These appeals arise from a Chapter 7 asset sale for the liquidating bankruptcy estate of C.W. Mining Co., a former coal mining operation in Emery County, Utah. The four appellants did business with C.W. Mining before its involuntary bankruptcy. They now claim various assets that the bankruptcy trustee, Kenneth A. Rushton, sold to an unrelated entity, Rhino Energy LLC.
Standing in the way of the appellants’ claims is one of the Bankruptcy Code’s mooting provisions, 11 U.S.C. § SbSOn).1 Under this statute, we can grant the appellants no relief that would affect the validity of Rushton’s sale to Rhino. The question then for each appellant is whether any relief can be granted that would not affect *552the sale’s validity. The district court, which first addressed these appeals from the bankruptcy court, answered that question in the negative and thus dismissed the appeals as moot.
As we further explain below, we DISMISS Rhino and its wholly owned subsidiary, Castle Valley Mining LLC, from these appeals, and exercising jurisdiction under 28 U.S.C. § 158(d)(1), we AFFIRM Nos. 12-4091, 12-4102, 12-4112, 12-4132, and 12-4144, and we REVERSE No. 12-4106.
In summary, we dismiss Rhino and Castle Valley from all appeals because no appeal seeks any relief affecting either entity
As against the remaining appellee, Rushton, we agree with the district court that ANR Co.’s appeal (No. 12-4091), COP Coal Development Co.’s first appeal (No. 12-4112), and Hiawatha Coal Co.’s first appeal (No. 12-4102) are moot. By raising only those claims that affect the sale order, ANR and COP waived any relief besides that which would violate § 363(m). And Hiawatha failed to contest Rushton’s arguments showing that no theories of relief are available except those that affect the sale order. Accordingly, we affirm those appeals.
We also affirm the district court’s judgment in OOP’s second appeal (No. 12-4132) and Hiawatha’s second appeal (No. 12-4144) because both appeals seek only to protect COP and Hiawatha’s first appeals from waiver for failing to appeal the sale order itself. But because we do not find any waiver for that reason, we cannot offer relief in either appeal and thus find both moot as well.
That said, in Charles Reynolds’s appeal (No. 12-4106), Reynolds has consistently raised a statutory claim for relief that does not affect the validity of the sale, and the district court mistakenly relied' on an unpublished opinion to decide otherwise. Accordingly, we reverse his appeal and remand it to the district court for proceedings consistent with this opinion.
I. Background
Before it was forced into bankruptcy, C.W. Mining mined coal on land belonging to two related entities, COP and ANR. C.W. Mining had the exclusive right to mine coal on COP and ANR’s property per leases C.W. Mining had with both.2
*553Hiawatha also mined coal, but on a much smaller scale than C.W. Mining. Originally, Hiawatha had been in charge of operations at ANR’s mine, but after Hiawatha ran into trouble with mining regulatory agencies, Hiawatha and ANR jointly agreed to pass control of the operations to C.W. Mining.
Of the two mines, only OOP’s mine, the Bear Canyon mine in Emery County, Utah, was active. Charles Reynolds ran C.W. Mining’s coal mining operations there. He and his family, including ten children, lived in a house connected to the mine’s major operations center (the “scale house”). COP owned the scale house, but because the scale house was under C.W. Mining’s exclusive control per its mining contract with COP, Reynolds lived at the home with C.W. Mining’s permission.
A.The Bankruptcy
C.W. Mining’s bankruptcy arose from a breach of contract action brought by Aquila, Inc., which claimed that C.W. Mining failed to deliver coal as contracted. In 2007, Aquila obtained a favorable judgment for $24.8 million. See C.O.P. Coal Dev. Co. v. C.W. Mining Co. (In re C.W. Mining Co.), 641 F.3d 1235, 1236 (10th Cir.2011). After the judgment, C.W. Mining and COP attempted to terminate their mining contract. But before they could do so, Aquila (along with two other C.W. Mining creditors) filed an involuntary Chapter 11 bankruptcy petition against C.W. Mining in January 2008.
After the petition was filed, C.W. Mining tried to transfer all of its operations to Hiawatha in June 2008. COP and ANR then entered into postpetition agreements with Hiawatha to mine coal in C.W. Mining’s stead. Hiawatha, in turn, used only C.W. Mining’s existing mining operations and even, at times, C.W. Mining’s name.
In September 2008, the bankruptcy court granted Aquila’s petition to keep C.W. Mining in involuntary bankruptcy. Two months later, in November 2008, the bankruptcy court converted the case into a Chapter 7 bankruptcy. This changed the bankruptcy from one of reorganization (where C.W. Mining would continue to exist after the bankruptcy) to one of liquidation (where all of C.W. Mining’s assets would be sold to provide its creditors with as much relief as possible). In that same month, Rushton was appointed the C.W. Mining bankruptcy estate’s trustee.
B. The Adversary Proceedings
Rushton filed several adversary proceedings in bankruptcy court to recover C.W. Mining’s assets, including its coal mining operation at the Bear Canyon mine, its scale house at the mine (which Reynolds was occupying at the time), and its contracts with ANR and COP (which both had attempted to transfer to Hiawatha). After several evidentiary hearings, the bankruptcy court ordered all assets to be returned to the estate. ANR, Hiawatha, Reynolds, and COP each appealed to the district court.
