In these sentencing appeals, defendant-appellant Nimon Naphaeng, a convicted fraudster, challenges a restitution order entered pursuant to the Mandatory Victims Restitution Act (MVRA), 18 U.S.C. § 3663A, in the amount of $581,880. After pausing to smooth out two jurisdictional wrinkles, we reach the merits and conclude that the appellant's challenge is futile. Accordingly, we affirm.

I. BACKGROUND

We briefly rehearse the relevant facts and travel of the case. The appellant concocted a fraudulent scheme to obtain work permits for Thai nationals living in the United States. Specifically, he advertised through flyers and the internet that he could obtain employment-authorization documents (EADs) in exchange for fees ranging from $1,500 to $2,500 per person. He was, in fact, able to obtain EADs for the applicants-but he did so by filing asylum petitions on the applicants' behalf. These petitions, filed without the applicants' knowledge, were apocryphal. As the appellant admitted to the district court, concealing the asylum applications from his clientele was "at the heart" of the scheme.

The appellant perpetrated his fraud over a period of sixteen months-but the chickens eventually came home to roost. In January of 2015, an immigration officer noticed that around sixty-four Thai asylum applications were filed from two Rhode Island addresses. This spike in filings was extraordinary; typically, an average of twenty Thai asylum applications were filed each year. Nor were common addresses the only feature shared by these suspicious applications: they also contained exactly the same typographical errors, identical explanations for seeking asylum, matching supplemental forms, and the same coterie of supporting documents.

In due season, a federal grand jury sitting in the District of Rhode Island returned a twenty-six count indictment against the appellant. In addition, the government "froze" hundreds of thousands of dollars that had been accumulated by the appellant.

*176 After some preliminary skirmishing (not relevant here), the appellant pleaded guilty to seven counts of mail fraud, see 18 U.S.C. § 1341 , and two counts of visa fraud, see id. § 1546(a). 1 As part of the plea agreement, the parties agreed that the per-application fee charged by the appellant ranged from $1,500 to $2,500. Although the change-of-plea colloquy specifically identified only ten victims, the parties did not purport to make a definitive head count. Instead, identification of those victims who might be owed restitution was deferred to the sentencing phase.

On May 3, 2017, the district court held the first of two sentencing hearings. By then, the court had the benefit of certain additional filings: a presentence investigation report (PSI Report) and sentencing memoranda prepared by both the appellant and the government. The government's memorandum included a spreadsheet listing the total number of victims, specifying whether each such victim had been contacted by either a government investigator or the probation office, and indicating the amount of restitution arguably due.

At the first sentencing hearing, a Department of Homeland Security (DHS) agent verified the information contained in the spreadsheet. The appellant's counsel cross-examined the agent, attempting to undermine the reliability of the government's spreadsheet, questioning the number of victims, and suggesting that some victims may have had knowledge that asylum applications were being filed on their behalf.

Two months later, the district court convened a second sentencing hearing. The appellant's counsel resumed her questioning of the DHS agent. This time, however, the questioning zeroed in on the appropriate amount of loss for restitution purposes (a finding separate and apart from the amount of loss needed to construct the guideline sentencing range, see USSG § 2B1.1 cmt. n.3(A) ). The district court eventually interrupted this line of questioning and proceeded to sentence the appellant. To allow the government more time to collect victim-related information, though, the court entered a provisional restitution order of $400,000, "subject to amendment." Judgment entered on July 27, 2017, and the appellant promptly filed a notice of appeal.

Having completed its information-gathering, the government filed two supplemental memoranda and sought a total of $581,880 in restitution on behalf of 368 victims. Its supplemental memoranda identified four categories of victims: 87 victims who had contact with both the probation office and the DHS; 46 victims who had contact only with the DHS; 16 victims who were identified through material submitted to the grand jury; 219 victims who were identified only by their asylum applications. According to the government, the first group of victims was due $168,620 in restitution, the second group of victims was due $72,100 in restitution, the third group of victims was due $17,160 in restitution, and the fourth group of victims was due $324,000 in restitution. The appellant countered that the government's recommended restitution over-counted the number of victims and rested on insufficient evidence. As a fallback, the appellant contended that the district court had denied him a full and fair opportunity to test the government's proffer. The court rejected the appellant's arguments, adopted the *177 government's calculations, and ordered restitution accordingly. 2 The appellant filed a second notice of appeal-but he did so before the district court entered its final judgment on the docket.

II. ANALYSIS

We divide our analysis into two parts, first addressing a pair of jurisdictional concerns and then addressing the substance of the appellant's challenge.

