THOMPSON, Circuit Judge.

The Defendants in this case made millions off infomercials shilling purported panaceas, products that they claimed cured literally every disease, from cancer to Parkinson's to obesity. Having been ordered to restore these millions to the customers they deceived, the Defendants now raise a multitude of challenges to two decisions of the district court: first, the court's grant of summary judgment in favor of the plaintiff Federal Trade Commission (FTC), finding the Defendants liable for deceptive advertising; and second, the court's determination of damages after a bench trial on that issue. Despite the volume of the Defendants' arguments, we find no more substance in them than the district court found in their infomercials. We therefore affirm the district court in toto.

I. BACKGROUND

A. The Coral Calcium infomercial.

For purposes of introduction, a fairly simple recitation of only the uncontested facts will suffice. Greater detail will follow as necessary in the discussion section.

The Defendants on appeal are Direct Marketing Concepts, Inc. (DMC), ITV Direct, Inc. (ITV), Donald Barrett, Robert Maihos, and BP International (BP).1 Barrett and Maihos co-own ITV and DMC, both Massachusetts corporations; generally, ITV produces infomercials, and DMC distributes the infomercials, answers calls, and processes orders. BP is a holding corporation to which Barrett eventually (and secretly) transferred some of DMC's assets.

Beginning in late 2001, DMC, Barrett, and Maihos became involved in marketing the product Coral Calcium by producing and distributing an infomercial promoting that product. These Defendants then processed calls and sold Coral Calcium to consumers.

The infomercial for Coral Calcium relied on the purported expertise of Robert Barefoot. In the infomercial, Barefoot asserted a number of claims regarding coral-derived calcium2 and its supposed biological and medical properties. Barefoot claimed that all diseases are caused by a condition called acidosis:

Barefoot then claimed that calcium derived from Okinawan coral cures these diseases:

Barefoot asserted that coral-derived calcium was an effective cure for these diseases because it renders the body more alkaline, thereby curing acidosis:

Barefoot went on to claim that coral-derived calcium is superior to other sources of calcium because it is 100% bioavailable, meaning that all coral-derived calcium that is ingested is also absorbed into the body. To bolster his claims, Barefoot noted that unspecified articles from the Journal of the American Medical Association and the New England Journal of Medicine "said that calcium supplements reverse cancer... that's a quote."

The infomercial directed potential customers to call an 800 number, on the other end of which DMC-employed telemarketers would follow a script directing them to tell potential customers that the product Coral Calcium would be 100% absorbed by their bodies and would combat degenerative diseases by rendering an acidic body more alkaline. Telemarketers were also directed to tell sick customers that they should take higher doses of Coral Calcium, up to three times the standard dose. During the relevant time period (from January 2002 to July 2003), the Coral Calcium infomercial generated $54,034,394.82 in sales, of which approximately $575,000 were transferred to Defendant BP.

B. The Supreme Greens infomercial.

As with Coral Calcium, the Defendants were involved collectively in the production and airing of an infomercial for the product "Supreme Greens," also called "Supreme Greens with MSM." ITV produced the infomercial, which Barrett hosted; DMC processed calls and orders under Maihos's direction.

The infomercial for Supreme Greens relied on the purported expertise of "Dr." Alejandro Guerrero.4 Like Barefoot, Guerrero claimed that many major diseases are caused by acidosis, and that these diseases can be prevented and cured by rendering the body more alkaline:

Going beyond even Barefoot, Guerrero also claimed that Supreme Greens can cause weight loss by restoring alkalinity because "fat is your body's way of protecting itself from the acidic fluids."

The infomercial directed potential customers to call an 800 number, on the other end of which DMC-employed telemarketers would follow a script directing them to ask potential customers about their health issues and then explain how Supreme Greens supposedly could address those issues. For example, if a customer said she had cancer, the telemarketer was supposed to respond that "cancer is acidosis of the body and Supreme Greens alkalizes the body, and that's what you need, so you really want to take this." During the relevant time period (August 2003 to June 2004), Supreme Greens generated $14,683,436.24 in sales.

