense rather then the acts that the alien committed. See, e.g., Leocal v. Ashcroft, — U.S. —, 125 S.Ct. 377, 160 L.Ed.2d 271 (2004); Flores v. Ashcroft, 350 F.3d 666 (7th Cir.2003). If that is so of “aggravated felony” under subsection (iii), why not of “crime of moral turpitude” under subsections (i) and (ii)?

One answer is that “aggravated felony” is a defined term, while “crime of moral[*672] turpitude” is not. Section 1101(a)(43) defines “aggravated felony” at great length, and many parts of the definition point to precise locations in the criminal code. For example, § 1101(a)(43)(F) says that the term “aggravated felony” includes “a crime of violence (as defined in section 16 of Title 18, but not including a purely political offense) for which the term of imprisonment [is] at least one year”. Section 16(a) in turn uses the elements of the offense to specify a crime of violence. The Supreme Court held in Taylor v. United States, 495 U.S. 575, 600-02, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990), and reiterated in Shepard v. United States, — U.S. —, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005), that, when applying a similar provision in 18 U.S.C. § 924(e), a court should look no farther than the elements of the offense and the charging papers. That approach led to Leocal, where removal depended on the meaning of § 16. “Crime of moral turpitude” lacks any limit comparable to § 16, and in Wei Cong Mei we asked whether it was an apt description of the deeds the alien had committed (driving more than 100 miles per hour to escape apprehension, endangering bystanders in the process). Likewise the reference to “sexual abuse of a minor” in § 1101(a)(43)(A), a form of aggravated felony that is not defined elsewhere in the immigration law, allows the agency some discretion to look at what actually happened, as we held in Gattem. It is the language of § 16 (and some other provisions to which § 1101(a)(43) refers), and not anything in § 1227(a)(2)(A), that limits some inquiries to statutory elements.

A second answer is that even under Taylor’s approach — which we applied uncritically to “crime of moral turpitude” in Padilla v. Gonzales, 397 F.3d 1016, 1019 (7th Cir.2004), without considering either Wei Cong Mei or the role of § 16 has played in defining “aggravated felony” — it is permissible to look at the charging papers and admissions made as part of a guilty plea. Taylor recognized that many states lump into one statute offenses with different consequences under federal law. Federal law treats burglary of a dwelling as a crime of violence because of the risk that the intruder may encounter the householder. Entry of a railroad car does not pose the same risk and is not a “crime of violence” for federal purposes. But many states define “burglary” as surreptitious entry of any structure (not just a dwelling) with intent to commit a crime inside. That led the Supreme Court to allow a peek at the indictment and equivalent documents to see which component of the state offense the conviction entails. See Shepard, 125 S.Ct. at 1257. The goal is to determine what the accused was convicted of, not what he did in fact, so the scope of inquiry is correspondingly limited. See United States v. Lewis, 405 F.3d 511, 515 (7th Cir.2005). It does not exceed that limit, however, to learn from the charging papers and Abdelqadar’s admissions when pleading guilty that he purchased the food stamps for cash and arranged to deceive the State of Illinois about the stamps’ provenance so that he could make a profit. That concession puts his conviction on the “crime of moral turpitude” side of any divide.

Next in line is the question whether Abdelqadar was convicted “within five years ... after [his] date of admission”. The word “admission” has a definition in § 1101(a)(13)(A): “the lawful entry of the alien into the United States after inspection and authorization by an immigration officer.” That date, for Abdelqadar, is March 15, 1991, when he entered the United States on a visa. He was not convicted until August 17, 1999, more than eight years later, though his crimes were committed in September and October 1997.[*673] The parties agree that the date of the offense, and not the date of conviction, is the one that matters for purposes of § 1227(a)(2)(A)©; we need not decide whether that is correct. Still, September 1997 is more than six years after Abdelqa-dar arrived in the United States. Immigration officials used a date about 21 months after his physical entry: December 22, 1992, when Abdelqadar’s status was adjusted to that of lawful permanent resident. His offense was committed a little less than five years later.

