Mirror Worlds, LLC v. Apple, Inc.

MEMORANDUM OPINION AND ORDER LEONARD DAVIS, District Judge. Having considered the parties’ written submissions and oral arguments, the Court GRANTS IN PART and DENIES IN PART Apple’s Renewed Motion for Judgment as a Matter of Law, Motion for New Trial and Motion for Remittitur Pursuant to Federal Rules of Civil Procedure 50 and 59 (Docket No. 432); DENIES Apple’s Motion for a Finding of Inequitable Conduct and Good Cause to Re-Open the Record fora Bench Trial (Docket No. 433); 1 DENIES Mirror Worlds’ Motion for (1) Entry of Judgment, (2) Prejudgment Interest, (3) Post Verdict and Prejudgment Damages, (4) Post Judgment Royalties, (5) Enhanced Damages, (6) Attorneys’ and Experts’ Fees, (7) Costs, and (8) Post Judgment Interest (Docket No. 435); GRANTS Apple’s Motion to Strike the October 29, 2010 Declaration of Walter Bratic and Documents Not in Evidence (Docket No. 446); and DENIES Apple’s Motion Regarding Mirror Worlds’ Waiver of Privilege for Documents Listed on the December 9, 2010 Privilege Log (Docket No. 465). BACKGROUND Mirror Worlds’ Complaint, filed March 14, 2008, alleges that Apple infringes U.S. Patent Nos. 6,006,227 (“the '227 patent”), 6,638,313 (“the '313 patent”), 6,725,427 (“the '427 patent”) (collectively “the patents-in-suit” or “the patents”), and 6,768,-999. 2 The Patents-In-Suit The '227 patent issued on December 21, 1999, the '313 patent on October 28, 2003, and the '427 patent on April 20, 2004, all to Eric Freeman and David Gelernter. The '227, '313, and '427 patents stem from the same application and are of the same family. 3 The patents-in-suit disclose a document stream operating system and method *708 where: 1) the documents are stored in one or more chronologically ordered streams; 2) the location and nature of file storage is transparent to the user; 3) information is organized as needed instead of at the time the document is created; 4) sophisticated logic is provided for summarizing a large group of related documents at the time a user wants a concise overview; and 5) archiving is automatic. '227, '313, & '427 patents at [57]. At the time of the invention, the inventors recognized that operating systems had increasing abilities to store data. The inventors noticed the potential problems associated with efficiently retrieving a growing amount of stored information and sought a way to uniquely display, organize, and access the data. The patented invention uses a “stream” to organize the data. A stream is a diary that organizes documents into a time ordered sequence with a past, present, and future. 4 See '227 patent at 4:6-8, 5:53-6:7. The documents in the stream can be text, pictures, animations, software programs, or any other type of data. See '227 patent at [57], As illustrated below, the patents describe displaying the stream as stacked images so the images appear to be receding and foreshortened: [[Image here]] '227, '313, & ’427 patents at Fig. 1. The documents represented in the stream are automatically archived, and a time stamp is used to identify the data. See '227 patent at [57], 16:9-25. As a user scrolls through the documents in the stack, an *709 abbreviated version of the document is presented, giving the user a glimpse of the document. See '313 patent at 15:21-22, 16:35-36. The inventors represented these attributes were advantageous over conventional operating systems in organizing and accessing electronic data. The Accused Products Mirror Worlds accused Apple’s operating system, Mac OS X, of infringement. The “Tiger,” “Leopard,” and “Snow Leopard” operating systems are the various accused versions of Mac OS X. Mirror Worlds accused Apple’s computers and servers that use Leopard and Snow Leopard of infringing the '227, '427 and '313 patents and computers and servers that use Tiger of infringing the '227 patent. 5 The accused Apple computers include the eMac, MacBook, MacBook Air, MacBook Pro, Mac mini, iMac, Mac Pro, iBook, PowerBook, Power Mac, and PowerPC. In addition to accusing Mac OS X, Mirror Worlds accused Apple’s mobile devices, including the iPhone, iPod Touch, iPod Classic, iPod Nano, and iPad, of infringing the '427 patent. Mirror Worlds identified three Mac OS X features — Spotlight, Cover Flow, and Time Machine — as practicing the patented invention. Transcript of Trial Proceedings 9/28/10 p.m. at 87:12-22 (hereinafter “TT”). Specifically, Mirror Worlds alleges that Spotlight implements the stream using Spotlight Store, Cover Flow practices displaying items in a stack, and Time Machine automatically archives as claimed by the patents. The Spotlight feature allows a user to search across the various contents (e.g. documents, picture, videos, music, calendar events) on the operating system. Spotlight is implemented through Spotlight Store, which has a Content Index, a Metadata Store, and an interface. 