C. The FTC action.

In June 2004, the FTC filed a complaint in the United States District Court for the District of Massachusetts against a number of parties,5 alleging violations of the FTC Act, 15 U.S.C. §§ 45 and 52. The FTC sought both injunctive relief and monetary equitable relief in order to redress customers who had purchased Coral Calcium or Supreme Greens in reliance on the Defendants' allegedly deceptive infomercials. In July 2008, the district court granted summary judgment against the Defendants on the issue of liability, holding that the challenged infomercials were misleading as a matter of law. In August 2009, after a bench trial, the district court entered two Final Orders and Judgments permanently enjoining the Defendants from running their deceptive infomercials and ordering disgorgement from the Defendants (excluding BP) in the amount of $48,220,499.12 and from BP in the amount of $574,274.23. The Defendants now appeal.

II. DISCUSSION

The Defendants take a shotgun approach to their appeal, asserting that: (1) the district court applied an incorrect standard in finding them liable for deceptive advertising; (2) the record contained issues of fact as to whether they possessed sufficient substantiation for the claims asserted in the infomercials; (3) the claims made in the infomercials were mere puffery and were mollified by disclaimers, and therefore were not actionable; (4) Maihos is not individually liable as a matter of law; (5) the district court erred in calculating damages on the basis of the Defendants' gross receipts rather than net profits; (6) the district court erred in determining damages from January 2002 to February 2003; (7) the district court erred in determining damages from March 2003 to July 2003; and (8) the district court erred in determining damages from August 2003 to June 2004.

The FTC seeks to uphold the judgment of the district court in all respects, asserting that: (1) the district court applied a correct standard in finding the Defendants liable for deceptive advertising; (2) the record contained vast swaths of uncontradicted evidence supporting the Defendants' lack of adequate substantiation for the claims asserted in the infomercials; (3) the claims in the infomercials were specific and definite and therefore not exempted from liability under the puffery or disclaimer rules; (4) as half-owner and officer of DMC, Maihos is individually liable; (5) the district court has broad discretion to fashion an equitable remedy, and exercised the discretion appropriately and in accordance with precedent; (6) the district court did not err in determining damages from January 2002 to February 2003; (7) the district court did not err in determining damages from March 2003 to July 2003; and (8) the district court did not err in determining damages from August 2003 to June 2004.

This Court has jurisdiction under 28 U.S.C. § 1291. We review de novo both the district court's decision to grant a summary judgment motion, see Zimmerman v. Puccio, 613 F.3d 60, 70 (1st Cir.2010), and the district court's legal determinations after a bench trial, overturning the district court's factual determinations after a bench trial only in the case of clear error, see Wojciechowicz v. United States, 582 F.3d 57, 66 (1st Cir.2009). Applying these familiar standards to the Defendants' arguments as appropriate, we see no need to diverge from the district court on any point.

A. The "reasonable basis" test is appropriate for deceptive advertising claims.

The Defendants challenge both the legal and factual bases for the district court's grant of summary judgment. We begin by teasing out the applicable law.

Our starting point is the FTC statute, which provides that both "unfair or deceptive acts or practices in or affecting commerce" (15 U.S.C. § 45(a)(1)) and "disseminat[ing], or caus[ing] to be disseminated, any false advertisement ... in or having an effect upon commerce" (15 U.S.C. § 52(a)) are "unlawful." 15 U.S.C. § 55 defines the term "false advertisement" as "an advertisement, other than labeling, which is misleading in a material respect...." Given the strong similarity between the terms "deceptive" and "misleading", it is no surprise that sections 45 and 52 are sometimes applied in tandem as the basis for an FTC action against an alleged false advertiser; indeed, such a tandem reading is expressly allowed by 15 U.S.C. § 52(b).

When the FTC brings an action based on the theory that advertising is deceptive because the advertisers lacked a reasonable basis for their claims, the FTC must: (1) demonstrate "what evidence would in fact establish such a claim in the relevant scientific community"; and (2) "compare[] the advertisers' substantiation evidence to that required by the scientific community to see if the claims have been established." Removatron Intern. Corp. v. FTC, 884 F.2d 1489, 1498 (1st Cir.1989) (applying to administrative determination of deceptive advertising); see also FTC v. Garvey, 383 F.3d 891, 901 (9th Cir.2004) (applying the same test to claims by FTC in court). Where the advertisers lack adequate substantiation evidence, they necessarily lack any reasonable basis for their claims. See Removatron, 884 F.2d at 1498. And where the advertisers so lack a reasonable basis, their ads are deceptive as a matter of law. Id.