While their appeals were pending in the district court, Rushton sold the Bear Canyon mining operations, scale house, and mining contracts to another mining company, Rhino, for $15 million. Rushton and Rhino relied on the bankruptcy court’s prior rulings that established the estate’s ownership of the mining operations, scale house, and mining contracts. After reviewing the sale, the bankruptcy court issued an order finding that Rhino was a *554good faith purchaser and entitled to the protection of § 363(m). None of the appellants moved to stay the sale order, and the sale closed in August 2010 — months after the district court appeals were filed. On August 25, 2010, Rhino took possession and transferred the mining operation to its wholly owned subsidiary, Castle Valley, which promptly began mining.
After the sale closed, Rushton and Rhino moved to dismiss as moot the various appeals still pending in district court, citing § 363(m) mootness and, in the alternative, equitable mootness. The district court agreed with both mootness rationales and dismissed the underlying appeals. ANR, Hiawatha, Reynolds, and COP now appeal the district court’s mootness decisions to this court.
We provide additional background information as relevant to each claim.
II. Analysis
The appellants challenge the district court’s determination that their bankruptcy appeals are both statutorily and equitably moot. We review de novo the district court’s decision that a bankruptcy appeal is statutorily moot. Search Market Direct, Inc. v. Jubber (In re Paige), 584 F.3d 1327, 1334 (10th Cir.2009). Thus, we review de novo whether the appellants have no possibility of relief under § 363(m)3 (“ § 363(m) mootness” for short). See id. at 1336-37. The district court’s determination that these appeals are equitably moot is normally reviewed for abuse of discretion. In re Paige, 584 F.3d at 1335.
We begin our analysis with § 363(m) mootness. We first dismiss the appeals against Rhino and Castle Valley, as no appellant is seeking any relief that would affect those appellees. Then we address the remaining appeals against Rushton. We ultimately affirm the district court’s dismissal on § 363(m) mootness for every appellant except Reynolds. Thus, we need not address equitable mootness for those appeals. And because Rushton conceded that equitable mootness did not apply to Reynolds’s live claim, as we discuss below, we need not address equitable mootness for Reynolds’s appeal either. Finally, we address the extra appeals filed by two appellants, COP and Hiawatha. We affirm those appeals because they are mooted by both parties’ first appeals, respectively.
A. Appellees Rhino and Castle Valley
All appellants expressly disclaim any relief that would affect Rhino or Castle Valley or Rhino’s purchase from the bankruptcy estate.4 Since no appellant seeks relief affecting Rhino or Castle Valley, these appeals are moot as to both.
*555We now consider what effect § 363(m) has on the remaining appeals.
B. Nos. 12-4091, 12-4102, 12-4106, & 12-4112 Against Rushton
The appellants do not dispute that § 363(m) applies to the asset sale in question, that Rhino was a good-faith purchaser, and that no party requested a stay of the sale order. The only remaining question is whether § 363(m) permits the relief available to the appellants if they prevailed in these appeals.
The appellants first contend that § 363(m) applies only to appeals of the sale order itself, and since these four appeals are not of that order in particular, § 363(m) does not apply. But § 363(m)’s effect is not limited to appeals of the sale order itself where, as here, the sale order depends on the other orders on appeal. If these other orders are reversed or modified, the sale order would be effectively “modifi[ed]” as well, which is contrary to § 363(m)’s text.
Further, allowing such modifications would frustrate § 363(m)’s purpose of “protecting] the public’s interest in finalizing bankruptcy sales.” See Osborn v. Durant Bank & Trust Co. (In re Osborn), 24 F.3d 1199, 1203 (10th Cir.1994), abrogated in part on other grounds by Eastman v. Union Pac. R.R., 493 F.3d 1151, 1156 (10th Cir.2007). Section 363(m)’s protection is vital to “encouraging] buyers to purchase the debtor’s property” and thus “insuring] that adequate sources of financing remain available.” Id. In this way, § 363(m) ultimately “prevents] injury to creditors.” Id. But, as a result, “ § 363(m) [will] moot[] some appeals, namely, those in cases where the only remedies available are those that affect the validity of the sale.” Id. at 1203-04.
The appellants are correct, however, that the trustee bears the burden of proving that a bankruptcy appeal is moot under § 363(m). In re C.W. Mining Co., 641 F.3d at 1239. Even so, Rushton can carry his burden if the appellants fail to offer a permissible theory for relief. See In re W. Pac. Airlines, Inc., 181 F.3d at 1197 (finding an appeal moot under the Bankruptcy Code’s other mooting provision, 11 U.S.C. § 364(e),5 because the appellant “fail[ed] to point us to any other provision of the Bankruptcy Code or state law that would permit us to fashion a remedy that would not disturb the validity of the financing and terms of its collateralization”); see also Clarke v. United States, 915 F.2d 699, 703 (D.C.Cir.1990) (en banc); Ctr. for Biological Diversity v. Kempthome, 498 F.Supp.2d 293, 296-97 (D.D.C.2007). In other words, although the appellants bear no burden to produce evidence or argument, the appellants will not overcome a motion to dismiss for § 363(m) mootness simply because the trustee fails to disprove every possible legal remedy imaginable. Instead, the appellants must at least identify an available remedy that will not affect the sale’s validity.
And before us, the appellants point to various remedies that do not affect the sale’s validity. The crux of these remedies *556is whether the appellants can obtain part of the sale proceeds from the estate. The appellants contend that merely asserting that they may be entitled to some of the sale proceeds is enough to reverse the district court here. They point to a prior appeal arising out of this same bankruptcy where we found that § 363(m) did not moot the appeal because the appellant there, COP, claimed “it may be able to recover monetary relief,” and the appellee, Rushton, had not “affirmatively foreclosed” that possibility. In re C.W. Mining Co., 641 F.3d at 1239. They contend the same holds true here.
