Before Elrod, Haynes, and Willett, Circuit Judges. Don R. Willett, Circuit Judge: This consolidated appeal concerns the injunctive and monetary sanctions that the district court imposed after a company and three individuals violated the court’s protective order. The company and the individuals challenge the sanctions on several grounds, many of which have merit. We hold that the district court erred by sanctioning the individuals without notice, by imposing litigation-ending sanctions without first finding bad faith, and by failing to adequately explain and failing to consider essential factors in its calculation of attorney fees. We AFFIRM in (small) part, VACATE in (large) part, and REMAND for further proceedings. I A CEATS, Inc. is a non-practicing intellectual property company that owns patents for technologies used in online ticketing. TicketNetwork, Inc. and Ticket Software LLC (together “Ticket”) maintain an online marketplace for tickets to live events. More than a decade ago, CEATS filed a patent-infringement lawsuit against Ticket and other providers (the “2010 Lawsuit”). Two years later, CEATS and Ticket settled that suit. The settlement agreement gave Ticket a license to use CEATS’s patents in exchange for a lump-sum payment from Ticket and for ongoing royalty payments from Ticket and its affiliates (the “License Agreement”). CEATS continued its litigation against the remaining, non-settling defendants, but the jury in that case found that CEATS’s patents were invalid. The Court of Appeals for the Federal Circuit affirmed.[1] Ticket then filed this suit seeking declarations that Ticket did not infringe CEATS’s patents, that the CEATS patents at issue in the License Agreement are invalid, and that the License Agreement is unenforceable. CEATS counterclaimed, arguing that Ticket breached the License Agreement. CEATS also sought an accounting of payments due under the License Agreement (because Ticket had stopped paying). After the district court denied summary judgment, Ticket moved to dismiss its claims voluntarily. The district court granted that motion, and it dismissed all three counts from Ticket’s complaint. The parties then moved forward with discovery on CEATS’s counterclaims. At trial, the jury found that Ticket breached the License Agreement by using CEATS’s intellectual property without payment, and it awarded compensatory damages. The district court also awarded fees and costs to CEATS. B The protective-order violation at the center of this appeal occurred after the jury trial was over and while CEATS’s claim for attorney fees was still pending. Ticket allows its affiliate websites to view and sell Ticket’s own inventory. During this case’s discovery phase, CEATS moved to compel Ticket to produce a list of those affiliates. Following two contentious hearings, the district court ordered Ticket to produce the list. But the court made clear that the parties’ protective order prohibited CEATS from using the list for any purpose other than the present litigation. The protective order also prohibited CEATS’s in-house representatives from accessing “highly confidential” documents, and it required anyone who did access such documents to take reasonable care to ensure confidentiality. Because the list was so sensitive, the district court further required CEATS to certify that the list would not “be viewed by attorneys who are identifying or targeting licensing prospects.” Ticket produced the affiliate list in a password-protected, encrypted ZIP file containing an Excel spreadsheet. The file also included an image bearing the Bates number TN002528 and the designation “HIGHLY CONFIDENTIAL—OUTSIDE COUNSEL EYES ONLY.” But the native spreadsheet itself—that is, the actual affiliate list—did not include a confidentiality designation in the file name or in the spreadsheet’s text. Milford Skane was CEATS’s CEO. Sonja McAuliffe and Dr. Brian Billett were CEATS’s litigation consultants. Because Skane was CEATS’s CEO, the protective order prohibited him from viewing the affiliate list (or any other of Ticket’s “highly confidential” documents). Nonetheless, Skane asked the litigation consultants for a “non-confidential” list of Ticket’s affiliates to aid in global settlement negotiations with Ticket. McAuliffe and Billett each separately sent Skane a copy of the Ticket affiliate list. Neither copy bore any confidentiality designation. CEATS, Skane, McAuliffe, and Billett argue that this discovery violation was inadvertent. According to them, because the native Excel sheet did not contain the “highly confidential” designation in the document title when Ticket produced it, the consultants did not realize that it had been so designated. CEATS also insists that Skane was relying on the consultants to avoid sending him protected documents and that he was unaware that the list was designated “highly confidential.” Skane then emailed a settlement demand to Ticket’s CEO, attaching the affiliate list as a “starting point” for negotiations. Skane wrote (in part): Don: We both know the sites involved (attached) and what the numbers are. These can certainly be our starting point. As previously indicated, I am willing to discount past claims and future royalties reasonably. For guidance purposes . . . we are willing to consider an 8-figure (not $99m, but not $10m either) global settlement for any and all Ticket[] owned affiliates. Ticket responded by filing a “Motion for an Order to Show Cause why CEATS or Others Should Not Be Sanctioned for Violation of Protective Order.” The district court held an initial evidentiary hearing in April 2019. The court ordered further discovery, and it appointed forensic investigators to prepare and submit a report to the court and the parties. The court held additional hearings nearly two years later, after the investigators had completed their report, including an all-day evidentiary hearing in January 2021.The district court issued an opinion and order(the “Sanctions Order”) finding that Skane, McAuliffe, and Billett (together, the “Individuals”) violated the protective order. The court also found that CEATS violated the protective order, because Skane’s violation occurred within the course and scope of his employment as CEO. The Sanctions Order had two parts. First, the district court enjoined CEATS and the Individuals from “contacting, seeking licensing fees, suing, or seeking damages from or related to Ticket[] or any of the companies or websites contained in the . . . affiliate list” for a thirty-month period (the “Licensing Bar”). Second, the district court imposed joint and several liability on CEATS and the Individuals (in their individual capacities), ordering them to pay Ticket’s reasonable attorney fees, costs, and expenses incurred in connection with prosecuting the protective-order violation. The Sanctions Order also provided that CEATS, Skane, McAuliffe, and Billett could file “a memorandum containing any objections, not to exceed seven (7) pages.” The Individuals had testified as witnesses at the hearings, but this was their first chance to submit briefing on sanctions. The court then issued a ruling containing a calculation of all reasonable expenses related to the protective-order violations (the “Calculation Order”). The court imposed a total monetary sanction of about $500,000 on CEATS and the Individuals, jointly and severally. CEATS and the Individuals timely (but separately) appealed both the Sanctions Order and the Calculation Order. We consolidated the appeals. II Before addressing the merits, we must confirm our jurisdiction. Ticket’s complaint for declaratory relief invoked jurisdiction for federal claims generally (under 28 U.S.C. § 1331) and for patent claims specifically (under 28 U.S.C. § 1338). CEATS’s state-law counterclaims invoked supplemental jurisdiction under 28 U.S.C. § 1367(a) and diversity jurisdiction under § 1332(a)(1). Ticket later moved to voluntarily dismiss its federal-question claims under Federal Rule of Civil Procedure 41(a)(2). The district court granted the motion, dismissing Count One of Ticket’s complaint with prejudice and Counts Two and Three without prejudice. All of Ticket’s claims having been dismissed, the district court proceeded with discovery on CEATS’s state-law counterclaims. The Federal Circuit has exclusive jurisdiction “of an appeal from a final decision of a district court of the United States . . . in any civil action arising under . . . any Act of Congress relating to patents.”[2] To determine whether a civil action arises under federal patent law, we use the well-pleaded complaint rule to examine the plaintiff’s statement of their claims.[3] At first glance, Ticket’s complaint appears to plead claims arising under federal patent law such that the Federal Circuit would have exclusive jurisdiction over this appeal. But the district court dismissed Ticket’s claims. “[T]he dismissal of a [] claim without prejudice operate[s] as an amendment of the complaint.”[4] By contrast, a “dismissal . . . with prejudice constitutes an adjudication of the claims on the merits.[5] Here, the district court dismissed Counts Two and Three of Ticket’s complaint without prejudice. But it dismissed Count One with prejudice—that is, on the merits. For jurisdictional purposes, then, those dismissals essentially left Count One as the only claim in Ticket’s suit. Thus, we must determine whether Ticket’s Count One arises under federal patent law. An action arises under federal patent law and thereby triggers the Federal Circuit’s exclusive jurisdiction when federal patent law creates the cause of action, or when there is a “substantial question of patent law” that is “disputed and require[s] resolution on the merits.”