The Defendants argue that there is a third prong to a deceptive advertising claim, asserting that the FTC was required —and failed—to prove that the infomercials were actually false. However, that argument is at odds with the cases cited above. Indeed, the Defendants cannot point to any source adequate to disrupt the FTC's and district court's firm grounding in case law.6

Instead, the Defendants cite haphazardly to a federal statute (the Dietary Supplement Health and Education Act of 1994, Pub.L. No. 103-417, 108 Stat. 4325), whose legal relevance (if any) the Defendants never explain, and to a smattering of First Amendment case law, without engaging in any application of those sources or attempting to produce so much as a rough sketch of a rule that might support their proposition. We can make neither heads nor tails of these citations, which have no clear relevance and which are completely devoid of context or developed argument. We therefore hold that the Defendants have waived any argument they might have raised under those sources, if any exists. See, e.g., United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990) ("[I]ssues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.").

In light of the Defendants' failure to raise any principled objection to the "reasonable basis" framework, which was carefully applied by the district court, the remainder of our analysis will follow that framework.

B. The Defendants produced no actual substantiation for their health claims.

We must now consider the application of the Removatron "reasonable basis" test to the record on summary judgment. To recap, under this test (and applying the summary judgment standard), we must determine whether there was uncontroverted evidence regarding: (1) what sort of evidence would scientifically establish the claims the Defendants made in their infomercials; and (2) whether the Defendants were actually possessed of such evidence. See Removatron, 884 F.2d at 1498. It is uncontested that the Defendants asserted the following claims in their infomercials: (1) coral-derived calcium supplements cure cancer, multiple sclerosis, and other degenerative diseases by rendering acidic bodies more alkaline, and they are 100% absorbed by the human body; and (2) Supreme Greens cure cancer and cause weight loss by rendering acidic bodies more alkaline. If these claims are not supported by sufficient scientific evidence, then liability follows. The Defendants claim that there are issues of fact on both prongs as applied to both infomercials.

On the first prong, the FTC produced four expert declarations which demonstrated that the claims could be substantiated by double-blind, placebo-controlled human studies. Specifically, Dr. Richard Wood averred that "[i]t is generally accepted that human studies are required to support a scientific finding concerning the bioavailability of a test compound in the human body." Dr. Maryfran Sowers provided specific examples of the scientific standards for, e.g., a chemical compound's effect on heart health: "It is generally accepted among scientists that for a test compound or product to be considered as having a clinically meaningful effect on blood pressure, the changes in blood pressure caused by the compound or test must reach certain established thresholds," which she then described in numerical detail. Dr. Sowers outlined other contours of reliability, noting that prospective studies of 50,000 and 90,000 subjects were "considered very reliable because of the large cohort involved and the breadth of information collected," whereas "the early data collected in a longitudinal study is scientifically suspect until adequate temporal distance is established between when the calcium intake data was collected and the time when new or incident blood pressure could develop." Dr. Landon King averred that "[i]n order to evaluate whether an intervention compound ... changed the pH balance of the body, researchers would develop a protocol for a controlled clinical trial that would measure the subjects' pH balance prior to receiving the test compound (or placebo) and at an appropriate period(s) after receiving either the test compound or a placebo." Dr. King noted specifically that "[i]n order to claim that a product increases alkalinity, reasonable scientists would expect the product to have been subject to such an appropriate clinical study." Dr. Barrie Cassileth averred that "[t]he most scientifically valid way to determine whether Supreme Greens (or any other product) produces any results is a double-blind, placebo controlled study."

To be sure, there may be other scientific evidence that could be sufficient, and we may assume for these purposes that a double-blind study is not necessarily required. But the government established that some scientific evidence is required for substantiation, and thus satisfied the first prong of the Removatron test. Because the FTC produced affidavits which are more than adequate on their face to satisfy the first prong of a "reasonable basis" claim, and because the Defendants neither produced nor pointed to any evidence to raise even the tiniest of fact issues, summary judgment was appropriate on the first prong.