We disagree. In In re C.W. Mining Co., we were not reviewing a lower court’s decision on the merits of a motion to dismiss for mootness, as here; instead, we were reviewing a motion to dismiss the appeal in the first instance. While the In re C.W. Mining Co. appeal was pending, the asset sale to Rhino closed. Rushton and Rhino then moved to dismiss the appeal as moot, a motion we denied. But because of the posture of that case, the appellants could raise whatever arguments they thought helpful to avoid mootness. In this appeal, however, we are limited by the arguments made below, and not those minted on appeal. See, e.g., Somerlott v. Cherokee Nation Distribs., Inc., 686 F.3d 1144, 1148 (10th Cir.2012) (“[W]hen an argument was not raised before the district court but is instead advanced for the first time on appeal, the court will only reverse if the appellant shows the district court’s decision amounted to plain error.”); Turner v. Pub. Serv. Co. of Colo., 563 F.3d 1136, 1143 (10th Cir.2009) (“Absent extraordinary circumstances, we will not consider arguments raised for the first time on appeal.”).
More importantly, in In re C.W. Mining Co., we did not discuss what relief COP had sought below or whether COP had presented arguments to support finding a monetary remedy in that case. We also did not discuss what arguments Rush-ton made, if any, to affirmatively show that COP’s proffered remedy was not available. “Questions which merely lurk in the record [of earlier cases], neither brought to the attention of the court nor ruled upon, are not to be considered as having been so decided as to constitute precedents.” Cooper Indus., Inc. v. Aviall Svcs., Inc., 543 U.S. 157, 170, 125 S.Ct. 577, 160 L.Ed.2d 548 (2004) (internal quotation marks omitted). Thus, our opinion in In re C.W. Mining Co. does not control.
And in this appeal, the limits of appellants’ requests for relief are front and center. Rushton argues that, in the district court, each waived or abandoned any relief not barred by § 363(m). He also argues that, even if we reach their various claims for monetary relief here, the relief they request is not available under the facts of this case.
We decide whether Rushton is correct as to each appeal in turn.
1. Appeal No. 12-4091 — ANR’s Appeal
In the bankruptcy court, ANR sought only a determination that its agreement with C.W. Mining had in fact been terminated. See ANR App. 337. The bankruptcy court denied this request for relief because “ANR never provided [C.W. Mining] with any notice of default as required before termination of the ANR Operating Agreement,” thus ANR’s agreement with C.W. Mining had not been terminated. Id. at 13. In the alternative, ANR requested that Rushton “pay all unpaid royalties due to ANR” and others “as provided in” a set of documents ANR submitted to the bankruptcy court. Id. at 337-38. The bankruptcy court denied this request because the documents contained no evidence that *557C.W. Mining’s bankruptcy estate owed ANR any royalties. See id. at 14.
ANR appealed to the district court. In the meantime, the asset sale to Rhino was completed and the bankruptcy court issued the sale order. ANR’s mining agreement was included in the assets sold. Accordingly, Rushton and Rhino moved to dismiss ANR’s appeal. In response, ANR argued that its requested relief did not affect the validity of the sale order. Rather, ANR said, the “proper remedy” for its appeal was “declaratory relief through contract interpretation.” Id. at 326. In other words, ANR wanted the district court to find that its mining agreement with C.W. Mining was no longer in effect. The district court found that “[a]ny such declaratory relief would necessarily call into question the bankruptcy court’s interpretation of the ANR Agreement and, therefore, would affect the validity of the Sale Order.” Id. at 445. Thus, the district court granted the motion to dismiss. ANR again appealed.
Before this court, ANR does not contest that the declaratory relief it sought would affect the sale order. Rather, it argues, first, that reversing the bankruptcy court’s contract interpretation would not substantially affect the sale order and, second, that it is entitled to monetary relief from the bankruptcy estate in the form of a constructive trust.
Both arguments fail. First, §'363(m) does not speak in gradations; it “forecloses any remedy ... that would affect the validity of the ... sale,” even if the remedy would not bring about a significant change to the sale. See In re C.W. Mining Co., 641 F.3d at 1239 (emphasis added).
Second, ANR has waived any right to a constructive trust in this case. Neither before the bankruptcy court nor before the district court did ANR seek a constructive trust. And “we generally will not consider issues on appeal that were not presented” below. Golfland Entm’t Ctrs., Inc. v. Peak Inv., Inc. (In re BCD Corp.), 119 F.3d 852, 857 (10th Cir.1997) (internal quotation marks omitted).
Granted, we do have the discretion to consider such issues. See id. For instance, in In re BCD Corp., we exercised our discretion to hear an appeal where § 363(m) disallowed the relief requested below because “the evidence and legal arguments relating to the claim for proceeds are the exact same as” those made for the relief requested below. Id.
But those circumstances are not present here. Instead, after three stages of litigation, ANR still has yet to set forth the evidence and legal arguments showing it is entitled to an equitable remedy like a constructive trust. Before the bankruptcy court, ANR’s alternative claim for monetary relief lacked any evidence showing that ANR was due financial compensation. See, e.g., ANR App. 357 (listing ANR’s purported evidence of royalties owed, none of which showed royalties owed to ANR). And both before the bankruptcy court and district court, ANR has failed to demonstrate any financial losses to itself or any unjust enrichment to the bankruptcy estate resulting from the estate’s retention and subsequent sale of C.W. Mining’s ANR mining agreement.