[6] Count One of Ticket’s complaint sought a declaratory judgment that the royalty provisions in the Licensing Agreement are unenforceable. That is a state-law contract claim, not a federal-law patent claim. Nor did Count One require resolution of a disputed question of patent law. Ticket’s argument that the License Agreement was unenforceable hinged entirely on the jury’s invalidation of CEATS’s patent claims in the 2010 Lawsuit. All substantive questions of patent law relevant to Count One were already resolved in the 2010 Lawsuit. Therefore, Ticket’s suit, as amended after the district court’s dismissals, did not arise under federal patent law. And as a result, the Federal Circuit does not have exclusive jurisdiction. This conclusion invites the question whether federal jurisdiction exists here. After all, Count One’s state-law claim is the only part of Ticket’s complaint that the district court adjudicated on the merits. The simple answer is that this is an appeal from CEATS’s counterclaims—not Ticket’s original complaint. “If an independent jurisdictional ground exists for a counterclaim, the district court can retain jurisdiction over the counterclaim even if the original claims are dismissed for lack of subject-matter jurisdiction.”[7] So, regardless of Ticket’s pleadings, the district court had subject-matter jurisdiction over the counterclaims because CEATS invoked diversity jurisdiction under 28 U.S.C. § 1332(a)(1). Finally, we have appellate jurisdiction over the parties’ appeals of the Sanctions Order pursuant to 28 U.S.C. § 1292, because that order grants an injunction. And we have appellate jurisdiction over the parties’ appeals of the Calculation Order pursuant to 28 U.S.C. § 1291, because that order is a final decision which disposed of all remaining sanctions issues. When a court imposes sanctions under Federal Rule of Civil Procedure 37, we review for abuse of discretion.[8] “We review de novo a district court’s invocation of its inherent power and the sanctions granted under its inherent power for an abuse of discretion . . . .”[9] A court abuses its discretion regarding sanctions when it bases its ruling “on an erroneous view of the law or on a clearly erroneous assessment of the evidence.”[10] III The Individuals argue that the district court never gave them notice that it was considering monetary sanctions against them personally. We agree that the Individuals did not receive the process that our precedent says was due. As a preliminary point, the district court did not specify whether it sanctioned the Individuals under Rule 37 versus under its inherent power. Yet Rule 37 authorizes sanctions only against a party (or a party’s attorney).[11] The Individuals were neither parties nor attorneys, so the district court must have drawn on its inherent power when it sanctioned them. When a court contemplates sanctions under its inherent power, “it must comply with the mandates of due process,”—both “in determining that the requisite bad faith exists” and “in assessing fees.”[12] Due process requires “fair notice and an opportunity for a hearing on the record.”[13] Notice is fair if it is “reasonably calculated, under all the circumstances, to apprise interested parties of the pendency of the action.”[14] The court must provide a hearing that allows the party facing sanctions “an opportunity to present their objections”[15] and “an opportunity to mount a defense.”[16] Here, the Individuals did not receive notice that monetary sanctions were “pend[ing]” against them.[17] Ticket’s show-cause motion after it discovered the protective-order violation asked for sanctions against “CEATS or Others.” This vague request did not put the Individuals on notice that they might be personally on the hook for fees and costs. And while the motion did ask the court to sanction McAuliffe and hold him in contempt, it did not mention him or any of the Individuals when it asked for monetary sanctions. Instead, Ticket asked the court to “order CEATS to pay all attorney[] fees and costs . . . associated with CEATS’s breach of the Protective Order, including the fees and costs for investigating the breach.” Similarly, the district court’s show-cause orders did not flag the possibility of individual monetary sanctions against the Individuals. The Individuals also did not get a hearing that allowed them to defend their state of mind. While Skane and McAuliffe testified in the first evidentiary hearing, and while all three Individuals testified in the second, they had no indication that they were testifying as more than witnesses. Instead, the Individuals learned that they might face sanctions at the same time that they learned that they would face sanctions. The Sanctions Order made findings about the Individuals’ states of mind, and it held them jointly and severally liable for Ticket’s fees and costs. But that was after the discovery, forensic investigation, and evidentiary hearings had ended. True, the district court did allow the Individuals to submit briefing before it issued the Calculation Order. But that post-deprivation opportunity to respond (in a brief not to exceed seven pages) is no substitute for the pre-deprivation notice and hearing that due process here requires.