
616 F.3d 642 (2010)
In re AIRADIGM COMMUNICATIONS, INC., Debtor.
Federal Communications Commission, Appellant,
v.
Airadigm Communications, Inc., and Telephone and Data Systems, Inc., Appellees.
Nos. 08-3585, 08-3587, 08-3588, 08-3590.
United States Court of Appeals, Seventh Circuit.
Argued May 4, 2009.
Decided August 4, 2010.
*647 Kathryn A. Pamenter, Attorney, Goldberg, Kohn, Bell, Black, Rosenbloom & Moritz, Chicago, IL, for Debtor.
Jeffrey A. Clair (argued), Attorney, Department of Justice, Civil Division, Appellate Section, Washington, DC, for Appellant.
Before KANNE and EVANS, Circuit Judges, and DOW, District Judge.[*]
DOW, District Judge.
The parties are here because of the continuing saga that has been the Chapter 11 reorganization of Airadigm Communications, Inc. ("Airadigm"). The latest appearance involves three claims of Telephone and Data Systems, Inc. ("TDS"). The claims were filed in Airadigm's 2006 bankruptcy, but have roots in Airadigm's 1999 bankruptcy and 2000 plan of reorganization. The Federal Communications Commission ("FCC") objected to all three claims. The bankruptcy court overruled the objections to two of the claims, but sustained the objection to the third and disallowed that claim. The district court affirmed in part and reversed in part, concluding that the objections to all three claims should be overruled.
To resolve the appeal, we combine three ingredientsequal parts bankruptcy law, stipulation interpretation, and estoppel. The admixture leads us to agree with the district court's treatment of two of the three claims at issue. The judgment of the district court is affirmed in part and reversed in part.

I. Background

A. Airadigm, its Licenses, and the 1999 Bankruptcy
Airadigm is a telecommunications company whose principal assets are fifteen mobile phone service licenses that it won at auction in the late 1990s. The FCC issued the licenses and retained a security interest in them. In the FCC's argot, the licenses were "C-block" and "F-block" licenses. The C-block licenses were 30 megahertz each and the F-block licenses were 10 megahertz each. With the licenses in hand, Airadigm had the capacity to provide mobile phone service in Wisconsin, Iowa, and Michigan.
The licensing scheme and its nomenclature come from an amendment to the Communications Act of 1934; the amendment set aside 120 megahertz of the electromagnetic spectrum for mobile communications devices. We described the scheme and its attendant regulations in some detail the last time that the parties were here. In re Airadigm Communications, Inc. (Airadigm II), 547 F.3d 763, 765 (7th Cir.2008). The C- and F-blocks were set aside for small businesses and rural telephone companies (among others). Unlike licenses that could be purchased by the large telecommunications companies, these licenses could be purchased on installment plans with favorable interest rates. See Federal Communications Commission v. NextWave Personal Communications, Inc., 537 U.S. 293, 296, 123 S.Ct. 832, 154 L.Ed.2d 863 (2003) (detailing the statutory and regulatory regime applying to C- and F-block licenses).
*648 The favorable licensing scheme, however, was not without shoals: the Congressional Budget Office ("CBO") predicted that many successful license-bidders would be forced into bankruptcy "unless the debt owed to the government by the * * * licensees is sharply reduced." Congressional Budget Office, IMPENDING DEFAULTS BY WINNING BIDDERS IN THE FCC's C BLOCK AUCTION: ISSUES AND OPTIONS 4 (1997), http://www.cbo.gov/ftpdocs/0xx/doc37/cblock.pdf.
In 1999, Airadigm unintentionally proved the CBO's prescience by defaulting on its obligation to make payments on the licenses and filing a Chapter 11 bankruptcy petition in the United States District Court for the Western District of Wisconsin. At that time, and pursuant to FCC regulations, the FCC revoked the licenses. See 47 C.F.R. § 1.2110(g)(4)(iv). The decision to revoke the licenses made waves, because a bankruptcy estate springs into existence by operation of law whenever a bankruptcy petition is filed. The estate consists of all property of the debtor "wherever located and by whomever held." 11 U.S.C. § 541(a). So revoking the licenses issued to Airadigm had two major effects: (1) it removed (at first blush) the licenses from the estate, and (2) it made (again, at first blush) the FCC an unsecured creditor. See also Airadigm II, 547 F.3d at 766 (describing the FCC's early litigation position).
In keeping with the FCC's license revocation, the plan of reorganization ("2000 Plan") that Airadigm proposed treated the licenses as if they were not part of the bankruptcy estate. The bankruptcy court confirmed the 2000 Plan over the FCC's objections. The linchpin of the plan was Airadigm's petition to the FCC for reinstatement of the licenses; treatment of various claims in the 2000 Plan depended on how and when the FCC acted on Airadigm's petition.

B. Salient Features of the 2000 Plan the OEDA and Ericsson Claims
The 2000 Plan provided treatment of two creditors' claims that are of consequence to this appealthe Oneida Enterprise Development Authority ("OEDA") and Ericsson, Inc. ("Ericsson"). The claims of each were to be paid under the 2000 Plan, and they were to be financed by loans provided by TDS. Both of the claims have since been assigned to TDS.
The claims were to be given different treatment depending on whether the 2000 Plan's "Primary Plan" or "Back-up Plan" applied. Article V of the 2000 Plan detailed the treatment of the claims under the Primary Plan. If the FCC denied reinstatement of all the licenses or failed to act on Airadigm's petition in a timely manner, then Article X, the Back-up Plan, would apply to OEDA's claim.
Here is how OEDA's claim would shake out: under the Primary Plan, OEDA would receive $49 million, "[p]rovided that the FCC grant[ed] reinstatement of at least the Minimum Licenses," a term of art.[1] The $49 million was to be paid when the FCC's order reinstating the license became final. 2000 Plan § 5.3.
Under the Back-up Plan in Article X, however, OEDA's claim was to be slashed. The Back-up Plan stated: "On the Back-up Transfer Date * * * Buyers"TDS "shall pay OEDA $2 million in full satisfaction of its secured Claims." 2000 Plan *649 § 10.7. The Back-up Transfer Date was ten days after the date on which TDS no longer had to fund one of the loans that TDS made as part of the 2000 Planthe so-called "Funding Termination Date." See 2000 Plan §§ 2.5, 2.24, 6.7. Section 6.7 of the 2000 Plan gave TDS the option to extend the Funding Termination Date beyond that which was spelled out in the plan.
Ericsson filed the other important claim that was to be paid under the 2000 Plan. Under the 2000 Plan's Primary Plan, Ericsson would receive $41 million "[p]rovided that the FCC grant[ed] reinstatement of at least the Minimum Licenses."[2] The $41 million was to be paid when the FCC's order reinstating the license became final. If fewer than the Minimum Licenses were reinstated, the amount owed to Ericsson would be reduced pursuant to a formula based on the number of licenses that were reinstated. See 2000 Plan §§ 5.2(b), 6.12. Under the Backup Plan, Ericsson generally was not entitled to any payments but was entitled to keep the liens securing the claim. 2000 Plan §§ 10.2, 10.5, 5.2.
Payment of OEDA's and Ericsson's claims would be financed by a loan provided by TDS. 2000 Plan §§ 6.4-6.5. The holders of allowed claims were entitled to go to court to force payment of the loans that would pay their claims. 2000 Plan § 12.6 ("[T]he holder of an Allowed Claim shall be entitled to take any steps necessary to enforce this Plan against the Debtor, the assets of Debtor or [TDS].").