A. Jurisdictional Concerns.

Even though the appellant advances only a single assignment of error-a claim that the district court blundered in fashioning the restitution order-we are held at the starting line by jurisdictional concerns. While the government has eschewed any challenge either to the district court's jurisdiction or to this court's appellate jurisdiction, "we have an independent obligation to explore" potential jurisdictional infirmities. United States v. George , 841 F.3d 55 , 70 (1st Cir. 2016). We start there, dealing with two jurisdictional questions that lurk in the penumbra of this case.

1. District Court Jurisdiction. The initial question concerns whether the pendency of the first notice of appeal divested the district court of jurisdiction to enter the final restitution order. It is settled that once an appeal is taken, a district court generally loses jurisdiction to proceed with any matter related to the appeal's substance during the pendency of the appeal. See id. at 71 . In such a situation, the conventional practice is for the district court to ask the court of appeals to stay the original appeal and effect a temporary remand, thus enabling the district court to make a further ruling. See Fed. R. App. P. 12.1(b) ; see also United States v. Maldonado-Rios , 790 F.3d 62 , 64-65 (1st Cir. 2015) ; Puerto Rico v. SS Zoe Colocotroni , 601 F.2d 39 , 42 (1st Cir. 1979). Notwithstanding this general rule, though, we have concluded that a district court retains jurisdiction to modify a previously existing forfeiture order even after an appeal has been taken. See United States v. Ferrario-Pozzi , 368 F.3d 5 , 10-11 (1st Cir. 2004) (confirming district court's jurisdiction to issue final forfeiture award when that award was "an amendment of an existing order" that provisionally set a forfeiture amount); cf. George , 841 F.3d at 72 (finding district court jurisdiction lacking when forfeiture order was entered for the first time following appeal). The Ferrario-Pozzi panel based its conclusion on Federal Rule of Criminal Procedure 32.2(e), which recognizes that circumstances sometimes exist in which a district court may have to amend its initial forfeiture order (including, for example, the government's subsequent identification of additional property subject to forfeiture). See 368 F.3d at 11 . The MVRA contains an analogous provision with respect to restitution orders. See 18 U.S.C. § 3664 (d)(5). If victim losses are not sufficiently ascertainable by the date of sentencing, the court "shall set a date for the final determination" of restitution. Id.

The timetable here is reminiscent of that in Ferrario-Pozzi . The first notice of appeal was filed on July 27, 2017. The appeal was taken from a judgment that included a restitution order that had been clearly denominated as provisional. The district court entered the final restitution order while that appeal was pending. Given the teachings of Ferrario-Pozzi as well as the MVRA's statutory guidance, we conclude *178 that the pendency of the first appeal did not strip the district court of jurisdiction to enter the final restitution order.

This conclusion is reinforced by our own order staying the appellant's first appeal. That stay, issued six days before the district court entered the amended judgment, recognized the district court's intention to file an amended judgment. Although no formal remand was made, the practical effect was the same: when the district court amended the restitution order, the first appeal had been stayed and concerns about shared jurisdiction had been abated. In these unusual circumstances, we think that the district court's jurisdiction was intact. 3

2. Appellate Jurisdiction. The remaining jurisdictional question relates to our appellate jurisdiction. It arises because the appellant's second notice of appeal was filed after the district court's final restitution order was announced but before the amended judgment was actually entered on the docket. At first blush, then, the second notice of appeal would seem to be premature. The Supreme Court recently considered a similar issue in Manrique v. United States , --- U.S. ----, 137 S.Ct. 1266 , 1270, 197 L.Ed.2d 599 (2017). There, the Court found a notice of appeal insufficient to confer appellate jurisdiction in a restitution case when it was "filed between the initial judgment and the amended judgment." Id. The Court made pellucid that the defendant should instead have filed a timely "notice of appeal from the amended judgment imposing restitution." Id. at 1274 .

But we have said before that "appearances can be deceiving." Moreno v. Holder , 749 F.3d 40 , 43 (1st Cir. 2014) (citing Aesop, The Wolf in Sheep's Clothing (circa 550 B.C.) ). And in the last analysis, this case is distinguishable from Manrique . Here-unlike in Manrique -the appellant did file a second notice of appeal. Of course, his timing was imperfect: the second notice of appeal was filed after the district court modified the restitution award but before the court actually entered the amended judgment. Thus, the appellant (in the government's turn of phrase) "jumped the gun." He should have waited to file the second notice of appeal until after the amended judgment was entered on the docket. See Fed. R. App. P. 4(b)(1).

In the circumstances of this case, however, the infelicitous timing of the second notice of appeal is harmless. That notice of appeal, albeit premature, is rescued by Federal Rule of Appellate Procedure 4(b)(2), which provides that "[a] notice of appeal filed after the court announces a[n] ... order-but before the entry of the judgment ... is treated as filed on the date of and after the entry." Consequently, we treat the second notice of appeal as if it were filed on March 15, 2018 (the date of entry of judgment). 4 Given this convenient legal fiction, we have jurisdiction over the second appeal.