In short, the only remedy ANR has preserved on appeal would unwind the sale order, and that is something ANR cannot do under § 363(m).
2. Appeal No. 12-4102— Hiawatha’s Appeal
Unlike ANR, Hiawatha did request relief below that would not affect the validity of the sale order. But before this court, Hiawatha does not rebut Rushton’s *558arguments showing that such relief is not available to Hiawatha. Therefore, although we disagree with the district court’s reasons for finding Hiawatha’s appeal moot, we agree that the appeal is in fact moot under § 363(m).
We briefly describe the background unique to Hiawatha’s appeal before explaining our decision.
a. Procedural History
Bankruptcy Court Action. In June 2008, during the “gap period” between when C.W. Mining’s creditors filed an involuntary bankruptcy petition and when the bankruptcy court granted that petition, C.W. Mining attempted to transfer essentially all of its assets to Hiawatha. Once Rushton became trustee of C.W. Mining’s bankruptcy estate, he filed an adversary action against Hiawatha to recover the transferred property under §§ 549(a) (avoiding the transfer) and 550(a) (recovering the transferred property).
Hiawatha opposed the action. It argued that Rushton could not avoid the transfer because Hiawatha was entitled to the protection of § 549(b), which disallows avoiding transfers in an involuntary bankruptcy where the transferee gave “value” (other than by assuming prepetition debts) in exchange for the assets. Hiawatha claimed it gave value to C.W. Mining by agreeing to hire C.W. Mining’s former employees and by agreeing to pay C.W. Mining’s trade creditors, royalties owed, property taxes, and any interest that accrued on C.W. Mining’s prepetition debt.
The bankruptcy court rejected this argument because Hiawatha’s only evidence of giving value — a declaration by Hiawatha’s president — did not show that Hiawatha (as opposed to C.W. Mining itself) actually made those various payments, let alone that Hiawatha did so “in exchange for” C.W. Mining’s assets. The district court also noted that to the extent Hiawatha actually made these payments as part of its own “ongoing business operations,” the payments did not count as “value” anyway. Hiaw. App. 336.
In response, Hiawatha filed a counterclaim for an improver’s lien under § 550(e), arguing that as a good faith transferee, it was entitled to a lien on the property based on its alleged expenditures to improve the property.
The bankruptcy court rejected Hiawatha’s counterclaim, too, because Hiawatha still had not produced any “credible evidence” showing that it had expended its own money to satisfy C.W. Mining’s post-petition debts. Rushton’s Supp. Hiaw. App. 680. More to the point, the court concluded that Hiawatha was not a good faith transferee. First, the court found that Hiawatha was “undercapitalized” at the time it took possession of C.W. Mining’s property because, up until then, Hiawatha’s “total annual receipts ... from its [prior] coal salvaging operations” were “only a few thousand dollars.” Id. at 682. Plus, Hiawatha “had no full-time employees, and its president ... was and remains employed as a full-time computer technician at another company.” Id. Thus, if Hiawatha actually had paid any of C.W. Mining’s debts, the court determined it had done so from the mine’s proceeds or by borrowing from C.W. Mining’s existing lenders. And second, the court found that, when Hiawatha received C.W. Mining’s assets, Hiawatha already knew that C.W. Mining was in involuntary bankruptcy and that Aquila had a $24 million judgment against C.W. Mining. Id. The court thus concluded Hiawatha was not acting in good faith.
Consequently, the bankruptcy court denied Hiawatha a lien on C.W. Mining’s assets and ordered that Hiawatha turn *559them over to Rushton. Hiawatha complied and then appealed the bankruptcy court’s decisions to the district court.
District Court Appeal. While Hiawatha’s appeal was pending, Rushton sold the estate’s assets to Rhino, including the mining assets that Hiawatha had claimed as its own. Rushton and Rhino, along with Rhino’s subsidiary Castle Valley, then moved to dismiss Hiawatha’s appeal as moot under § 363(m) because Hiawatha sought to recover assets that were included in the sale to Rhino.
In response, Hiawatha made various arguments about why its appeal was not moot under § 363(m), only two of which are relevant here. First, Hiawatha claimed “entitlement to the proceeds of the [asset] sale” based on.its improver’s lien theory in the bankruptcy court. Hiaw. App. 493 (citing § 550(e)) (emphasis in original). And second, in lieu of recovering the assets themselves, Hiawatha suggested the court “could order that Hiawatha be paid [their value] from the estate.” Id. at 505.
In Rushton’s reply, he rebutted all of Hiawatha’s claims for relief from the sale proceeds by citing “a bright-line rule” from Freightliner, LLC v. Central Refrigerated Svc., Inc. (In re Simon Transp. Svcs., Inc.), 138 Fed.Appx. 52 (10th Cir.2005), which states, in effect, that “if the proceeds of a § 363 asset sale have not been segregated, then the claimant cannot recover those proceeds.” Hiaw. App. 519. Because the sale proceeds had not been segregated from the estate’s other funds, Rushton reasoned that § 363(m) mooted Hiawatha’s monetary claims as well.