On the second prong, the FTC relied on the same four expert declarations, in which the experts compared the Defendants' evidence to the available literature and concluded in each case that the Defendants' evidence was woefully inadequate. The experts specifically opined that: (1) there was some evidence that calcium might help to prevent colorectal cancer but no evidence that calcium cures cancer; (2) there was some evidence that calcium might lower blood pressure but none that it cures heart disease; (3) there was no evidence whatsoever that calcium has any effect on autoimmune disorders; (4) there has been no research published in the Journal of the American Medical Association or the New England Journal of Medicine indicating that calcium "reverses" cancer; (5) there is no evidence that any kind of calcium is 100% absorbed; (6) there is no evidence that any disease is caused by "an overly acidic body"; (7) there is no evidence that alkalinity cures cancer or heart disease; (8) there is no evidence that any ingredient of Supreme Greens can prevent, treat, or cure cancer, heart disease, or diabetes; and (9) there is no evidence that Supreme Greens may cause weight loss.

The record contains a slew of other documents, including excerpts from Barefoot's books, excerpts from Barefoot's deposition testimony, excerpts from Guerrero's deposition testimony, a number of popular science and pseudoscientific articles, and one preliminary study. The Defendants claim that this evidence provided them with a reasonable basis for accepting the infomercials' claims as true. However, it is clear that none of this material comes close to establishing an issue of fact regarding the Defendants' woefully inadequate substantiation evidence.

Barefoot's books present jumbles of quotes from scientists, scientific review articles, and scientific studies interspersed with references to Reader's Digest and other general-consumption reductions of these studies. His sources support such uncontroversial propositions as "[t]he connection between the electrical activity of the cell and the release of the neurotransmitter is not direct; an essential intermediary is the calcium ion." Robert R. Barefoot & Carl J. Reich, The Calcium Factor (2000) (internal citation removed) (emphasis Barefoot's). However, none of these scientists or studies supports the panacean claims made in the Coral Calcium infomercial; the claims are extrapolations, distortions, and sometimes, seemingly, utter fabrications. It appears to be no accident that neither Barefoot, nor any Defendant, nor any of the Defendants' attorneys has at any point in these proceedings identified any particular scientific study or studies to support the specific claims presented in the Coral Calcium infomercial. Indeed, Barefoot's deposition testimony primarily relies on appeals to generic authority; his standard rhetorical practice is to assert that there are myriad studies that support a given claim, without identifying any specifically.7 When pressed for specificity, he generally refers the questioner to his books.8 Nowhere in the record is there any support for, e.g., the following propositions: all diseases are caused by acidosis; calcium supplements cure cancer; calcium supplements cure multiple sclerosis; or coral-derived calcium is 100% absorbed into the body.

Guerrero's testimony is even less compelling, given that he relies primarily on his own general experience as an alternative medicine practitioner, without reference to any studies at all. The Defendants make much of a double-blind, controlled, but also unpublished and preliminary study, which they assert supports the health claims advanced in the Supreme Greens infomercial; however, the study found, based on a sample size of sixteen people, that one of the ingredients in Supreme Greens—Methyl-Sulfonyl-Methane, or MSM—might relieve arthritis pain and was therefore worthy of further study. This study on its face is grossly insufficient to support the Defendants' claims of Supreme Greens' efficacy in treating all diseases. And even the abstracts and excerpts from pseudoscientific articles, published in journals such as the non-peer reviewed and now-defunct Healthy & Natural Journal and Natural Way for Better Health, do not support the specific claims made in either infomercial—e.g., there is no support for the claims that the product Supreme Greens or any of their ingredients cure cancer, cure heart disease, or cause weight loss by alkalizing the body and thereby curing its need for fat as a protection against acid.

Given the complete absence of support for the vast majority of the Defendants' health claims—which absence the FTC's four experts also testified to on the basis of their own literature reviews—we easily could conclude that the Defendants lacked adequate substantiation under even the most lax standard of scientific reliability. Here, however, the FTC produced evidence establishing a rigorous standard of scientific reliability, and the record reveals that the Defendants fell well and unquestionably short of this standard. In all, the strong evidence establishing a scientific standard for evaluating the Defendants' advertising claims, the overwhelming evidence supporting the Defendants' lack of substantiation evidence, and the failure of the Defendants to indicate any evidence to raise an issue of fact on either point, compel the legal conclusion that the Defendants lacked a reasonable basis for the health claims they used to sell their products. Cf. Removatron, 884 F.2d at 1498. The Defendants therefore engaged in deceptive advertising as a matter of law. See id.