C. Financing the 2000 Planthe Claim 14 Loans
In addition to the TDS loan that would pay for the Ericsson and OEDA claims, three other TDS loans are important to our story.[3] The loans were part of the 2000 Plan and have become the subject of a new claim in the 2006 bankruptcy. We will call these advances of funds the "Claim 14 Loans." The Claim 14 Loans comprise the Confirmation Loan, the Working Capital Loan, and the Construction Loan. The Confirmation Loan furnished funds for a $30 million collateral payment to Ericsson that is not in issue, as well as funds to pay administrative expense claims, priority claims, and a few other claims that are not important to this case. The loan was to be secured by a first priority security interest in all of Airadigm's Unlicensed Assetsa term defined in the 2000 Plan to include every Airadigm asset except the FCC licenses and the proceeds of the licenses. However, the 2000 Plan and the loan documents suggest that the loan was not a loan at all, but an asset sale. Although the loan accrued interest at a yearly rate of 8.5%, the 2000 Plan also stated that "[t]he Confirmation Loan will be repaid by the surrender to Buyers"that is, TDS"of all collateral securing the Confirmation Loan, and Buyers shall be obligated to accept a surrender of the collateral in full and complete satisfaction of the Confirmation Loan." 2000 Plan § 6.3 (emphasis added). That feature, repayment solely by collateral surrender, is the FCC's problem with the loan.
The second TDS loan was the "Working Capital Loan." The Working Capital Loan was secured by a negative pledge of Airadigm's assets and was to be used by Airadigm for "its ongoing working capital *650 needs." Under the 2000 Plan, the loan amount was for up to $600,000 per month, an amount which would be reduced to the extent Airadigm could stand on its own. Interest on the Working Capital Loan was to accrue at a yearly rate of 8.5%. The amount of the loan and the interest were due and payable on the Funding Termination Date. 2000 Plan §§ 6.6, 6.7. The loan was to be repaid by surrendering Airadigm's non-license assets. App. 135.
The third TDS loan was the "Construction Loan." The Construction Loan was for "not less than $1.5 million * * * for the purpose of financing [Airadigm's] acquisition and construction of additional cell sites." The loan was secured by a first priority purchase money security interest in the equipment and property that was purchased with the loan. The loan contained the same now-controversial provision that appeared in the other loans: "The Construction Loan will be repaid by the surrender of the collateral securing the Construction Loan to [TDS], and [TDS] shall be obligated to accept a surrender of the collateral in full and complete satisfaction of the Construction Loan." 2000 Plan § 6.8.

* * *
The bankruptcy court confirmed the 2000 Plan over the FCC's objections.

D. NextWave, the Stipulation, and the 2006 Bankruptcy
After the bankruptcy court confirmed the 2000 Plan, the Supreme Court ruled in Federal Communications Commission v. NextWave Personal Communications, Inc., 537 U.S. 293, 123 S.Ct. 832, 154 L.Ed.2d 863 (2003), that the FCC's automatic license revocation rule violated 11 U.S.C. § 525. Section 525 says that agencies "may not * * * revoke * * * a license * * * [issued to] a debtor under this title * * * solely because" the debtor has not paid "a debt that is dischargeable" in bankruptcy. The Supreme Court held that the FCC's license revocation rule violated Section 525 and therefore was an invalid exercise of authority under the Administrative Procedures Act. 537 U.S. at 300-02, 123 S.Ct. 832; 5 U.S.C. § 706(2)(A). After NextWave came down, the FCC denied as moot Airadigm's petition to have the licenses reinstated. "[B]ecause Airadigm was under the protection of Chapter 11 of the U.S. Bankruptcy Code, the Commission's automatic cancellation rule was ineffective." In re Airadigm Communications, Inc., 18 F.C.C.R. 16296, 16299 (F.C.C. 2003).
The legal effect of the FCC's ruling was not just to restore the licenses, but to declare that Airadigm always had the licenses. As a practical matter, the FCC acknowledges that the ruling had the effect of restoring the licenses. But by the time that the FCC's 2003 ruling came around, TDS was no longer obligated under the 2000 Plan to fund the loans that were to pay creditors. In other words, even though the 2000 Plan would have paid the claims of OEDA and Ericsson that are discussed above, and even though the 2000 Plan made the claims enforceable after the Plan was confirmed (2000 Plan § 12.6), the funding to pay the claims had dried up.
In May 2006, Airadigm filed a new Chapter 11 bankruptcy petition. It also filed a motion for a final decree closing the 1999 bankruptcy. See Fed. R. Bankr.P. 3022. The FCC objected to closing the 1999 bankruptcy and argued instead that the parties should discuss modifications to the 2000 Plan, apparently pursuant to 11 U.S.C. § 1127(b), which gives the proponent of a plan and the bankruptcy court authority to modify a plan post-confirmation "if circumstances warrant such modification."
*651 The parties settled the dispute over whether to allow a new bankruptcy to proceed by entering into a "Stipulation." As originally drafted it had five operative paragraphs, four of which matter and are set out below:
1. Except as otherwise specifically set forth in this Stipulation, all of the rights of Airadigm as debtor, and the FCC and TDS as creditors, under the 2000 Plan, including their respective rights as holders of the Allowed Claims they hold pursuant to the 2000 Plan (including the rights of TDS as assignee of certain Allowed Claims), are in no way prejudiced by closing the 1999 Bankruptcy Case and proceeding with the 2006 Bankruptcy Case.
2. The FCC's Allowed Claim in the 1999 Bankruptcy Case shall be allowed in the 2006 Bankruptcy Case. The claims of TDS as assignee of the Allowed Claims of Ericsson, Inc. and Oneida Enterprise Development Authority in the 1999 Bankruptcy Case shall be allowed in the 2006 Bankruptcy Case. In addition, the claims of TDS arising from its advances of funds in accordance with the 2000 Plan shall be allowed in the 2006 Bankruptcy Case in the amount of such loans with interest to the extent provided in the 2000 Plan.
3. In reliance on these Stipulations, (a) the FCC does not object to the closing of the 1999 Bankruptcy Case and will withdraw its Objection to the Motion, and (b) the FCC waives any right it may have to dispute Airadigm's right to commence the 2006 Bankruptcy Case, with prejudice.
4. All other rights of the parties hereto (including, without limitation, the right of the FCC and TDS to seek the inclusion and allowance of interest on their Allowed Claims (including assigned Allowed Claims) in the 2006 Bankruptcy Case) are expressly reserved.
* * *
When the Stipulation was entered, in June 2006, counsel for TDS, Airadigm, and the FCC sought to "clarify" its meaning on the record. In doing so, the parties made the Stipulation more difficult to interpret. The comments to the bankruptcy court by counsel for TDS were representative:
[T]here is an unresolved issue as to the right to claim interest accrued on [the claims from the 2000 case]. And there are also, as not referenced in the stipulation, open questions with respect to the nature or extent of security for various claims.
As to those two unresolved issues, the parties do not intend by this stipulation to waive a right as might be appropriate or as might be authorized under the code or the rules to pursue disputes, should they choose to do so in the future.
With that clarification, we believe the stipulation resolves the objection of the FCC * * *.
The FCC's lawyer spoke briefly, but in similarly broad and opaque terms. Counsel emphasized that while the FCC was waiving its objection to closing the 1999 bankruptcy case, the Stipulation was not intended to speak to "substantive arguments" between the parties that the FCC had made elsewhere. The FCC has not identified for us precisely where that elsewhere is, however, nor has it contended that the unidentified substantive arguments included the argument that it presses on appeal.
The bankruptcy judge gave the parties an opportunity to ensure that something more coherent was placed in the record: "Once again, you're all welcome to write down what you mean here if you want *652 * * * I'm not exactly sure why you don't write down what you mean, but if you want this entered as it is with the modifications on the record, that's fine with me." It was fine with TDS and the FCC, too. With that, the bankruptcy judge approved the Stipulation as modified and later entered an order that allowed the 2006 bankruptcy to proceed.
The parties are here now because TDS filed three claims in the 2006 bankruptcy, and the FCC objected.[4] Claim 14 was based on the Confirmation Loan, the Working Capital Loan, and the Construction Loan that was contained in the 2000 Plan. Claim 15 was based on the OEDA claim from the 1999 bankruptcy. Claim 16 was based on the Ericsson claim from the 1999 bankruptcy. The bankruptcy court overruled the FCC's objections to Claims 14 and 16; the bankruptcy court sustained the objection to Claim 15 and disallowed the claim. The district court affirmed with respect to Claims 14 and 16, but reversed with respect to Claim 15. We think that the bankruptcy court reached the correct result, although we rest our decision on grounds that are different from those set out in the bankruptcy court's opinions.