The district court granted the motion to dismiss. Adopting In re Simon’s bright-line rule, the court concluded that “because the relief Hiawatha seeks in this appeal would necessarily affect the validity of the Sale Order or would improperly seek recovery from commingled sale proceeds, ... [Rushton] ha[s] met [his] burden to establish mootness under § 363(m).” Id. at 535.
b. Discussion
Before us, Hiawatha concedes that recovering the assets Rhino purchased or imposing an improver’s lien on those assets Would affect the validity of the asset sale. Hiawatha now claims its appeal is not moot because the court can still grant relief by imposing a constructive trust on the sale’s proceeds.
As an initial matter, Hiawatha did not present this constructive trust theory to the district court below. Hence, as with ANR, we could consider the theory waived and decline to address it. But, unlike ANR, Hiawatha did inform the district court that the estate’s sale proceeds could be used in lieu of the assets themselves. And, in the context of supporting its improver’s lien theory, Hiawatha quoted language from In re Osborn explaining how the availability of a constructive trust can defeat § 363(m) mootness. Nonetheless, we can still affirm the district court on § 363(m) mootness grounds without finding that Hiawatha’s constructive trust theory has been waived, so we proceed to the constructive trust arguments on appeal.
Hiawatha first argues that In re Simon’s bright-line rule against granting relief from commingled funds should not apply. In In re Simon, an unpublished order and judgment-from this court, a divided panel of judges held that “the only course consistent with the purpose of § 363(m)” is limiting the recovery of asset sale proceeds to only those funds that “have been segregated” from the estate’s other funds. In re Simon, 138 Fed.Appx. at 56.
*560We agree with Hiawatha and reject this bright-line rule. First, the rule conflicts with published precedent in this circuit. In In re Osborn, a creditor asked this court to find a bankruptcy appeal moot under § 363(m) because “distributions have been made without objection, and the proceeds of the sale ... have been commingled with the other funds, [so] there is no res that could be recovered.” In re Osborn, 24 F.3d at 1209 (emphasis added). We rejected that argument, saying, “The Bank cites no [state], federal or other authority in support of its dogmatic position.” Id. We concluded, “[Here, t]here is a possibility of equitable relief. It is only if there is no such possibility that the appeal should be dismissed as moot.” Id. at 1209-10. And, in fact, on remand, some relief was granted despite the funds’ commingling. See In re BCD Corp., 119 F.3d at 856. Thus, contrary to In re Simon’s rule, relief can be granted even if the sale proceeds are commingled with other funds — In re Osborn shows as much.
Second, In re Simon’s reliance on In re BCD Corp. is also unavailing. Although In re BCD Corp. correctly notes that equitable relief was possible in that case because proceeds were segregated pending the appeal, relief was also possible because state law “provide[d] for equitable remedies” and “the sale proceeds ha[d] not been disbursed.” Id. at 856-57. Thus, far from identifying segregation as the necessary factor for possible relief, In re BCD Corp. named a number of factors suggesting relief was possible in that case — all, some, or none of which may have been necessary.
Third, In re Simon’s factors do not support its no-commingled-funds rule. The first factor cited — preventing “uncertainty as to the sale” — is irrelevant. See In re Simon, 138 Fed.Appx. at 56. When an estate sells assets, the purchaser receives the assets and the estate receives proceeds. If, sometime thereafter, a court reallocates some of the estate’s proceeds to a third party, the validity of the original sale agreement remains unaffected. The sale is already complete; whatever happens to the proceeds thereafter is of no concern to the purchaser. Congress’s purpose behind § 363(m) — assuring that asset sales are final — is undisturbed.
In re Simon’s second factor — preventing “uncertainty as to paid-out creditors” — is likewise inapplicable. Id. As long as the funds are not fully disbursed, the trustee can satisfy an equitable award of money against the estate; paid-out creditors need not be concerned. See id. at 58 (Murphy, J., dissenting).
And the third factor — “segregation is not overly burdensome” — also is of no help to the rule. See id. at 57. The implication of In re Simon’s rule is that an appellant can obtain either a stay or a segregation of sale proceeds in order to later seek relief from the sale order, but the appellant must obtain one or the other. Yet § 363(m) only requires a stay — it says nothing about whether funds must be segregated. See Elwell v. Okla. ex rel. Bd. of Regents of the Univ. of Okla., 693 F.3d 1303, 1312 (10th Cir.2012) (“Common sense, reflected in the canon expressio unius est exclusio alteri-us, suggests that the specification of [one provision] implies the exclusion of others.” (internal quotation marks and alteration omitted)). Easy or not, segregating funds is simply not required.
Accordingly, we disapprove of In re Simon’s bright-line rule. But rejecting the district court’s rationale for § 363(m) mootness in this case does not end our inquiry, as we may affirm on different grounds. Thus, we proceed to Hiawatha’s second argument — that Rushton failed to meet his burden of proving that no remedy is available in this appeal.
*561Rushton argues that a constructive trust — the only proposed remedy before this court that does not affect the sale order’s validity — is not available to Hiawatha here. He explains that, under Utah law, Hiawatha must identify “specific property that can be traced to [Rushton’s allegedly] wrongful behavior” in order to receive a constructive trust. Rushton’s Hiaw. Br. at 13 (quoting Wilcox v. Anchor Wate Co., 164 P.3d 353, 362 (Utah 2007)). And that tracing requirement is impossible to meet here, Rushton says, because “[t]here is no evidence that any part of [Rhino’s] $15 million purchase price ... was allocated or attributable to the [assets] recovered from Hiawatha.” Id. at 14.