*179 B. The Merits.

Having allayed any jurisdictional doubts, we reach the merits. Our standard of review is uncontroversial: "We review restitution orders for abuse of discretion, examining the court's subsidiary factual findings for clear error...." United States v. Chiaradio , 684 F.3d 265 , 283 (1st Cir. 2012).

To place the appellant's arguments in perspective, we begin by differentiating between the calculation of loss demanded by the sentencing guidelines and the calculation of loss demanded by the MVRA. In a fraud case resulting in financial loss, the defendant's guideline sentencing range is determined in part by calculating the greater of either the intended loss or the actual loss. See USSG § 2B1.1, cmt. n.3(A). Intended loss is quantified by measuring "the loss the defendant reasonably expected to occur." United States v. Innarelli , 524 F.3d 286 , 290 (1st Cir. 2008). So viewed, intended loss serves a punitive purpose, punishing the defendant for the harm that he sought to inflict. See id.

In contrast, restitution is designed to compensate the victim, not to punish the offender. To this end, the MVRA mandates that a defendant convicted of certain federal crimes, including those "committed by fraud or deceit," must make restitution to victims commensurate with the victims' actual losses. 18 U.S.C. § 3663A(c)(1)(A)(ii) ; see Innarelli , 524 F.3d at 293 (noting that restitution is meant to "make the victim whole again"). For this purpose, actual loss is "limited to pecuniary harm that would not have occurred but for the defendant's criminal activity." United States v. Alphas , 785 F.3d 775 , 786 (1st Cir. 2015). It follows that, a court must base a restitution order on "the full amount of each victim's losses ... without consideration of the economic circumstances of the defendant." 18 U.S.C. § 3664 (f)(1)(A). Consistent with this logic, an order for restitution ought not to confer a windfall upon a victim. See United States v. Cornier-Ortiz , 361 F.3d 29 , 42 (1st Cir. 2004).

When determining restitution, a sentencing court is not expected to undertake a full-blown trial. See S.Rep. No. 104-179, at 18 (1995), as reprinted in 1996 U.S.C.C.A.N. 924, 931 (cautioning that the restitutionary phase of a criminal case is not to "become fora for the determination of facts and issues better suited to civil proceedings"). As a result, " 'absolute precision is not required' in calculating restitution under the MVRA." United States v. Mahone , 453 F.3d 68 , 74 (1st Cir. 2006) (quoting United States v. Burdi , 414 F.3d 216 , 221 (1st Cir. 2005) ). Rather, a restitution award requires only "a modicum of reliable evidence." United States v. Vaknin , 112 F.3d 579 , 587 (1st Cir. 1997) ; see United States v. Curran , 525 F.3d 74 , 84 (1st Cir. 2008).

This is not to say that Congress "conceive[d] of restitution as being an entirely standardless proposition." Vaknin , 112 F.3d at 587 . Mere guesswork will not suffice. The government bears the burden of proving a victim's actual loss by preponderant evidence. See 18 U.S.C. § 3664 (e). What is more, "a court may only order restitution for losses that have an adequate causal link to the defendant's criminal conduct." Alphas , 785 F.3d at 786 .

In the case at hand, neither party disputes the appropriateness of a restitution order. Their disagreement is only as to the amount of the award. The appellant argues that restitution should be limited to those victims named in the indictment who submitted proofs of loss. With respect to any and all other putative victims, the appellant submits that the government's *180 evidence was insufficient to undergird the restitution order.

The appellant places too heavy a burden on the government. The law is transparently clear that "[a]s long as the court's order reasonably responds to some reliable evidence, no more is exigible." United States v. Sánchez-Maldonado , 737 F.3d 826 , 828 (1st Cir. 2013). In this instance, the government proffered a detailed spreadsheet, describing its extensive efforts to trace and contact all of the persons defrauded over the sixteen-month duration of the scheme. This spreadsheet identified four groups of victims and summarized all of the relevant information in the government's possession, including how much money each victim had paid to the appellant and the method of payment. The government recommended specific restitution amounts for each victim based on the data in the spreadsheet and the amounts that the appellant routinely charged to his customers. 5 The government's information, coupled with the appellant's own admissions, supplied more than a modicum of reliable evidence. See Curran , 525 F.3d at 84 .