[18] The Individuals did not receive notice that monetary sanctions were pending against them, and they did not receive a pre-deprivation opportunity to defend themselves at a hearing. By the time the district court heard their response, it had already decided against them. That was an abuse of discretion. Therefore, we VACATE the Sanctions Order insofar as that order imposes monetary sanctions against the Individuals. IV A CEATS first argues that the district court made an error of law by imposing the Licensing Bar as a sanction for CEATS’s protective-order violations. The Licensing Bar is one component of the Sanctions Order. It prohibits CEATS from “contacting, seeking licensing fees, suing, or seeking damages from or related to Ticket[] or any of the companies or websites contained in the TN002528 Ticket[] affiliate list” for 30 months. The district court sanctioned CEATS under Federal Rule of Civil Procedure 37(b)(2). That rule empowers a court to sanction a party that disobeys a discovery order. “District Courts have broad discretion in determining whether to impose a sanction under Rule 37, and, if so, what sanction to impose.”[19] Sanctions under this rule must be both “just” and “related to the particular ‘claim’ which was at issue in the order to provide discovery.”[20] Yet “[o]ur caselaw imposes a heighted standard for litigation-ending sanctions (sometimes called “death penalty” sanctions),” as so: [T]he district court must make four additional findings to impose a litigation-ending sanction: (1) the discovery violation was committed willfully or in bad faith; (2) the client, rather than counsel, is responsible for the violation; (3) the violation “substantially prejudice[d] the opposing party”; and (4) a lesser sanction would not “substantially achieve the desired deterrent effect.”[21] We agree with CEATS that the Licensing Bar was a litigation-ending sanction. Dismissals with prejudice and default judgments are both litigation-ending.[22] Ticket argues that this case is different than those prototypical examples, though, because the Licensing Bar prohibits CEATS from initiating future actions against Ticket and its affiliates. Our caselaw takes a more practical view of what counts as litigation-ending. For example, we have held that a sanction is litigation-ending when the court strikes a defendant’s answer and denies a request to replead (something that would occur only in the future).[23] And we have treated a dismissal without prejudice as litigation-ending when the statute of limitations will prohibit the party from refiling (also in the future).[24] Likewise here. The Licensing Bar is litigation-ending because it prohibits CEATS from filing any lawsuits that it may have a right to bring against Ticket and its affiliates for a 30-month period. That is perhaps even harsher than “the severest remedies under Rule 37(b)— striking pleadings or dismissal of a case.”[25] We also agree with CEATS that the district court did not make the bad-faith finding that is a prerequisite to litigation-ending sanctions under Rule 37(b).[26] Instead, the district court found that CEATS acted recklessly, and then it equated recklessness with bad faith. We have rejected that equivalence. Evidence of “negligent or even reckless” discovery conduct does not show that a party acted “in bad faith or that it willfully abused the judicial machinery” sufficient to permit litigation-ending sanctions.[27] Ticket argues that CEATS forfeited the bad-faith argument by failing to assert it in the district court. While it is true that we tend not to entertain arguments that a party asserts for the first time on appeal, “an argument is not [forfeit]ed on appeal if the argument on the issue before the district court was sufficient to permit the district court to rule on it.”[28] Here, CEATS told the district court that a discovery violation “must be committed willfully or in bad faith for the court to award the severest remedies available under Rule 37(b).” CEATS also argued that it did not violate the Protective Order willfully or in bad faith, because the “communications . . . were clearly inadvertent.” That argument was enough to put the district court on notice that CEATS opposed any definition of “bad faith” that includes inadvertent conduct.[29] We VACATE the Sanctions Order insofar as that order applies the Licensing Bar to CEATS and the Individuals.[30] B Next, CEATS argues that the district court erred by denying its motion to toll the statute of limitations for certain of CEATS’s potential claims against Ticket and Ticket’s affiliates. CEATS had asked the district court to toll limitations for the period during which the district court considered Ticket’s show-cause motion.” As part of the Sanctions Order, the district court denied that motion as moot. However, if the district court chooses not to re-impose the Licensing Bar against CEATS on remand, then that motion will no longer be moot. If that happens, the district court may wish to revisit CEATS’s tolling motion. Accordingly, we VACATE the Sanctions Order as it pertains to the tolling motion. C CEATS’s final objection to the Sanctions Order is that the district court violated Rule 37(b) by imposing joint and several liability on CEATS. But CEATS forfeited this argument by failing to press it in the district court.