In addition, Rushton notes that Utah’s constructive trust law requires proving “unjust enrichment,” which in turn requires showing that Rushton “accepted or retained the benefit [conferred by Hiawatha] under circumstances making it inequitable to retain the benefit without making payment of its value.” Id. at 16 (quoting Thorpe v. Washington City, 243 P.3d 500, 507 (Utah 2010)). And this is impossible for Hiawatha to show, according to Rush-ton, because Hiawatha’s “conduct in this matter has been consistently devoid of equity.” Id. at 19. Rushton explains, “[H]aving mined a million tons of coal to which it had no lawful right in willful violation of the automatic stay, [Hiawatha asks] this Court [to] rule that the Trustee must compensate Hiawatha for the cost of its illegal behavior.” Id.
In the face of these arguments, Hiawatha replies only that “it was the Trustee’s burden ... to show impossibility of relief to Hiawatha; not Hiawatha’s burden to show entitlement [to a constructive trust].” Hiaw. Reply Br. at 11 (emphasis in original). But Hiawatha never actually contests Rushton’s arguments.
We are thus persuaded that Rushton has met his burden on the record here. Hiawatha does not contest that it cannot trace its claimed assets to a certain portion of the sale proceeds, as is required by Utah law for a constructive trust. And Hiawatha does not contest that it mined a million tons of coal in willful violation of the automatic stay, making an equitable remedy impossible in light of such inequitable behavior. See Mfrs. Fin.Co. v. McKey, 294 U.S. 442, 449, 55 S.Ct. 444, 79 L.Ed. 982 (1935) (“he who seeks equity must do equity” (internal quotation marks omitted)). Nor does it point to wrongful conduct by Rushton. In sum, it is clear from the undisputed facts in this particular record that Hiawatha cannot prevail on its constructive trust theory even if its appeal were permitted to proceed below.
With this analysis, we do not mean to suggest that, at the mootness stage, we decide a claim’s merits. Rather, pursuant to § 363(m), we decide only whether the claim is available. Here, Rushton has shown that Hiawatha cannot prevail under a constructive trust theory, thereby making that remedy unavailable and Hiawatha has given us no reason to believe otherwise.
On these grounds, we affirm the district court’s dismissal of Hiawatha’s appeal for § 363(m) mootness.
3. Appeal No. 12-4106— Reynolds’s Appeal
Reynolds and his family lived at the Bear Canyon mine’s scale house while Reynolds ran the mine for C.W. Mining. After C.W. Mining was forced into bankruptcy, Rushton filed an adversary proceeding in bankruptcy court to establish ownership of the scale house and to evict the Reynolds family. Reynolds opposed Rushton’s action, arguing that he was the rightful owner of the scale house, not C.W. *562Mining’s bankruptcy estate. Reynolds also filed a counterclaim under the Utah Occupying Claimant Statute (UOCS), Utah Stat. Ann. § 57-6-1 et seq., seeking $175,000 for purported improvements to the scale house. This counterclaim served as an alternate remedy in the event that the bankruptcy court determined the estate owned the house. See Reynolds App. 176-77. Ultimately, the bankruptcy court did in fact find that the estate owned the scale house, and the court also rejected Reynolds’s counterclaim. Reynolds then appealed both decisions to the district court.
In the meantime, Rushton sold the mining assets, including the scale house, to Rhino, and the sale closed without a stay. Then, Rushton, Rhino, and Castle Valley moved to dismiss Reynolds’s appeal as moot under § 363(m) and equitable mootness, both of which the district court adopted as independent reasons to dismiss Reynolds’s appeal. Reynolds then appealed to this court.
As an initial matter, Rushton contends that Reynolds waived any available relief in the district court by arguing only that the scale house should be returned to him. But in fact, Reynolds also mentioned that relief was available through his UOCS counterclaim. Id. at 81. Granted, he did so in only one sentence, but the counterclaim was also included in his notice of appeal, id. at 11, and the district court discussed the counterclaim at several points in its opinion, see id. at 140, 144-45. Thus, whether Reynolds could obtain monetary relief under the UOCS was squarely before the district court.
Before this court, Reynolds now disclaims any relief that would affect the validity of the sale to Rhino. See, e.g., Reynolds Br. at 4-5 (“The purpose of ... the present appeal ... is not to undo the sale of the Reynolds Home or to invalidate the Sale Order, but rather to preserve [Reynolds’s] right to damages from the loss of his home.... ”); id. at 19 (“To be clear, such a remedy would come from the estate and not Rhino.”). He seeks only the value of his home or, alternatively, the value of the improvements to his home from the estate’s sale proceeds. And under the UOCS, just such relief is available to Reynolds, at least as to the value of any improvements he made to the scale house. See Hidden Meadows Dev. Co. v. Mills, 590 P.2d 1244, 1249 (Utah 1979) (concluding that the UOCS “ameliorate[s] the strict common law rule that the owner is entitled to the improvements placed by another upon his property” by allowing a good faith improver to receive monetary compensation for the value of improvements he made to property he possessed under color of title).
For his part, Rushton does not dispute the availability of relief for Reynolds under the UOCS. Instead, Rushton argues that Reynolds cannot obtain relief from a constructive trust, with which we agree.6 And Rushton argues that Reynolds “cannot assert a damage claim for the loss of use of the [house] ... [because] he consented ... [to] vacate[ ] the premises,” Rushton’s Reynolds Br. at 21, but that has nothing to do with whether Reynolds can assert a claim for the value of improvements he made to the scale house. Hence Rushton has failed to meet his burden of proving § 363(m) mootness because relief is still available under the UOCS. On § 363(m) mootness, the district court’s opinion cannot stand.