II. Standard of Review
We review the bankruptcy court's judgment under the same standards employed by the district court. Miller v. LaSalle Bank Nat'l Assoc., 595 F.3d 782, 785 (7th Cir.2010) ("When reviewing a bankruptcy court's decision, an appeals court applies the same standard of review as does the district court."); In re Ingersoll, Inc., 562 F.3d 856, 863 (7th Cir. 2009); In re Marrs-Winn Co., Inc., 103 F.3d 584, 589 (7th Cir.1996). Matters of law are reviewed de novo. Wiese v. Cmty. Bank of Cent. Wis., 552 F.3d 584, 588 (7th Cir.2009); Frierdich v. Mottaz, 294 F.3d 864, 867 (7th Cir.2002); In re Platter, 140 F.3d 676, 678 (7th Cir.1998). However, the bankruptcy court's interpretation of a plan that it confirmed receives deferential, abuse-of-discretion review, as an interpretation of the court's own order. Airadigm II, 547 F.3d at 768; Matter of Greenig, 152 F.3d 631, 633 (7th Cir.1998); Matter of Weber, 25 F.3d 413, 416 (7th Cir.1994). "Generally speaking, a court abuses its discretion when its decision is premised on an incorrect legal principle or a clearly erroneous factual finding, or when the record contains no evidence on which the court rationally could have relied." Corporate Assets, Inc. v. Paloian, 368 F.3d 761, 767 (7th Cir.2004). Ultimately, we may affirm on any basis that is supported by the record, so long as it has been fairly presented. Stockwell v. City of Harvey, 597 F.3d 895, 901 n. 2 (7th Cir.2010).

III. Discussion
Airadigm's 2000 Plan preceded NextWave and depended on whether and when the FCC reinstated the licenses; the underlying premise was that the licenses were not part of the bankruptcy estate. The 2000 Plan did not envision that, like Dorothy in the Wizard of Oz, Airadigm had the licenses all along.
NextWave produced interpretive difficulties as to whether a given claim should receive Primary or Backup treatment under the 2000 Plan. In addition, the 2000 Plan, particularly when combined with the Stipulation, produces interpretive difficulties as to the status of the Claim 14 Loans. On appeal, the FCC contends that the debts resulting from the Claim 14 Loans should be "recharacterized" as equity, an ownership interest. Equity typically gets *653 wiped out in bankruptcy, so TDS is disinclined to accept the FCC's position. We are similarly disinclined, although for reasons that are different from those articulated by the bankruptcy court.
And as to two other claims, we conclude that the bankruptcy court did not abuse its discretion in interpreting a plan of reorganization that it had confirmed. Claim 15 was properly disallowed; Claim 16 was properly allowed.

A. Claim 14
The bankruptcy court concluded that the FCC's challenge to Claim 14 must live or die on the viability in this circuit of a cause of action for recharacterization. Recharacterization is a theory, adopted by the overwhelming majority of courts to have considered the question, that bankruptcy courts may place the proper label of "claim" (generally, debt) or "interest" (equity) on an advance of funds, regardless of what the parties call it. The bankruptcy court concluded that this Court would not likely recognize a cause of action for recharacterization and therefore overruled the FCC's objection to Claim 14.[5] The district court affirmed. On appeal, the FCC argues primarily not that the claim should be recharacterized as an equity interest but that Claim 14 should be disallowed because it was an asset sale agreement and not a bona fide loan.
We conclude that the only issue that the FCC preserved for appeal was foreclosed by the Stipulation. Therefore, we affirm the judgment of the district court.

1. The FCC Preserved Only its Recharacterization Argument
At the outset, we have to determine which of the FCC's arguments have been preserved for appeal. The bankruptcy court, too, heard both arguments that the FCC made to usthat Claim 14 should be disallowed because the Claim 14 Loans were in actuality a disguised sale of assets and that Claim 14 should be "recharacterized" as equity. The bankruptcy court addressed only the recharacterization argument. When the FCC appealed that ruling to the district court, the FCC spent most of its brief arguing that the bankruptcy court's recharacterization ruling was incorrect. The FCC did not argue that Claim 14 should be disallowed because it was a sale of assets. Thus, the only argument that was preserved was the recharacterization argument. In re Qualitech Steel Corp., 276 F.3d 245, 248 (7th Cir.2001) (ruling that a matter not timely presented to the district court was forfeited); see also In re UAL Corp., 468 F.3d 444, 449 (7th Cir.2006) (appellee in bankruptcy appeal could seek to affirm judgment on any issue preserved in the district court); Boyers v. Texaco Ref. and Mktg., Inc., 848 F.2d 809, 812 (7th Cir.1988) (reasoning that reversing a district court on grounds not presented to it would undermine the "essential function of the district court").
The FCC contends that it preserved the argument that Claim 14 should be disallowed and not just recharacterized. Specifically, the FCC points out in its reply brief to us that in the "issues presented on appeal" portion of its district-court brief, the FCC included the question of "[w]hether TDS's alleged loans to the Debtor were, in reality, capital contributions, equity investments or an agreement to purchase Debtor's non-License assets" (emphasis added). There are multiple *654 problems with that position. First, given the lack of subsequent briefing on the now-italicized issue, the FCC did not do enough to flesh out its argument. APS Sports Collectibles, Inc. v. Sports Time, Inc., 299 F.3d 624, 631 (7th Cir.2002) (conclusory analyses construed as waived). Second, it is not even clear that the argument as presented to the district court is distinct, because at least one case suggests that asset sales agreements may be recharacterized as equity. See In re Official Comm. of Unsecured Creditors for Dornier Aviation (N. Am.), Inc., 453 F.3d 225, 234 (4th Cir.2006).
In short, the FCC did not do enough to signal to the district court or TDS what it was arguing. Therefore, the FCC has forfeited all but its recharacterization argument. However, the FCC should not bemoan the forfeiture of its "disguised-asset-sale-disallowance" argument, for as we construe the Stipulation, the FCC would be prohibited from making that argument in any event.