C. The Defendants made specific health claims which were not cured by general disclaimers.

The Defendants attempt to head off the above analysis by asserting that their infomercials advanced no actual health claims but, instead, presented only puffery which was further attenuated by the presence of general disclaimers. Where a claim is merely "exaggerated advertising, blustering, and boasting upon which no reasonable buyer would rely," it may be un-actionable puffery. See Clorox Co. Puerto Rico v. Proctor & Gamble Comm. Co., 228 F.3d 24, 38 (1st Cir.2000) (quotation marks omitted). However, "specific and measurable" claims and claims that may be literally true or false are not puffery, and may be the subject of deceptive advertising claims. Id. (quotation marks omitted). As set forth above, passim, the Defendants' infomercials presented specific and measurable health claims. These claims included definite statements that coral calcium cures cancer, autoimmune diseases, and pain by rendering acidic bodies more alkaline, as well as statements that Supreme Greens cure cancer, heart disease, and cause weight loss by rendering acidic bodies more alkaline. Due to their specificity and concreteness, such claims go far beyond puffery as a matter of law. See id. at 39.

The presence of disclaimers does not provide any more assistance to the Defendants. This court has held that "[d]isclaimers or qualifications in any particular ad are not adequate to avoid liability unless they are sufficiently prominent and unambiguous to change the apparent meaning of the claims and to leave an accurate impression. Anything less is only likely to cause confusion by creating contradictory double meanings." Removatron, 884 F.2d at 1497. The disclaimers at issue here did nothing to affect the meaning of the infomercials' health claims and were not even sufficient to cause confusion, given the clarity and concreteness of the claims. The infomercial transcripts reveal only disclaimers that the infomercials are paid advertising. The Defendants have presented no concrete evidence of any other attenuating messages.9 In contrast, the health claims were bold and straightforward, presented by supposed experts as testable observations backed up by clinical trials and studies. Given the Defendants' lack of substantiation for these concrete claims framed by do-nothing disclaimers, we affirm the district court's grant of summary judgment on the issue of the Defendants' liability for deceptive advertising.

D. Maihos is individually liable as an owner and corporate officer who lacked appropriate substantiation.

The Defendants present one last argument on liability, arguing that the district court erred in holding Maihos individually liable. Individual liability for deceptive advertising is appropriate where an individual (1) was a corporate officer with the capacity to make decisions regarding the challenged conduct, and (2) knew or should have known that there was no reasonable basis for the deceptive claims. See, e.g., FTC v. Publishing Clearing House, Inc., 104 F.3d 1168, 1170 (9th Cir. 1997). The FTC produced ample support for each proposition, and the Defendants produced no evidence to the contrary.

The FTC produced evidence that Maihos was a 50% owner of DMC and ITV, that he controlled both companies' purse strings and day-to-day operations, and that he was the contact for an attorney retained to review the infomercials for their legality under federal trade law.10 Maihos (ignoring his status as an officer and half-owner of DMC) focuses on gaps in his responsibilities, relying on, e.g., his testimony that he did not edit the content of advertising. This is simply irrelevant. The question is whether he could have nipped the offending infomercials in the bud; the FTC produced evidence that he could, and he has produced no evidence— even his own testimony—to indicate that he couldn't. See FTC v. Freecom Comm., Inc., 401 F.3d 1192, 1205 (10th Cir.2005) (finding individual liability where "[e]verybody knew that [the defendant] was the principal shareholder of the company and his opinions and advice and direction were listened to very carefully and were generally followed or heeded").