*563As for equitable mootness, at oral argument, Rushton conceded that equitable mootness would not apply to a purely statutory claim for money — e.g., Reynolds’s UOCS counterclaim here. And while “[a] party’s concession of legal error ... cannot, standing alone, justify reversing a district court,” United States v. Avery, 295 F.3d 1158, 1169 (10th Cir.2002) (emphasis added), Rushton’s concession is not the only basis for reversal. In addition to Rushton’s concession, the district court’s equitable mootness finding is undermined by a false premise. The district court concluded the appeal was equitably moot in part by assuming that Reynolds’s only relief was recovery of the scale house. See, e.g., Reynolds App. 152 (“The Court is also persuaded that a return of the Reynolds family to the scale house would result in a devaluation of the C.W. Mining estate .... ”). In fact, the monetary relief Reynolds seeks under the UOCS does no such thing.
Therefore, we reverse the district court’s dismissal of Reynolds’s appeal.
4. Appeal No. 12-4112 — COP’s Appeal
COP owns the Bear Canyon mine at which C.W. Mining mined coal before its bankruptcy and asset sale. In a prior appeal, COP sought to establish that its mining agreement with C.W. Mining “automatically terminated shortly after the bankruptcy petition was filed,” so the bankruptcy court had erred in determining that the agreement was still property of the estate. In re C.W. Mining Co., 641 F.3d at 1236. We disagreed with COP’s contract interpretation and affirmed the bankruptcy court’s order. See id. at 1241-42. Consequently, the COP mining contract remained C.W. Mining’s asset and, after the asset sale, became Rhino’s asset.
With this appeal, COP seeks to reverse the bankruptcy court’s interpretation of another clause from that mining contract, the continuing operations clause. This clause requires the mine’s operator to “diligently and continuously operate” the mine. COP App. 443. COP has alleged that, during C.W. Mining’s bankruptcy, C.W. Mining was in default of this provision. For this claim, COP sought alleged damages of over $10 million in the bankruptcy court. But the bankruptcy court disagreed with COP’s more expansive definition of the clause and, as a result, concluded that the estate owed COP only $1,320,930.89 for C.W. Mining’s defaults. Id. at 434. COP then appealed to the district court. But while the appeal was pending, COP’s contract with C.W. Mining was sold to Rhino as part of the bankruptcy estate’s asset sale, and Rushton, Rhino, and Castle Valley moved to dismiss COP’s appeal under § 363(m) mootness.
In opposition to their motion to dismiss, COP argued that § 363(m) did not moot the appeal because its appeal “merely seek[s] a determination or explanation of contractual rights, without seeking reversal of the sale.” Id. at 327. More specifically, COP was seeking “a different interpretation of [the continuing operations clause] going forward.” Id. at 331.
The district court rejected this remedy as impermissible under § 363(m), and the district court was correct to do so. By changing the interpretation of COP’s mining contract, which Rhino purchased in good faith from the estate, COP would be altering the definition and value of the assets Rhino purchased, which would violate § 363(m)’s bar on any “modification ... [that] affect[s] the validity of [the] sale.”
In this appeal, COP effectively concedes that the remedy it sought in the district court cannot be granted in light of § 363(m). See, e.g., COP Br. at 17 (“COP is entitled to monetary remedies against *564the [e]state.... To be clear, such a remedy would come from the estate and not Rhino.”). Now, COP seeks compensation only from the sale proceeds in the estate’s possession.
Yet as with ANR’s appeal, we will not reverse the district court based on a theory not presented to it. And monetary relief was not adequately presented to the district court. Granted, in a footnote, COP told the district court, “[M]onetary relief is another available remedy that will not disturb the Sale Order. The sale proceeds from the sale of the mine assets have not been completely disbursed and may be used to provide an effective or ‘meaningful’ remedy to COP.” COP App. 331 n.21. But “[arguments raised in a perfunctory manner, such as in a footnote, are waived.” United States v. Berry, 717 F.3d 823, 834 n. 7 (10th Cir.2013) (emphasis added; internal quotation marks omitted).
And even if we find that COP actually preserved monetary relief as a possible remedy,7 we still conclude that Rushton satisfied his burden of proving that COP cannot obtain any relief. In his brief, Rushton explains how COP’s contract claim cannot succeed because COP cannot show damages, and he explains how COP’s constructive trust theory cannot succeed because COP cannot trace the value of its mining agreement to specific assets in the estate’s possession and because COP cannot show that the estate was unjustly enriched. COP’s only counter is that the “mere existence” of these theories of relief preclude § 363(m) mootness. But COP is mistaken: The mootness question does not turn on what relief “merely exists.” Rather, “[t]he mootness question turns on what relief is available to COP if it were to prevail in this appeal.” In re C.W. Mining Co., 641 F.3d at 1239 (emphasis added); cf. Arbaugh v. Y & H Corp., 546 U.S. 500, 513 n. 10, 126 S.Ct. 1235, 163 L.Ed.2d 1097 (2006) (“A claim ... may be dismissed for want of subject-matter jurisdiction if it is not colorable, i.e., if it is ‘immaterial and made solely for the purpose of obtaining jurisdiction’ or is ‘wholly insubstantial and frivolous.’ ”). And COP has not rebutted Rushton’s arguments that COP’s proposed theories are not available here, thus making it clear that, under the undisputed facts in this record, COP cannot prevail on its alternate theories even if its appeal were permitted to proceed below.