2. The Stipulation Bars the FCC from Pressing its Preserved Argument
TDS argued below that the FCC's objection to Claim 14 is barred by the Stipulation. The bankruptcy judge disagreed. After noting that the in-court modifications to the Stipulation produced internal inconsistencies, he stated, "I still do not understand exactly what the parties intended when they entered the stipulation, but its unclear and sometimes contradictory language prevents me from finding in it any intent to preclude them from objecting to each other's claims."
We respectfully disagree with the bankruptcy court (and the FCC). Although we agree that the Stipulation gave the parties the right to make certain objections to one another's claims, we think that the Stipulation was sufficiently clear to bar the FCC from raising the only objection that it has preserved for appeal. Thus, we need not reach the portion of the bankruptcy judge's opinion that addresses the viability of recharacterization actions in this circuit. Sierra Club v. Morton, 405 U.S. 727, 732 n. 3, 92 S.Ct. 1361, 31 L.Ed.2d 636 (1972) (federal courts are not authorized to issue advisory opinions); see also Hayburn's Case, 2 U.S. 408, 2 Dall. 409, 1 L.Ed. 436 (1792).
The parties do not contest whether a stipulation allowing a claim in bankruptcy is valid. See Airadigm II, 547 F.3d at 773 (giving effect to the Stipulation at issue in this case); Matter of Superior Toy & Mfg. Co., 78 F.3d 1169, 1175 (7th Cir.1996) (quoting Seidle v. GATX Leasing Corp., 778 F.2d 659 (11th Cir.1985)); Matter of Stoecker, 5 F.3d 1022, 1029 (7th Cir.1993); cf. also Standard Brass Corp. v. Farmers Nat'l Bank of Belvidere, 388 F.2d 86, 89 (7th Cir.1967). They disagree merely as to the Stipulation's meaning. We start there. As with matters of contract interpretation, the meaning of a stipulation presents a question of law subject to de novo review.[6]Braxton v. United States, *655 500 U.S. 344, 350, 111 S.Ct. 1854, 114 L.Ed.2d 385 (1991); Tidemann v. Nadler Golf Car Sales, Inc., 224 F.3d 719, 723 (7th Cir.2000) (meaning of stipulation reviewed de novo).
Applying those principles in this case is relatively straightforward.[7] Paragraph 2 of the Stipulation speaks directly to Claim 14. The second sentence provides that "the claims of TDS arising from its advances of funds in accordance with the 2000 Plan shall be allowed in the 2006 Bankruptcy Case in the amount of such loans with interest to the extent provided in the 2000 Plan" (emphasis added).
The language of Paragraph 2 yields at least two possible readings of how much the FCC was allowed to challenge. The most expansive reading of Paragraph 2, which we reject, is that the FCC was completely unfettered to argue about Claim 14. On this reading, Claim 14 was allowed only "to the extent" of its treatment under the 2000 Plan. The construction is unwieldy and assumes that the antecedent of "to the extent provided in the 2000 Plan" at the very end of the quoted sentence in Paragraph 2 is the "claims of TDS" at the very beginning of the sentence. That reading would allow the FCC to argue that TDS was only ever entitled to the purported collateral securing the cash advances, rather than limiting the attack to the amount of the loans actually advanced. Thus, if Claim 14 was really an asset sale, then it would leave TDS with only an unsecured claim for the value of that collateral. See § 101(5) (claim broadly defined to encompass damages claims for breach of contract).
The expansive reading, however, is not the best reading. Basic principles of contract interpretation teach that "to the extent provided in the 2000 Plan" refers to "interest" or, at most, "amount of such loans with interest" because of the "last antecedent rule."[8] The last antecedent rule provides that "[r]elative and qualifying phrases, grammatically and legally, where no contrary intention appears, refer solely to the last antecedent." Shelby County State Bank v. Van Diest Supply Co., 303 F.3d 832, 836 (7th Cir.2002) (quoting J.G. Sutherland, STATUTES AND STATUTORY CONSTRUCTION § 267, at 349 (1st ed. *656 1891)); see also Barnhart v. Thomas, 540 U.S. 20, 26, 124 S.Ct. 376, 157 L.Ed.2d 333 (2003) (illustrating that "antecedent" for purposes of the rule means the immediately adjacent "noun or phrase"); Miniat v. Ed Miniat, Inc., 315 F.3d 712, 715 (7th Cir.2002) (employing the last antecedent rule in contract interpretation); Peterson v. Sinclair Ref. Co., 20 Wis.2d 576, 123 N.W.2d 479, 486 (1963). Applying the last antecedent rule means that the parties were generally free to fight about, at most, the amount of funds that were actually advanced and the calculation of the interest.
And although the last antecedent rule will give way where a contrary intention appears (Miniat, 315 F.3d at 715; O'Kane v. Apfel, 224 F.3d 686, 690 (7th Cir.2000)), the rest of Paragraph 2 only bolsters the reading. The Stipulation states that Claim 14 shall be allowed in the "amount" of the loans with interest. If the FCC were free to contend that the loans were really a sale of assets, it would not only require a "bookend antecedent rule," it would read out the part of the sentence that describes the amount of the claim. Language supporting the FCC's argument would look quite different from that contained in the Stipulationsomething like, "TDS shall have an allowed claim based on its advance of funds to Airadigm." Language along those lines would have left the parties free to fight about the economic substance of the advances of funds.
None of the issues reserved in the Stipulation, including the oral modifications, mandates a different result. When a contract is modified, its terms consist "of not only the new terms agreed upon, but also as many of the terms of the original contract which were not abrogated by the modification." Estreen v. Bluhm, 79 Wis.2d 142, 255 N.W.2d 473, 479 (1977); see also Curia v. Nelson, 587 F.3d 824, 830 (7th Cir.2009) (a modified contract "introduces new elements into the details * * * but leaves the general purpose and effect undisturbed," except to the extent the modification cancels the earlier agreement). As originally drafted, Paragraph 4 of the Stipulation reserved the ability to challenge, "without limitation, the right of the FCC and TDS to seek the inclusion and allowance of interest on their Allowed Claims." The in-court modifications expanded Paragraph 4: As counsel for TDS elaborated before the bankruptcy court, "[T]here is an unresolved issue as to the right to claim interest on those claims. * * * [T]here are also * * * open questions with respect to the nature or extent of security for various claims."[9] TDS's counsel also referred to "other unresolved issues." Counsel for Airadigm said that Paragraph 4 reserves "all rights" but then listed only matters related to security interests as being reserved.[10] The canon of construction ejusdem generis teaches that the general reservation of rights claimed by Airadigm should be limited to "items of the same type or nature as those specifically enumerated." United States v. Sec. Mgmt. Co., 96 F.3d 260, 265 (7th Cir.1996) (discussing Wisconsin law). In other words, the FCC had to argue that its challenge to Claim 14 is like the specific items that were reserved; it has not attempted to do so.
*657 As to the "substantive arguments" that the FCC alludes to, the FCC essentially leaves us in the dark as to what those arguments might be. In the absence of extrinsic evidencewhose absence is puzzling given that these were the FCC's argumentsit must do more. First, it is axiomatic that courts interpret contracts so as to give effect to all of their provisions. Premcor USA, Inc. v. Am. Home Assurance Co., 400 F.3d 523, 527 (7th Cir. 2005) (describing the principle as a "cardinal rule" of contract interpretation); First Am. Title Ins. Co. v. Dahlmann, 291 Wis.2d 156, 715 N.W.2d 609, 616-17 (2006) (a construction of a contract that neutralizes one provision should not be adopted if another construction "which gives effect to all of its provisions is consistent with the general intent"); Pierce v. Physicians Ins. Co. of Wis., Inc., 278 Wis.2d 82, 692 N.W.2d 558, 566 (2005) (same principle with respect to stipulations). So the argument that the breadth of the ambiguous, in-court modification swallows Paragraph 2 of the Stipulation is as close to a non-starter as is possible.
More importantly, we have stated that although an ambiguous contract presents a factual issue, parties may not rest on their laurels at summary judgment: a court should provide the most plausible reading of an ambiguous contract where parties do not point to extrinsic evidence at summary judgment. N.E. Communications of Wis., Inc. v. CenturyTel, Inc., 516 F.3d 608, 611 (7th Cir.2008) ("When only the contract's language is in evidence, however, a court renders its own decision whether or not the document is ambiguous."). That rule is in keeping with the numerous cases from this circuit that teach that summary judgment is the "put up or shut up" moment in the life of a case. E.g., Everroad v. Scott Truck Sys., Inc., 604 F.3d 471, 476 (7th Cir.2010). The FCC has not presented the Court with extrinsic evidence that suggests that the broader issues that the parties intended to reserve include disallowing a claim in its entirety. Given that Paragraph 2 allows the Claim 14 Loans in the amount of the loans, the argument that Paragraph 4 similarly permits parties to argue that a claim is disallowed is not just implausible, it does violence to the rest of the Stipulation. Cardinal principles of interpretation militate against adopting the FCC's position. Premcor USA, 400 F.3d at 527. On these grounds alone, the FCC's challenge to Claim 14 must be rejected.
Moreover, even if the Stipulation had left room to argue that Claim 14 should be disallowed, we still would conclude that a recharacterization action is off the table. Again, recharacterization was the only issue that the FCC preserved. To see why it is off the table, we need to say a little about recharacterization actions. In doing so, we repeat that this case does not require us to decide whether and under what circumstances recharacterization actions may be appropriate in this circuit.
The overwhelming weight of authority supports the proposition that bankruptcy courts act within their equitable powers when they recharacterize loans as infusions of equity. In re SubMicron Sys. Corp., 432 F.3d 448, 454-55 (3d Cir.2006); In re Official Comm. of Unsecured Creditors for Dornier Aviation (N. Am.) Inc., 453 F.3d 225, 233 (4th Cir.2006); In re AutoStyle Plastics, Inc., 269 F.3d 726, 748 (6th Cir.2001); In re Hedged-Invs. Assocs., Inc., 380 F.3d 1292, 1298 (10th Cir. 2004); but see In re Pac. Express, Inc., 69 B.R. 112, 115 (9th Cir.BAP 1986).[11] Invariably *658 citing the seminal case of Pepper v. Litton, 308 U.S. 295, 60 S.Ct. 238, 84 L.Ed. 281 (1939), these cases reason that bankruptcy courts should look to the substance rather than the form of transactions. Likewise, these cases reason that courts have equitable authority to properly characterize a transaction because the term "claim" is a Bankruptcy Code term of art (see 11 U.S.C. § 101(5)), and allowed claims in bankruptcy receive better treatment than equity interests. E.g., In re Insilco Techs., Inc., 480 F.3d 212, 218 & n. 10 (3d Cir.2007) ("[E]quity holders receive nothing unless all creditors are paid in full.").
Critically for our purposes, actions for recharacterization differ from actions for equitable subordination pursuant to Section 510(c) of the Bankruptcy Code. In an equitable subordination action, the analysis focuses on the behavior of a creditor, knocking down the status of a claim where a creditor engages in inequitable conduct. See In re Kreisler, 546 F.3d 863, 865 (7th Cir.2008) ("Equitable subordination is generally appropriate only if a creditor is guilty of misconduct that causes injury to the interests of other creditors."); Matter of Lifschultz Fast Freight, 132 F.3d 339, 344 (7th Cir.1997) (equitable subordination allows the bankruptcy court to root out illgotten gains). In contrast, recharacterization focuses on the underlying substance of the disputed transactionthat is, whether the filed claim satisfies the Bankruptcy Code's definition of "claim." Hedged-Invs., 380 F.3d at 1297; Dornier Aviation, 453 F.3d at 232; cf. also United Airlines, Inc. v. HSBC Bank USA, N.A., 416 F.3d 609, 612 (7th Cir.2005) ("It is unlikely that the [Bankruptcy] Code makes big economic effects turn on the parties' choice of language rather than the substance of their transaction * * *."). In other words, recharacterization is a definitional attack.
Determining whether a claim should be recharacterized as an interest thus comes logically prior to determining whether a claim should be subordinated: equitable subordination presumes that the claim is in fact a "claim" within the meaning of the Code. Recharacterization occurs when one has mislabeled a transaction. SubMicron Sys., 432 F.3d at 454 (explaining that recharacterization is focused on whether "a debt actually exists"). As one bankruptcy court judge explained, "Determining the equitable subordination issue prior to determining whether the advance is a loan or a capital contribution is similar to taking the cart before the horse." Diasonics, Inc. v. Ingalls, 121 B.R. 626, 630 (Bkrtcy.N.D.Fla.1990). Less colloquially, when a claim is equitably subordinated, a court disregards a party's formal rights; when a claim is recharacterized, a court determines what those formal rights are in the first instance.
With that broader understanding of recharacterization actions, it becomes evident why the FCC is barred by the Stipulation from seeking to have Claim 14 recharacterized as an equity interest. The Stipulation acknowledges ad nauseum that TDS had claims that would be allowed in the 2006 bankruptcy. The caption of the Stipulation reads "STIPULATION OF CLAIMS OF THE FEDERAL COMMUNICATIONS COMMISSION AND TELEPHONE & DATA SYSTEMS, INC." And with respect to the Claim 14 Loans, the parties agreed that "the claims of TDS arising" from the loans "shall be allowed in the 2006 *659 bankruptcy" (emphasis added). The language makes the case similar to In re Insilco Techs., Inc., 480 F.3d 212 (3d Cir. 2007). That case concerned a Chapter 11 liquidation in which the creditors' committee moved to have a trustee appointed. There was a dispute, but the motion was resolved through a settlement agreement. The settlement agreement specified that the "Senior Lenders' * * * claims against the Debtors * * * are fully and finally allowed" in an amount that was spelled out in the agreement. Insilco, 480 F.3d at 216.
In rejecting an effort to have the claims recharacterized as equity, the Third Circuit noted that in bankruptcy law, the terms "claim" and "allowed" are terms of art. A claim is a "right to payment, whether or not such right is reduced to judgment, liquidated, unliquidated, fixed, contingent, matured, unmatured, disputed, undisputed, legal, equitable, secured, or unsecured." 11 U.S.C. § 101(5)(A). The term is broadly defined, so as to include legal rights. E.g., Fogel v. Zell, 221 F.3d 955, 960 (7th Cir.2000); McClellan v. Cantrell, 217 F.3d 890, 895 (7th Cir.2000) (claim based on fraud). When a claim is "allowed," that means that it is accepted as valid. See 11 U.S.C. § 502(a); Fed. R. Bankr.P. 3001(f) (properly filed and executed proof of claim is prima facie evidence that a claim is valid); Adair v. Sherman, 230 F.3d 890, 894 (7th Cir.2000).
Given the specialized meanings of the terms involved, the Insilco Court reasoned that the settlement agreement by its terms precluded an action for recharacterization. Because a recharacterization action implicates the validity of the underlying claim, a claim could not be deemed both valid (allowed) and not a claim at all: "[L]oans cannot be both allowable claims and equity investments; * * * the latter (an interest) is not a claim at all. By agreeing that the [disputed loans] are * * * allowable claims, [the parties] necessarily agreed that the [disputed loans] were true loans." Insilco, 480 F.3d at 218.
Although Insilco involved a settlement that the bankruptcy court approved as part of a consent order and reorganization plan, its reasoning is equally apt here. A contrary result would ignore the fact that claims and interests are separate animals in bankruptcy law. As one noted commentator has observed, the definitional provisions are "[t]he heart of any code" (Douglas G. Baird et al., BANKRUPTCY: CASES, PROBLEMS, AND MATERIALS 31 (Rev. 3d ed. 2001)), and the parties cannot claim ignorance of building-block terms. As in Insilco, the parties agreed that the "claims" would be "allowed." There is simply no way that a claim could be "allowed" as a claim if it were, in fact, an equity interest. Moreover, Paragraph 2 of the Stipulation does Insilco one better by referring to TDS's advances of funds as "loans." Attempting to call the loans equity is too much for any plausible construction of the Stipulation to bear.
Thus, even if the Stipulation had included a broad reservation of rights, we would not accept the FCC's argument on the only issue that the FCC preserved for appealrecharacterization. Accordingly, the judgment of the district court with respect to Claim 14 is affirmed.