On the second prong, Maihos's knowledge, the FTC produced Maihos's own deposition testimony admitting that DMC did not have any substantiation for the claims made in either infomercial. Maihos also testified about an email he received from his then-girlfriend, a registered dietitian. The email provides both direct and circumstantial evidence of Maihos's knowledge. The email is direct evidence that the girlfriend informed Maihos that "[c]alcium from anything cannot be 100 percent bioavailable" and that "[t]here's no evidence at all that Coral Calcium is better than ordinary calcium or has any special health-boosting properties." The girlfriend also asked Maihos, "do you think there is a product ([over the counter] no less) that can prevent heart disease, diabetes, arthritis AND cancer?" Maihos testified that he dismissed the email as mere skepticism. However, the email is also circumstantial evidence that Maihos actually requested the information from the girlfriend, who consulted third parties on Maihos's behalf. The email begins, "Hello, as requested here are the responses I got." It also attached an email from the address Wic-talk@NAL. USDA.GOV, which a quick internet search reveals is an electronic discussion group promoted by the United States Department of Agriculture "for use by individuals involved in providing nutrition services." See WIC-Talk, http://www.nal.usda.gov/ wicworks/Talk/index.html (last visited Oct. 19, 2010). Thus, the imputed exchange giving rise to the girlfriend's email implies that Maihos himself questioned the infomercials' claims. The FTC also produced evidence that Maihos had attended DMC meetings regarding the production of "clean" and "re-edited" versions of the infomercials while earlier versions of the infomercials still ran. Finally, the FTC produced evidence that an attorney suggested to Maihos in October 2003, well before the Defendants pulled the Supreme Greens infomercial off the air,11 that the Supreme Greens infomercial required voluminous support and advanced "BS" claims.

Again, the Defendants point to nothing that might challenge any of this evidence, relying instead on Maihos's protestations that he sincerely believed in the infomercials' health claims. It is true that two district court cases support the proposition that sincere belief may be an element in the individual liability calculus; however, even sincere belief is not sufficient here to overcome the overwhelming evidence that Maihos knew or, at the very least, should have known that the infomercials lacked any reasonable basis in scientific fact. See FTC v. Medical Billers Network, Inc., 543 F.Supp.2d 283, 320-22 (S.D.N.Y.2008) (finding individual liability); FTC v. Patriot Alcohol Testers, Inc., 798 F.Supp. 851, 860 n. 3 (D.Mass.1992). This is particularly so given that the patent ridiculousness of the infomercials' health claims was presented multiple times by multiple people to Maihos, who chose to remain willfully blind. Thus, there is no question that Maihos knew that the infomercials' claims lacked substantiation, that he had the authority to control DMC and ITV, and, nevertheless, that he did little or nothing. The district court did not err in holding Maihos individually liable for deceptive advertising, and we affirm.

E. Gross receipts are an appropriate basis for calculating damages.

Turning now to the issue of damages, the Defendants begin by arguing that damages for deceptive advertising are limited to actual profits, not gross receipts. If this were so, then at least part of the district court's damages award would be erroneous. However, the law allows for broad discretion in fashioning a remedy for deceptive advertising; many cases uphold rescission (effectively, restoring the parties to pre-sale status) or restitution (under these facts, the same) as appropriate remedies. See Trudeau, 579 F.3d at 771 (noting that "[c]onsumer loss is a common measure for civil sanctions in contempt proceedings and direct FTC actions" and listing cases). Thus, consumer loss, as represented by the Defendants' gross receipts, would appear to be an appropriate measure of damages.

Nevertheless, the Defendants ask us to rely on FTC v. Verity Int'l, Ltd., 443 F.3d 48 (2d Cir.2006), for the proposition that the FTC's remedy is limited to the Defendants' profits rather than their gross receipts. Verity's limited rule does not apply here.

In Verity, a series of unrelated, non-party middlemen partook of the proceeds from the defendants' scheme before the defendants themselves got a bite. See 443 F.3d at 53 (describing the relationship as a "multitiered, cascading-payment structure"). The court found this payment structure highly relevant to the issue of damages, noting that "in many cases in which the FTC seeks restitution, the defendant's gain will be equal to the consumer's loss" but casting Verity's facts as an exception limited to the situation "when some middleman not party to the lawsuit takes some of the consumer's money before it reaches a defendant's hands." Id. at 68 (emphasis added); see also Trudeau, 579 F.3d at 772 (describing Verity as holding only that "certain circumstances require courts to limit disgorgement to the defendant's profits"). Here, the Defendants seek to inflate Verity's exception so that it overshadows the rule.