Abdelqadar accuses the agency of engaging in word play by equating “admitted for permanent residence” with “the date of admission.” The former is a legal status, the latter an entry into the United States. Section 1101(a)(13)(A) defines admission as a lawful entry, not as a particular legal status afterward. See Succar v. Ashcroft, 394 F.3d 8, 14 (1st Cir.2005); Matter of Rainford, 20 I & N Dec. 598, 601 (1992).

Yet things are not quite this simple. The Board of Immigration Appeals relied on Matter of Rosas-Ramirez, 22 I & N Dec. 616 (1999) (en banc), which posed the question what the word “admission” means in § 1227(a)(2)(A)(iii), which says that “[a]ny alien who is convicted of an aggravated felony at any time after admission is deportable.” Section 1101(a)(13)(A) defines admission as a “lawful entry,” but Rosas-Ramirez entered the United States unlawfully, by stealth, before committing his aggravated felony, and he contended that because he had entered illegally he could not be removed under this provision. The Board found that too much to swallow; why should illegal entrants enjoy rights superior to those of lawful immigrants? Until amendments in 1996, the word “entry” had been used in passages such as that of § 1227(a)(2)(A)(iii). That word was changed across the board in 1996 to “admit” or “admission” — but without a corresponding adjustment to the definitional clause.

To make the word “admit” (and its variations) work in all of the places to which it had been added by the 1996 amendments, the Board decided to treat § 1101 as if it began — as many definitional provisions in the United States Code do — with the phrase “unless the context otherwise requires.” Context clauses reflect the fact that definitions rarely work universally, and that one word can have different connotations in different constructions. See Rowland v. California Men’s Colony, Unit II Men’s Advisory Council, 506 U.S. 194, 113 S.Ct. 716, 121 L.Ed.2d 656 (1993). Whether judges could engage in such repair work is doubtful, see Lamie v. United States Trustee, 540 U.S. 526, 542, 124 S.Ct. 1023, 157 L.Ed.2d 1024 (2004) (“It is beyond our province to rescue Congress from its drafting errors, and to provide for what we might think ... is the preferred result”) — after all, § 1101 does not have a context clause — but agencies charged with superintending a comprehensive scheme traditionally have been afforded additional latitude. See, e.g., Chevron U.S.A. Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984); United States v. Mead Corp., 533 U.S. 218, 121 S.Ct. 2164, 150 L.Ed.2d 292 (2001). So in Rosas-Ramirez the Board held that the word “admission” in § 1227(a)(2) (A) (iii) would be deemed to include an adjustment of status that put the illegal entrant on a lawful footing; by seeking and obtaining post-entry relief, the alien had engaged in a process analogous (though obviously not identical) to presenting oneself for inspection at the border.

To accept the way Rosas-Ramirez read “admission” in § 1227(a) (2) (A) (iii) is not, however, to imply that the word must have the same meaning in § 1227(a)(2)(A)®. In[*674] this case the Board cited Rosas-Ramirez as if it established a new meaning for “admission” everywhere in the Immigration and Nationality Act, and it applied that meaning so that Abdelqadar had been admitted twice: once in 1991 when he entered on a visa after inspection at the border, and again in 1992 when his legal status changed to permanent resident. Yet the whole point of contextual reading is that context matters — and the context of the word “admission” in § 1227(a)(2)(A)© differs substantially from its context in § 1227(a)(2) (A) (iii).

Section 1227(a)(2)(A)(iii) uses “admission” to distinguish between crimes committed in the United States and those committed abroad. An aggravated felony after the alien’s entry is a ground of removal, while discovery that the alien had committed a felony in his home country would not be a ground of removal. By contrast, “admission” in § 1227(a)(2)(A)® starts a clock. A provision such as § 1227(a)(2)(A)® ensures that people who turn to crime soon after their arrival are ejected. (Five years is “soon” in governmental parlance and reflects the fact that initial offenses may not be detected, or a wrongdoer may receive diversionary dispositions before finally being convicted.) Quickly turning to crime can be revealing about character, if not about the real reason for coming to the United States. This is parallel to the provision in 8 U.S.C. § 1612 that new arrivals do not qualify for public assistance. Both the criminal-removal and the welfare-disqualification approaches suppose that the clock runs from physical entry, not from a change in legal status after arrival.