B. Claim 15
Claim 15 stands on different footing with respect to the Stipulation. Although the Stipulation provides that the claim of TDS as assignee of OEDA "shall be allowed in the 2006 Bankruptcy case," the 2000 Plan provides two different treatments for the claim. Critically, the parties do not define OEDA's claim separate and distinct from its treatment under the 2000 Plan. E.g., *660 TDS Br. at 44 (implicitly agreeing with the district court's conclusion that the Stipulation transferred "the 2000 Plan rights"); id. at 48-49 (discussing whether the Primary Plan or Back-up Plan applied to Claim 15). We conclude both that the bankruptcy court did not abuse its discretion in interpreting the 2000 Plan and that TDS is judicially estopped to make the argument that it advances with respect to Claim 15.
Before OEDA assigned its rights to TDS, OEDA contended that the Primary Plan applied and that it was therefore entitled to $49 million. OEDA asked the bankruptcy court to order TDS to fund the Reinstatement Loan, which under the 2000 Plan would have paid the claim in the amount of $49 million. The bankruptcy court denied OEDA's motion and concluded that the Back-up Transfer Date occurred on November 14, 2002. Under Section 10.7 of the 2000 Plan, the Back-up Transfer Date triggered the $2 million payment in the Back-up Plan: "On the Back-up Transfer Date * * * [TDS] shall pay OEDA $2 million in full satisfaction of its secured claims."
In 2004, TDS filed a declaratory judgment action against OEDA. TDS took the position that OEDA was entitled only to $2 million under the 2000 Plan. See Loose Pleadings, Vol. V, Ex. 7; see also App. 221 (settlement agreement). As part of the settlement of that action, OEDA assigned to TDS whatever rights it had against Airadigm.[12] TDS filed Claim 15. Subsequently, the bankruptcy court sustained the FCC's objection and disallowed the claim; the bankruptcy court reasoned that the Back-up Plan applied to the OEDA claim. The Back-up Plan applied because the "Back-up Transfer Date" had been reached. Section 10.7 of the 2000 Plan provided that, on the Back-Up Transfer Date, OEDA was entitled to $2 million from TDS. Therefore, TDS (as the assignee of OEDA's rights) had only a right of payment from itself, rather than a claim for $49 million.[13]