We therefore affirm the district court’s conclusion that COP’s appeal is moot under § 363(m).
C. COP and Hiawatha Appeal the Sale Order—Nos. 12-4132 & 12-4144
With these appeals, COP and Hiawatha challenge the bankruptcy court’s order approving the sale of C.W. Mining’s assets to Rhino. But because neither COP nor Hiawatha requested a stay of the sale *565order, § 363(m) “forecloses any remedy ... that would affect the validity of the trustee’s sale.” In re C.W. Mining Co., 641 F.3d at 1239.
Recognizing this impediment, COP and Hiawatha ask us to acknowledge remedies they seek in other appeals. Specifically, both ask that we find arguments made in their first appeals (No. 12-4102 for Hiawatha and No. 12-4112 for COP) not waived for failure to appeal the sale order. But as discussed above, we do not find any arguments waived for that reason. Because COP and Hiawatha seek no other relief in their second appeals, there is no relief we can grant, and those appeals, Nos. 12-4132 and 12-4144, are accordingly moot.
III. Conclusion
For the foregoing reasons, we DISMISS Rhino and Castle Valley from these appeals, we AFFIRM Nos. 12-4091, 12-4102, 12-4112, 12-4132, and 12-4144, and we REVERSE and REMAND No. 12-4106 to the district court for further proceedings consistent with this opinion.
. All citations hereafter come from title 11 of the U.S.Code unless otherwise noted.
. Although COP and ANR are distinct entities, Joseph O. Kingston is the president of both. COP and ANR are also closely related to C.W. Mining and to the other appellants, Hiawatha and Charles Reynolds. In a prior proceeding, the Bankruptcy Appellate Panel outlined some of these entities' relationships with each other:
The relationship between [C.W. Mining] and COP is more than mere lessor-lessee. Although COP maintains there is no legal relationship between itself and [C.W. Mining], both entities are owned and operated, at least in part, by various members of the Kingston family and members of the Davis County Cooperative, a non-profit entity. The Davis County Cooperative, [C.W. Mining] and COP share various common directors, officers, shareholders and registered agents. Carl Kingston is the registered agent for [C.W. Mining] and COP, is a member of the Davis County Cooperative, and has acted as attorney for [C.W. Mining], Carl Kingston’s cousin, Joe Kingston, is the president and a shareholder of COP. Joe Kingston's brother, Paul Kingston, is a shareholder of [C.W. Mining] and COP, as well as the trustee (akin to the CEO) of the Davis County Cooperative. Charles Reynolds, the president of [C.W. Mining] since 2004, is a member of the Davis County Cooperative. John Gustafson, the vice president of [C.W. Mining] and one of its shareholders, sits on the board of directors of the Davis County Cooperative. Rachel Young, sister of Paul Kingston and Joe Kingston, is a shareholder of [C.W. Mining] and formerly a shareholder of COP. COP disputes that *553any of these connections gave it the ability to control [C.W. Mining].
C.O.P. Coal Dev. Co. v. C.W. Mining Co. (In re C.W. Mining Co.), 422 B.R. 746, 749 (10th Cir. BAP 2010) (footnotes omitted).
. Section 363(m) states:
The reversal or modification on appeal of an authorization under subsection (b) or (c) of this section of a sale or lease of property does not affect the validity of a sale or lease under such authorization to an entity that purchased or leased such property in good faith, whether or not such entity knew of the pendency of the appeal, unless such authorization and such sale or lease were stayed pending appeal.
. At oral argument, however, ANR seemed to suggest that if we found no monetary relief was available, as we do here, ANR might seek to unwind its portion of the asset sale. This request in the alternative would in fact affect Rhino and Castle Valley, because the request, if granted, would unwind part of their asset purchase. But for that very reason, this request is plainly barred by § 363(m) because it affects the validity of an unstayed asset sale to a good faith purchaser. Thus, to the extent ANR also seeks this alternative relief, its appeal is still moot as to Rhino and Castle Valley and is accordingly dismissed.
. Section 364(e) is identical with § 363(m) in all relevant respects here:
The reversal or modification on appeal of an authorization under this section to obtain credit or incur debt, or of a grant under this section of a priority or a lien, does not affect the validity of any debt so incurred, or any priority or lien so granted, to an entity that extended such credit in good faith, whether or not such entity knew of the pendency of the appeal, unless such authorization and the incurring of such debt, or the granting of such priority or lien, were stayed pending appeal.
11 U.S.C. § 364(e).
. Like ANR, Reynolds did not raise the issue of a constructive trust in the district court. Thus, like ANR, Reynolds has waived any such relief. Only a remedy under the UOCS has been preserved.
. We recognize COP may have preserved the issue of monetary relief, despite the issue being raised only in a footnote, because the district court still considered it. True, the district court then rejected the remedy by relying on In re Simon, an unpublished decision we reject. But we may affirm the district court on alternate grounds, as we do here, and the district court’s subsequent conclusion about COP’s monetary relief claim is correct: "It is unclear ... how COP could allege a claim against the proceeds of the sale to Rhino based upon the future interpretation and application of the Continuous Operations Clause.” COP App. 613. COP did not begin to explain how that remedy might work until its reply brief before this court, which is too late. See Hill v. Kemp, 478 F.3d 1236, 1250-51 (10th Cir.2007); Headrick v. Rockwell Int’l Corp., 24 F.3d 1272, 1277-78 (10th Cir.1994) (White, J., sitting by designation).