The Board not only borrowed the approach of Rosas-Ramirez without regard to the different function “admission” serves in § 1227(a)(2)(A)® but also assumed that every new admission resets the clock. Why would that be so? Then a crime of moral turpitude within five years of any pleasure trip to one’s native land would lead to mandatory removal, even of a permanent resident with a clean record for 20 or 50 years in the United States. The Board did not explain in this case— and, as far as we can tell, has never explained — why “admission” in § 1227(a)(2)(A)© means the most recent, rather than the initial, entry. Surely immigration officials read the timing rules in § 1612 as running from an alien’s first admission. Maybe there is a good reason why § 1227(a)(2)(A)® should work differently, but silence by an administrative agency does not carry the day. See Shivaraman v. Ashcroft, 360 F.3d 1142 (9th Cir.2004) (reference to “the” date of admission in § 1227(a)(2)(A) implies that each alien has only one admission date, which must be the initial entry). Both the Board’s transposition of Rosas-Ramirez to a different context, and its casual assumption that the latest of multiple admissions starts a new five-year period, show that the agency has not given this question the attention that it requires. Judges are not allowed to invent rationales that the agency has not supplied, so the order to remove Abdelqadar cannot rest on § 1227(a)(2)(A)®.

That leaves § 1227(a)(2)(A)(ii), which requires removal of any “alien who at any time after admission is convicted of two or more crimes involving moral turpitude, not arising out of a single scheme of criminal misconduct”. Abdelqadar has two convictions for violating 720 ILCS 5/17B-5 by purchasing food stamps. According to the criminal charge and his guilty plea, the purchases occurred two days apart. Abdelqadar says that he cannot remember the different transactions and insists that this implies that he was engaged in a single criminal scheme.[*675] Doubtless this is so in the sense that he had a criminal occupation. Just as grocers sell milk for a living, so Abdelqadar apparently made his living dealing in food stamps. Under the Sentencing Guidelines such a criminal occupation would be treated as one scheme for the purpose of aggregating relevant conduct. See U.S.S.G. § 1B1.3. The Board of Immigration Appeals has decided, however, that the phrase “a single scheme of criminal misconduct” is used in § 1227(a)(2)(A)(ii) the way it is employed in recidivist statutes rather than the way it is employed in the Guidelines’ relevant conduct system.

Matter of Adetiba, 20 I & N Dec. 506 (1992), concludes that two offenses are not part of a “single scheme of criminal misconduct” when the acts are distinct and neither offense causes (or constitutes) the other. Robbing six people at one poker game therefore would be a single scheme even if it led to multiple convictions, cf. Ashe v. Swenson, 397 U.S. 436, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970), as would all lesser included offenses of a criminal transaction. Likely the Board would treat conspiracy and its overt acts as a single scheme, even though the overt acts may be separate crimes as well. But the Board would treat a series of securities frauds by a broker who finds a new “mark” daily as distinct offenses rather than aspects of a single scheme, because the broker could stop after any of the frauds. This is exactly how federal courts approach recidivist statutes such as the Armed Career Criminal Act, the subject of United States v. Hudspeth, 42 F.3d 1015 (7th Cir.1994) (en banc). We held in Hudspeth that a series of burglaries counts as multiple predicate offenses, even though the crimes came close in time. (The intruders broke through one party wall after another to rob each store in a strip mall.) Section 1227(a)(2)(A)(n) is a recidivist provision, so it makes sense for the Board to use the approach common to recidivist clauses in the criminal law.

Adetiba does not exceed the latitude the Board possesses in interpreting the immigration laws. Its approach to “single scheme of criminal misconduct” has been sustained as reasonable by at least four other circuits. See Balogun v. INS, 31 F.3d 8 (1st Cir.1994); Akindemowo v. INS, 61 F.3d 282 (4th Cir.1995); Iredia v. INS, 981 F.2d 847, 849 (5th Cir.1993); Thanh Huu Nguyen v. INS, 991 F.2d 621, 623 (10th Cir.1993). But see Gonzalez-Sandoval v. INS, 910 F.2d 614 (9th Cir.1990). And as applied to Abdelqadar it makes a good deal of sense; otherwise aliens who are career criminals could stay in the United States as long as they kept committing the same crime over and over. Abdelqadar is a serial offender and thus is removable.

The petition to set aside the Board’s order is denied.