1. The Bankruptcy Court Did Not Abuse its Discretion
The plain language of the 2000 Plan provides that OEDA was entitled only to $2 million, meaning, as the FCC put it, that TDS stepped into satisfied shoes. In re Doctors Hosp. of Hyde Park, Inc., 337 F.3d 951, 956-57 (7th Cir.2003) (assignor can give only that which he has). Section 10.7 of the 2000 Plan, which is titled "Payment to OEDA," provides that "[o]n the Back-up Transfer Date * * * [TDS] shall pay OEDA $2 million in full satisfaction of its secured claims." As the bankruptcy court succinctly laid out, the Back-up Transfer Date is defined as the tenth business day after the Funding Termination Date. 2000 Plan § 2.5. The Funding Termination Date is defined as the date when TDS's obligation to fund the "Working Capital Loan" terminated. That date was extendable at TDS's option. 2000 Plan § 6.7.
Moreover, under the literal terms of the 2000 Plan, the Primary Plan could not govern, because claims were to be paid only when the licenses were reinstated something which, because of NextWave, never actually took place. And because it never took place, TDS never had the obligation to fund the loans that would have paid OEDA's claims. TDS's analysis accounts only for the general purpose of the *661 planone option if Airadigm had the licenses and another option if it did notwithout discussing the fact that the contingencies in the 2000 Plan were not just linked to whether Airadigm had the licenses, but also to whether Airadigm had the financing to pay the claims at issue.
To be sure, the conundrum presents thorny questions of interpretation, but we do not think that the bankruptcy court abused its discretion in interpreting the plan. Instead of pointing out how the bankruptcy court abused its discretion, TDS offered only its own conclusory assertions to the effect that the FCC's Claim, which was allowed, had to be treated the same as the OEDA claim. But TDS has not shown how, as a matter of plan interpretation, all creditors had to be subject either to Primary Plan treatment or Backup Plan treatment. In light of the labyrinthine nature of the 2000 Plan, TDS's conclusion is hardly self-evident. Therefore, we reverse the judgment of the district court and direct it to enter judgment consistent with the bankruptcy court's treatment of the claim.