We are not persuaded. Because this set of facts lacks the non-party middleman that gave rise to the exception in Verity, we will follow the general rule. Here, the Defendants on appeal took in proceeds directly, except for roughly one year when fellow defendant (but non-appellant) Triad processed Coral Calcium orders. The FTC introduced ample evidence of the overall proceeds from Coral Calcium during this period; however, the parties' financial records were in such disarray that the actual split among the parties could not be determined.12 The Defendants on appeal now claim that Triad siphoned off the vast majority of the proceeds, leaving them holding an empty bag, but we cannot tell whether this is the case. Because every entity that had received consumer money was a defendant, the district court held that gross receipts were an appropriate measure of damages; because records were unclear as to how much consumer money each defendant received, the district court evenly split the total receipts between DMC and Triad for the time period when Triad acted as a middleman. This was consistent with Verity and within the bounds of the district court's discretion in fashioning an equitable remedy. See Freecom, 401 F.3d at 1202 n. 6 (noting that the FTC Act's "grant of authority to provide injunctive relief carries with it the full range of equitable remedies, including the power to grant consumer redress").

Thus, the district court committed no error in resting its damages determination on the Defendants' gross receipts rather than their net profits, and we will proceed to review the court's calculation of what those gross receipts actually were. To determine the appropriate amount of damages in deceptive advertising cases, courts apply a burden-shifting scheme. First, the FTC must provide the court with a reasonable approximation of damages.13 See FTC v. Febre, 128 F.3d 530, 535 (7th Cir.1997). Both gross receipts and net customer loss are appropriate measures. See id.; Freecom, 401 F.3d at 1206. Once a reasonable approximation of damages has been provided, the defendant has an opportunity to demonstrate that the figures are inaccurate. See Febre, 128 F.3d at 535. Any fuzzy figures due to a defendant's uncertain bookkeeping cannot carry a defendant's burden to show inaccuracy. See id. The district court and all parties find a rare point of agreement in the notion that this exercise may be broken down into three constituent time periods—January 2002 to February 2003, March 2003 to July 2003, and August 2003 to June 2004—each of which we will address in turn.

F. The district court's determination of damages from January 2002 to February 2003 was not erroneous.

The Defendants first challenge the propriety of the damages award for sales of Coral Calcium from January 2002 to February 2003, during which time DMC and fellow defendant (but non-appellant) Triad cooperated to sell Coral Calcium. The FTC introduced Exhibit 185 to support a finding that these defendants collectively received $40.9 million from sales of Coral Calcium from January 2002 to February 2003. A witness—Steven Ritchey, Triad's vice president in charge of accounting —testified that gross receipts from this time period were $40.9 million. Even Defendant Barrett testified that gross receipts from this time period were around $40 million. The district court credited all of the above, found that gross receipts were $40.9 million, found that the records were unclear on the exact division of proceeds between DMC and Triad, and therefore judiciously split the award in two. This was all well within the court's discretion, and the Defendants do not raise any serious argument to the contrary.

The Defendants do challenge Exhibit 185 as improperly admitted. Although there is adequate evidence to support the district court's determination even absent Exhibit 185, we will briefly explain why that exhibit's admission was appropriate. Fed.R.Evid. 803(6) provides that business records may be admissible if certified according to Fed.R.Evid. 902(11). Rule 902(11) provides that "a duplicate of a domestic record of regularly conducted activity" is admissible "if accompanied by a written declaration of its custodian or other qualified person." This declaration must establish that the document:

Fed.R.Evid. 902(11).

The Defendants do not and cannot dispute that a declaration from Ilesh Sanghavi, who worked for Triad as an accountant, touched each of these elements, providing a solid basis in the record supporting the district court's decision.14 Instead, the Defendants take issue with the FTC's declarant's wording (use of "believe" and failure to use the magic words "regular course of business"), the format of the exhibit (arguing that CDs are not produced in the regular course of business), and their own speculation that the exhibit might include third party data. None of these arguments provides any reason that we can discern to override the district court's exercise of discretion; the only one that might have any legal basis is the third party data argument, which nevertheless fails.15 Similarly, the Defendants protest the FTC's relatively late submission of the authenticating affidavit without actually suggesting that they have suffered any prejudice or otherwise indicating that their protestations would support reversal or remand. Again, we are reminded of and apply the principle that insufficiently developed arguments are waived. Zannino, 895 F.2d at 17.