In a variation on his insufficiency-of-evidence theme, the appellant challenges the number of victims. He predicates this challenge largely on the notion that some of the persons that dealt with the appellant may have known that asylum applications were filed on their behalf. Relying primarily on a 2011 Second Circuit decision, the appellant suggests that those persons cannot be classified as victims for MVRA purposes. See United States v. Archer , 671 F.3d 149 , 173 (2d Cir. 2011) (explaining that persons who were complicit in and knew all along of defendant's fraudulent scheme are ineligible for victim status and thus restitution).

Archer is a horse of a different hue. Here-unlike in Archer -the appellant admitted that concealing the asylum applications was at the heart of his fraudulent scheme. Although the appellant now maintains that this admission applied only to those victims specifically identified in the indictment, the district court did not clearly err in inferring that the same narrative applied to all of the appellant's customers. This inference is buttressed by the testimony of the DHS agent, who vouchsafed that "[t]he people we talked to thought they were getting work cards only. They did not know about the asylum."

If more were needed-and we doubt that it is-victim declarations attached to the PSI Report are consistent with this inference. The majority of the declarations that stated a reason for the payment can fairly be summarized by saying that the money the victims lost was paid to obtain work permits, not to apply for asylum. 6 To cinch the matter, the record is barren of any indication that the appellant filed so much as a single bona fide asylum application *181 or told even a single victim that he was trumping up the paperwork undergirding the EADs.

Battling on, the appellant argues that the restitution order should not have extended to victims who had no contact with the government. This argument is unpersuasive. For one thing, restitution need not be limited to victims who have contacted the government. What counts is whether the government submits sufficiently reliable information to show that particular persons were in fact victims. See Curran , 525 F.3d at 84 ; United States v. Catoggio , 326 F.3d 323 , 327-28 (2d Cir. 2003) ; United States v. Berardini , 112 F.3d 606 , 609-10 (2d Cir. 1997). For another thing (as the government noted at the second sentencing hearing), the circumstances particular to the appellant's victims-foreign nationals seeking U.S. work permits-made it uniquely difficult for the government to communicate with them. When government agents made telephone calls, "people were so fearful that out of the blue they got ... a telephone call" that they asked whether the agents were coming for them.

That ends this aspect of the matter. The first step in fashioning a supportable restitution order is to identify particular victims who have suffered pecuniary losses as a result of the defendant's criminal activity. See Cornier-Ortiz , 361 F.3d at 42 . Here, the government stayed within appropriate bounds in taking this first step: it identified victims based on bogus asylum applications that shared unusual features common to those that the appellant admittedly filed. The district court acted well within the realm of its discretion in finding that the roster of identified persons comprised a roster of victims eligible for restitution.

The appellant has one last string to his bow. He importunes us to find that he was "denied a full and fair opportunity" to elicit testimony from the DHS agent through cross-examination. We reject his importunings.

The district court allowed the appellant's counsel to cross-examine the DHS agent at some length. The cross-examination was comprehensive and included grilling the agent about the asylum application procedure, the agent's conversations with victims, the victims' knowledge (or lack of knowledge) that asylum applications had been filed to their behoof, and the extent (if at all) to which any payments had been refunded to them.

To be sure, the district court cut cross-examination short near the end of the second sentencing hearing. Nevertheless, the right to cross-examination is not a right to endless cross-examination. See United States v. Laboy-Delgado , 84 F.3d 22 , 28 (1st Cir. 1996) ; see also Delaware v. Fensterer , 474 U.S. 15 , 20, 106 S.Ct. 292 , 88 L.Ed.2d 15 (1985) (per curiam) (explaining that the Constitution "guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish" (emphasis in original) ). The critical inquiry is whether a party has been accorded a fair and adequate opportunity to confront the witnesses against him. See Laboy-Delgado , 84 F.3d at 28 . On this chiaroscuro record, this inquiry produces an affirmative answer. Consequently, we discern no abuse of discretion in the district court's implicit determination that-by the time the cross-examination was halted-the appellant already had enjoyed a fair and adequate opportunity to cross-examine the witness.

III. CONCLUSION

Let us be perfectly clear. We readily acknowledge that a restitution order must entail more than a mere guess or a bald *182 approximation of actual loss. See Vaknin , 112 F.3d at 587 (cautioning that "an award cannot be woven solely from the gossamer strands of speculation and surmise"). But the calculation of a restitution order does not demand metaphysical certainty. Here, the district court's analysis is record-based and constitutes a fair appraisal of actual losses. That appraisal, in turn, rests on more than a modicum of reliable evidence. Taking into account the barriers to a more exact calculation (such as the length of the appellant's scheme, the number of victims, the lack of organized records, and the difficulty in communicating with non-English speakers), we think that the court did enough to satisfy the strictures of the MVRA.

We need go no further. For the reasons elucidated above, the district court's amended restitution order is

Affirmed.