2. TDS is Judicially Estopped to Argue that Claim 15 Should be Allowed
Independent of the foregoing, we also note that TDS is not entitled to judgment on Claim 15 because it is judicially estopped to argue that it is entitled to the $49 million claim. See Matter of Cassidy, 892 F.2d 637, 641-42 (7th Cir.1990).
Judicial estoppel is an equitable concept that prevents parties from playing "fast and loose" with the courts by prevailing twice on opposing theories. Butler v. Vill. of Round Lake Police Dep't, 585 F.3d 1020, 1022 (7th Cir.2009). The doctrine is "invoked by a court at its discretion." New Hampshire v. Maine, 532 U.S. 742, 750, 121 S.Ct. 1808, 149 L.Ed.2d 968 (2001) (quoting Russell v. Rolfs, 893 F.2d 1033, 1037 (9th Cir.1990)). The doctrine's purpose is to protect the integrity of the judicial process. Johnson v. ExxonMobil Corp., 426 F.3d 887, 891 (7th Cir.2005). Put a bit colorfully, judicial estoppel "protect[s] the courts from being manipulated by chameleonic litigants who seek to prevail, twice, on opposite theories." Levinson v. United States, 969 F.2d 260, 264 (7th Cir.1992). Without judicial estoppel, parties' inconsistent litigating positions could undermine the integrity of the judiciary by "creat[ing] the perception that either the first or the second court was misled * * *." Moses v. Howard Univ. Hosp., 606 F.3d 789, 792 (D.C.Cir. 2010) (quoting Maine, 532 U.S. at 750, 121 S.Ct. 1808).[14]
Although the Supreme Court has emphasized that there is no formula for judicial estoppel, it has identified at least three pertinent factors for courts to examine: (1) whether the party's later position was "clearly inconsistent" with its earlier position; (2) whether the party against whom estoppel is asserted in a later proceeding has succeeded in persuading the court in the earlier proceeding; and (3) whether the party "seeking to assert an inconsistent position would derive an unfair advantage or impose an unfair detriment on the opposing party if not estopped." Maine, 532 U.S. at 750-51, 121 S.Ct. 1808 (collecting cases and repeating that no rigid formula applies to the analysis); see also Thore v. Howe, 466 F.3d 173, 181 (1st Cir.2006) ("The contours of the *662 judicial estoppel doctrine are not sharply defined * * *."); Moses, 606 F.3d at 792 (party may not change positions "simply because his interests have changed").
Judicial estoppel does not come into play only when a party attempts to retreat in a second case from an argument on which it prevailed in a separate earlier case. It also "prevents a party from prevailing in one phase of a case on an argument and then relying on a contradictory argument to prevail in another phase." Pegram v. Herdrich, 530 U.S. 211, 227 n. 8, 120 S.Ct. 2143, 147 L.Ed.2d 164 (2000) (citing Rissetto v. Plumbers & Steamfitters Local 343, 94 F.3d 597, 605 (9th Cir.1996)); see also Al's Serv. Ctr. v. BP Prods. N. Am., Inc., 599 F.3d 720, 728 (7th Cir.2010) (reasoning that, even with regard to two separate suits, success at an early stage of the earlier litigation would be no bar to the application of the doctrine in subsequent litigation); Cont'l Ill. Corp. v. Comm'r, 998 F.2d 513, 518 (7th Cir. 1993) (although the doctrine is normally raised in successive suits "it is not so limited"); Charles Alan Wright, Arthur R. Miller & Edward H. Cooper, 18B FEDERAL PRACTICE AND PROCEDURE § 4477, at 552 (2d ed. 2002) (theories of judicial estoppel draw from the fact of inconsistency rather than the fact of adjudication). Likewise, there is no requirement that the parties be the same for judicial estoppel to apply. What matters for purposes of judicial estoppel is whether, in reaching its earlier decision, the court relied on the representation of the one against whom estoppel is asserted. Rederford v. U.S. Airways, Inc., 589 F.3d 30, 38 (1st Cir.2009); Lowery v. Stovall, 92 F.3d 219, 223 n. 3 (4th Cir.1996) (judicial estoppel does not have a mutuality requirement because the doctrine "is designed to protect the integrity of the courts rather than any interest of the litigants").
In this case, TDS successfully argued before the bankruptcy court that the Back-up Plan controlled with respect to the $49 million claim at issue. Before OEDA assigned its claim to TDS, OEDA filed a motion with the bankruptcy court which asked the court to interpret the 2000 Plan and force TDS to make the Reinstatement Loan and fund OEDA's claim. TDS opposed OEDA's motion, arguing that the Back-up Plan controlled with respect to OEDA. TDS's argument then was nearly identical to the description of the bankruptcy judge's ruling on Claim 15 that we set out above. Compare App. 251 (TDS's position with respect to OEDA's motion), with App. 84 (bankruptcy court's decision with respect to Claim 15). The bankruptcy court denied OEDA's motion on the merits, based on "the briefs and supporting papers of the parties," as well as oral argument (which was basically a repeat of TDS's position in its brief). As part of that ruling, the bankruptcy court determined that the Back-up Transfer Date occurred on November 14, 2002. App. 219. Because the Back-up Transfer Date occurred, TDS did not have to fund the Reinstatement Loan that would have paid OEDA's $49 million claim. The result of denying OEDA's motion was a savings of $47 million for TDS.
Application of judicial estoppel seems particularly appropriate in the setting of this case, in which the parties were assisting the bankruptcy court in interpreting the meaning of the 2000 Plan. In light of the numerous interpretive difficulties caused by the NextWave decision, the bankruptcy court was faced with no small task. If we accepted TDS's argument on appeal, it would give the impression that, rather than helping the bankruptcy court to interpret the plan, TDS hoodwinked that court. TDS's position is diametrically opposed to the position that it took before *663 the bankruptcy court. Moreover, TDS would receive an "unfair advantage" (Maine, 532 U.S. at 751, 121 S.Ct. 1808), because if OEDA had a $49 million claim under the Primary Plan, then TDS would have been obligated to pay it. Now that the bankruptcy is closed, not only would TDS be entitled to the value of the claim, it would be relieved from the burden of paying for the claim. Its inconsistent litigation position would yield a king's ransom.
Finally, we see in TDS's brief no "reasonable justification" for the change in its litigating position. Thore, 466 F.3d at 185; see also Johnson Serv. Co. v. Transamerica Ins. Co., 485 F.2d 164, 175 (5th Cir.1973) (reasoning that estoppel is appropriate for "cold manipulation and not an unthinking or confused blunder"). Based on our review of the matter, we conclude that the successful contention made by TDS when it disputed OEDA's right to payment cannot "exist side by side" (Cleveland v. Policy Mgmt. Sys. Corp., 526 U.S. 795, 803, 119 S.Ct. 1597, 143 L.Ed.2d 966 (1999) (SSDI and ADA claims not mutually exclusive)) with its current position. Therefore, TDS was not entitled to change positions based on the "exigencies of the moment" (Maine, 532 U.S. at 750, 121 S.Ct. 1808 (quoting United States v. McCaskey, 9 F.3d 368, 378 (5th Cir.1993))), and even if the bankruptcy court had abused its discretion, TDS would not be entitled to relief.