The Defendants also argue that they met their burden of demonstrating the inaccuracy of the FTC's figures by arguing that DMC and Triad split only the proceeds from Coral Calcium sales, not the gross receipts; however, they point to no hard evidence to support this assertion, nor do they present any counter to the argument that they could have been held liable for the whole $40.9 million under joint and several liability. How to weigh the evidence is a question of fact on which we must defer to the district court. And, in the end, the district court had plenty of good reasons for its determination of damages from January 2002 to February 2003, the Defendants have presented no good reasons to upset that determination,16 and we need go no further in order to affirm.

G. The district court's determination of damages from March 2003 to July 2003 was not erroneous.

The Defendants next challenge the damages award for sales of Coral Calcium from March 2003 to July 2003, at which point Triad was out of the picture and the Defendants on appeal acted in concert with one another exclusively. The only argument the Defendants can muster on this front is another challenge to the authentication of a set of business records admitted as Exhibits 187 and 209. These records are the products of DMC spreadsheets that show $13.1 million in sales of Coral Calcium from March 2003 to July 2003. These records were authenticated by live testimony, so only Fed.R.Evid. 803(6) and not Fed.R.Evid. 902(11) applies. To be admissible, a record must have been

Fed.R.Evid. 803(6).

Again, the Defendants do not and cannot dispute that an affidavit—this one from Karen Gorewitz, a DMC employee— touched each element of proper authentication, providing a solid basis in the record supporting the district court's decision.17 Instead, the Defendants generically attack Gorewitz's witness-stand testimony regarding the content of the affidavit, arguing that her lack of certainty on peripheral issues—e.g., she did not know much about the "Value" column in the spreadsheets, or whether DMC kept the records in any particular form—somehow undermines the documents' authenticity. As is frequently the case throughout their brief, the Defendants fail to tie their general attacks into any sort of legal theory, conducting no analysis but citing to Fed.R.Evid. 803(6) and 902(11) without comment. Even assuming that they might have raised a valid legal argument (although again we find ourselves reminded of the rule that inadequately briefed issues are waived, see Zannino, 895 F.2d at 17), their attack—concerning the style more than the substance of the witness's testimony—presents the sort of second-guessing, cold-record inquiry that cautions deference to the district court. See United States v. Freeman, 208 F.3d 332, 339 (1st Cir.2000). Accordingly, we affirm.

H. The district court's determination of damages from August 2003 to June 2004 was not erroneous.

Finally, the Defendants challenge the damages award for sales of Supreme Greens from August 2003 to June 2004. They essentially argue that the FTC did not meet its initial burden of demonstrating a reasonable approximation of damages. This is so, they argue, because the Defendants' own records were in such disarray that the FTC could not draw a connection from the Supreme Greens receipts to the particular version of the Supreme Greens infomercial that the FTC proved to be deceptive. Purportedly, numerous other versions of the Supreme Greens infomercial existed and were aired at various times and places, although no one knows which version was aired at what time in any given place.

The district court has discretion to determine a reasonable approximation of damages, and unclear financial records cannot carry a defendant's burden of demonstrating that such a reasonable approximation is inaccurate. See Febre, 128 F.3d at 535. Here, the Defendants could not or would not produce an accounting that suggested even a rough approximation of what percentage of their Supreme Greens proceeds were based on the offending infomercial. Instead, in response to an interrogatory, they represented to the FTC that their records were subject to "substantial confusion" and that "it is impossible to determine what sales are attributable to any specific version of the Supreme Greens infomercial." At this point, the FTC perhaps should have filed a motion to compel, given its apparent ability to produce order from chaos in this case. Instead, it allowed the records regarding which version of the Supreme Greens infomercial aired where and when to remain in disarray. This was the one hitch in an otherwise well-conducted case, but it is not enough to overcome the fact that, in the end, it is DMC's record-keeping that caused the uncertainty. And this hitch certainly does not establish the sort of clear error required to upset the district court's careful and considered ruling. Thus, the district court was within its discretion to estimate damages broadly based on the accounting information available to it, and the defendants produced nothing to overcome such an estimate. See Freecom, 401 F.3d at 1206-07. We affirm.

III. CONCLUSION

On a well-developed record that reveals no significant factual disputes, the district court correctly granted summary judgment to the FTC on the issue of the Defendants' liability for deceptive advertising. On an equally well-developed record after a bench trial on damages, the district court correctly applied its equitable authority to fashion an appropriate remedy, ordering the Defendants to cure their customers in a way that their bogus supplements could not.18 Accordingly, we affirm the district court in all respects.