[31] Even putting that forfeiture aside, the argument fails. CEATS says that it cannot face liability for others’ misconduct. But when the protective-order violation occurred, Skane was CEATS’s CEO, and McAuliffe and Billett were CEATS’s litigation consultants. We have not held that Rule 37 prohibits joint and several liability, but we have held that Rule 37 allows a court to sanction a party for discovery violations that its retained experts commit.[32] We therefore AFFIRM that part of the Sanctions Order that imposes joint and several monetary liability on CEATS. D Turning to the Calculation Order, CEATS argues that the district court abused its discretion when it tallied the monetary sanction. When a court awards attorney fees as part of a sanction under Rule 37, it generally still must use the familiar two-step lodestar process.[33] Here, Ticket provided the district court with an accounting of rates, hours, and costs, and it asked for about $750,000 in fees and costs. The district court reduced that amount after it saw discrepancies between Ticket’s request and its attorneys’ invoices, saw duplication in some attorneys’ work, concluded that some attorneys’ rates were excessive, and concluded that fees from in-house counsel were unrecoverable. The court granted Ticket costs and fees in the reduced amount of about $500,000. We agree with CEATS that the district court abused its discretion in both steps of this process. Under the first step, a court must calculate the “lodestar,” which is equal to the number of hours reasonably expended multiplied by an appropriate hourly rate (excluding hours that are excessive, duplicative, or inadequately documented).[34] To determine the rate, the court looks to the market rate in the community for similar work.[35] The court must give “a reasonably specific explanation for all aspects of a fee determination,” including its determination of appropriate hourly rates.[36] Here, there was a significant disparity between the rates that the district court approved when it awarded attorney fees to CEATS (at an earlier stage of litigation) versus the rates that it approved when it awarded attorney fees to Ticket (as part of the sanction against CEATS). For CEATS, the court approved hourly rates between $425 and $495 for partners, and between $175 and $275 for associates. But for Ticket, as part of the Calculation Order, the court approved much higher hourly rates— between $650 and $850 for partners, and between $499 and $650 for associates. We have never required parity in awards of attorney fees. Nor have we held that a finding that certain rates are reasonable precludes the possibility that higher rates are also reasonable. As between CEATS and Ticket, there may be good reasons for the discrepancy in reasonable hourly rates, especially since the forensic investigation was highly technical. But the district court failed to provide a “reasonably specific explanation” for the rates that it approved for Ticket. Instead, the court said only that it “d[id] not agree with CEATS that the Court’s prior decision on attorney fees in this case prevents it from finding different numbers also are reasonable.” It is true that the court’s prior approval of CEATS’s rates was in no sense binding for future fee requests. Nor did the court clearly err by setting plainly unreasonable rates for Ticket. Still, the district court did not explain why Ticket’s rates were reasonable.[37] An explanation is particularly necessary “where, as here, [the] sanctions are substantial in amount.”[38] Thus, the district court abused its discretion by failing to explain the rates that it approved under the first step of the calculation. Under the second step, a court must consider whether the lodestar amount should be adjusted up or down according to the 12 factors that appear in Johnson v. Georgia Highway Exp., Inc.[39] “If the Johnson factors are not evaluated and explained by the district court with a reasonable degree of specificity in making its fee award determination, the case will be remanded, if necessary, for an explanation to facilitate appellate review.”[40] Here, while the district court recited the Johnson factors and reduced some of the rates and hours based on CEATS’s objections, it failed to “use the Johnson factors to evaluate the fee award, or describe or discuss the application of Johnson in a manner that would facilitate meaningful appellate review.”[41] Therefore, we VACATE the Calculation Order and REMAND for the district court to recalculate the fees and to provide a “reasonably specific explanation”[42] of both any rates that it approves and the Johnson factors. V We AFFIRM that part of the Sanctions Order that imposes joint and several monetary liability against CEATS. We VACATE those parts of the Sanctions Order that impose joint and several monetary liability against the Individuals, that impose the Licensing Bar, and that deny CEATS’s tolling request. We also VACATE the Calculation Order, and we REMAND for further proceedings.