C. Claim 16
Finally, we affirm the judgment of the district court with respect to Claim 16. As with Claim 15, the Stipulation does not answer the question of whether the Backup Plan or the Primary Plan was intended to govern. The FCC argues that the value of the claim is zero because under the Back-up Plan, Ericsson was not entitled to payment and its liens would have been extinguished. We conclude that even if the Back-up Plan applied, the 2000 Plan did not extinguish the liens, and the liens may give rise to a claim in a subsequent bankruptcy.
The default rule is that a lien is extinguished as part of a plan of reorganization unless the plan says otherwise. 11 U.S.C. § 1141(c) (property dealt with by a plan is "free and clear of all claims and interest of creditors"); Matter of Penrod, 50 F.3d 459, 462-63 (7th Cir.1995). Section 5.2 of the 2000 Plan specifically retained Ericsson's liens:
If Ericsson fails to receive payment with respect to any of the Reinstated Licenses, Ericsson shall retain its Liens on such Reinstated Licenses and the proceeds thereof to secure payment of the unpaid portion of its [claim]. Ericsson shall retain its Liens on any Licenses that are terminated and not reinstated and the related proceeds thereof.
The Back-up Plan provided that no payments would be made "on account of Claims against the Debtor," except as specified in the Back-up Plan, but did not purport to extinguish Ericsson's liens on licenses that were not reinstated. That feature makes the treatment of Ericsson different from the treatment of OEDA: as we have already observed, OEDA's Backup treatment stated that the payment was in full satisfaction of its secured claim. 2000 Plan § 10.7. We presume that the difference in the language of the plan is purposeful. LaSalle Nat'l Trust, N.A. v. ECM Motor Co., 76 F.3d 140, 144 (7th Cir.1996) (contract interpretation should give effect to each term). That means that, at first blush, TDS retains the liens.
The FCC's attempted trump card is to argue that NextWave means that the licenses were neither "Reinstated" nor "terminated *664 and not reinstated." We are not persuaded.
Principles of contract law apply to interpreting a plan of reorganization: "A confirmed plan of reorganization is in effect a contract between the parties and the terms of the plan describe their rights and obligations." Ernst & Young LLP v. Baker O'Neal Holdings, Inc., 304 F.3d 753, 755 (7th Cir.2002). And the primary purpose of contract interpretation is to give effect to the objective intent of the parties. Solowicz v. Forward Geneva Nat'l, LLC, 323 Wis.2d 556, 780 N.W.2d 111, 124 (2010). "By intent we * * * mean * * * the scope and purpose of the document as manifest by the language used." Id. (brackets omitted). The language in Section 5.2 that we quoted above was designed to ensure that Ericsson retained its liens regardless of what happened with Airadigm's petition to have the licenses reinstated. Everyone, including the FCC, thought that Airadigm did not have the licenses when the 2000 Plan was drafted. Therefore, and in light of the manifest purpose of the 2000 Plan as revealed through the undisputed circumstances surrounding its adoption (cf. Ehlinger v. Hauser, 313 Wis.2d 718, 758 N.W.2d 476, 486 (2008)), we find no ambiguity as to the status of the Ericsson liens. The FCC has pointed us to no evidence that any of the parties contemplated any other treatment than to preserve the liens. "We will not bend the language of a contract to create an ambiguity when none exists, but neither will we follow a literal interpretation when [to do so] would lead to an unreasonable or absurd result." Chi Bd. of Options Exch. v. Conn. Gen. Life Ins. Co., 713 F.2d 254, 258 (7th Cir.1983) (citation omitted).
As a last ditch effort, the FCC points out that even if Ericsson retained the liens, a lien is not a right to payment. Not true. The term "claim" is defined broadly in the Bankruptcy Code. And under Johnson v. Home State Bank, a right that is purely in rem may give rise to a "right to payment." 501 U.S. 78, 84-86, 111 S.Ct. 2150, 115 L.Ed.2d 66 (1991) ("[W]e must infer that Congress fully expected that an obligation enforceable only against a debtor's property would be a `claim' under § 101(5) of the Code."). In Johnson, the Court ruled that a mortgage lien, which survived an individual debtor's discharge of personal liability in a Chapter 7 bankruptcy case, gave rise to a claim subject to inclusion in the debtor's subsequent Chapter 13 reorganization plan. Thus, the FCC's argument that TDS does not have a claim in the 2006 bankruptcy because there was no obligation to make payments on the Ericsson claim under the 2000 Plan's Back-up Plan (FCC Br. at 53) is unavailing. TDS had a claim as defined by the Bankruptcy Code in the 2006 bankruptcy because it had an in rem right that survived the 2000 Plan. That is a key lessonor at least a lesson that follows naturallyfrom Johnson. Under the 2000 Plan, Ericsson was going to get paid or keep its liens. TDS, as the assignee of Ericsson's claim, took the same right.
Therefore, the judgment of the district court is affirmed with respect to Claim 16.

IV. Conclusion
For the reasons set forth above, the judgment of the district court is AFFIRMED in part and REVERSED in part. The district court's judgment is affirmed, except as to the treatment of Claim 15. As to that claim, the district court is directed to enter judgment consistent with the bankruptcy court's treatment of the claim.
NOTES
[*]  The Honorable Robert M. Dow, Jr., of the United States District Court for the Northern District of Illinois, sitting by designation.
[1]  The Minimum Licenses was a number that varied based on the bandwidth of the licenses and the population covered by the licenses. If fewer than the Minimum Licenses were reinstated, a complicated formula governed the amount that OEDA was owed. See 2000 Plan § 6.12.
[2]  Ericsson's full claim was for $71 million. Of that, $30 million was paid as part of one of the cash advances made by TDS and is not in issue. The remaining $41 million provides the basis for the claim in this appeal.
[3]  By describing them as "loans," we do not mean to beg the questionalthough, as it happens, the case does not require us to answer the question either.
[4]  TDS moved for summary judgment on Claim 14, the parties filed cross-motions for summary judgment on Claim 16, and the bankruptcy court held a trial on Claim 15.
[5]  The bankruptcy court concluded that bankruptcy judges do not have equitable authority to recharacterize claims pursuant to Section 105(a) of the Bankruptcy Code. We do not reach that issue as part of this ruling.
[6]  The FCC urges that more deferential review is appropriate because the bankruptcy judge was uniquely situated to interpret the Stipulation. The idea is similar to the doctrine of extrinsic ambiguity, which teaches that in some cases even seemingly plain terms in a contract prove murky when placed within a broader factual context. See, e.g., Green v. UPS Health and Welfare Package for Retired Employees, 595 F.3d 734, 738 (7th Cir.2010). The FCC's argument is that the bankruptcy judge has the broader context and is therefore in a superior position to interpret the Stipulation. We are unconvinced. First, the bankruptcy judge's opinion does not suggest reliance on any specialized knowledge to which we ought defer. He based his interpretation of the Stipulation on the same writing and oral statements that are before us. And while it is true that the FCC stated in court that it intended to reserve other "substantive arguments" it had previously made to the court, the FCC has not informed us what those arguments weresomething that it plainly could have done.
[7]  The FCC notes that there may be a question as to whether federal or state law applies to the interpretation of a litigation stipulation in bankruptcy. However, we agree that general principles of contract interpretation yield the same result regardless of which substantive law is applied.
[8]  The word "such" often adds little meaning while introducing imprecision. See, e.g., H.W. Fowler, A DICTIONARY OF MODERN ENGLISH USAGE 602 (2d ed. 1965) (noting that the term in legal writing is often merely "a starchy substitute for that"). What meaning the term adds, however, undermines the FCC's argument. "Such" is often used by lawyers to mean "aforementioned." See Bryan A. Garner, GARNER'S MODERN AMERICAN USAGE 758-59 (2003) (referring to such as a "pointing word"). Yet, by referring to the "aforementioned" "advances of funds" as "loans," the Stipulation concedes their status as loans. In addition, if one substitutes "loans with interest" for the aforementioned "advances of funds," the Stipulation reads: "[T]he claims of TDS arising from its advances of funds in accordance with the 2000 Plan shall be allowed in the 2006 Bankruptcy Case in the amount of such [advances of funds] to the extent provided in the 2000 Plan." Courts frequently turn to rules of grammar to aid interpretation (e.g., Barnhart v. Thomas, 540 U.S. 20, 26, 124 S.Ct. 376, 157 L.Ed.2d 333 (2003)), and in this case those rules militate against the FCC's argument.
[9]  Matters related to security arguably were already referenced in the Stipulation as written, because Paragraph 4 reserved the right to challenge interest on claims, and only oversecured creditors may be entitled to interest on their claims under 11 U.S.C. § 506(b).
[10]  Counsel for Airadigm stated in full: "Your Honor, I think Paragraph 4 is broad. It reserves all rights. We just want to be clear it includes the rights of security interests, protection of security interests and value of secured claims."
[11]  This Court has acknowledged that recharacterization is distinct from equitable subordination but has never definitively stated whether we recognize a cause of action for recharacterization. See Matter of Lifschultz Fast Freight, 132 F.3d 339, 345 n. 3 (7th Cir.1997).
[12]  The parties dispute whether the assignment was valid, a question which we need not reach.
[13]  As the bankruptcy court noted, the actual proof of claim was filed for $40 million plus interest. App. 81, 89.
[14]  The FCC did raise the issue of judicial estoppel in its opening brief (FCC Br. at 46-47), although the doctrine can be raised by courts sua sponte because judicial estoppel concerns the integrity of the judicial system independent of the interests of the parties. Grigson v. Creative Artists Agency, L.L.C., 210 F.3d 524, 530 (5th Cir.2000).