9/28/10 TT at 89:13-93:9; 9/30/10 p.m. (pt. 1) TT at 89:17-91:11. The Content Index maintains an index of the contents of the data. Using a document as an example, the Content Index keeps track of the words in the document. Likewise, the Metadata Store maintains the metadata information. Again using a document as an example, the stored content could include the time and date of creation, author, or where the document is stored. Finally, the interface in Spotlight allows a user to submit search queries. The Tiger, Leopard, and Snow Leopard operating systems include Spotlight Store, and the Leopard and Snow Leopard operating systems also enter metadata in the Content Index. 9/28/10 TT at 104:8-15; 9/30/10 a.m. 39:13-15. Cover Flow is a graphical user interface that allows a user to flip through a stack of documents while representative versions of the document are displayed. 9/28/10 TT at 108:5-11. Time Machine is a backup utility that archives a user’s data. 9/28/10 TT at 108:16-109:5. The Claims Pursued at Trial Before proceeding to trial, Mirror Worlds narrowed its asserted claims and accused products. 6 Docket No. 353. Mirror Worlds asserted 12 claims at trial: method claims 13 and 22 of the '227 patent, method claims 1-3, 9, and 11 of the '313 patent, and claims 1, 8, 16, 18, and 25 of the '427 patent. Mirror Worlds alleged that Apple both directly and indirectly infringed its patents and that the infringe *710 ment was willful. Mirror Worlds also contended it was entitled to damages (not less than a reasonable royalty), interest and costs, enhanced damages, attorneys’ fees, and injunctive relief. After the close of Mirror Worlds’ casein-chief, the Court granted Judgment as a Matter of Law that: 1) Apple did not infringe under 35 U.S.C. § 271(f); 2) Apple did not induce or contributorily infringe any claims; 7 and 3) Apple did not literally infringe claims 16 and 18 of the '427 patent. 9/29/10 p.m. TT at 96:25-97:16 (Mirror Worlds’ confirmation that it did not claim literal infringement for the claims 16 and 18 of the '427 patent). The Court requested briefing regarding infringement under the doctrine of equivalents for claims 16 and 18 of the '427 patent. Upon consideration of the parties’ written submissions and oral argument, the Court granted judgment as a matter of law that Apple’s mobile devices did not infringe claims 16 and 18 of the '427 patent under the doctrine of equivalents, thereby removing the mobile devices from the case. Docket No. 400. Following these rulings, Mirror Worlds’ case went to the jury on Apple’s direct infringement of method claims 13 and 22 of the '227 patent; method claims 1-3, 9, and 11 of the '313 patent; and claims 1, 8, 16, 18, and 25 of the '427 patent by Apple making, using, offering to sell, selling, or importing Mac OS X 10.4-6. The jury found the patents-in-suit valid and infringed and listed damages of $208.5 million for each patent. Docket No. 409. LEGAL STANDARDS Judgment as a matter of law is only appropriate when “a reasonable jury would not have a legally sufficient evidentiary basis to find for the party on that issue.” Fed. R. Crv. P. 50(a). “The grant or denial of a motion for judgment as a matter of law is a procedural issue not unique to patent law, reviewed under the law of the regional circuit in which the appeal from the district court would usually lie.” Finisar Corp. v. DirecTV Group, Inc., 523 F.3d 1323, 1332 (Fed.Cir.2008). The Fifth Circuit “uses the same standard to review the verdict that the district court used in first passing on the motion.” Hilt-gen v. Summit, 47 F.3d 695, 699 (5th Cir.1995). Thus, a jury verdict must be upheld, and judgment as a matter of law may not be granted, unless “there is no *711 legally sufficient evidentiary basis for a reasonable jury to find as the jury did.” Id. at 700. A court reviews all evidence in the record and must draw all reasonable inferences in favor of the nonmoving party; however, a court may not make credibility determinations or weigh the evidence, as those are solely functions of the jury. See Reeves v. Sanderson Plumbing Prods., Inc., 530 U.S. 133, 150-51, 120 S.Ct. 2097, 147 L.Ed.2d 105 (2000). WAIVER As a threshold matter, the Court rejects Mirror Worlds’ argument that Apple waived its right to judgment as a matter of law for non-infringement of the Mac OS X products. Mirror Worlds argues that Apple’s motions at trial were limited to the mobile devices. Apple moved for judgment as a matter of law multiple times throughout the case. At the close of Mirror Worlds’ case-in-chief, among other grounds, Apple moved for judgment as a matter of law of non-infringement under the doctrine of equivalents. 9/29/10 p.m. TT at 89:13-90:1 (“Mirror Worlds has failed to establish any infringement under the DOE, because there is no evidence for a reasonable jury to find that the differences between the accused products and Mirror Worlds’ patents-in-suit are insubstantial.”). Again, after the close of evidence and before the case was submitted to the jury, Apple re-urged its motion. See 10/1/10 TT at 17:22-24,19:9-13. The Fifth Circuit construes Rule 50(a) liberally. See Blackboard, Inc. v. Desire2Learn, Inc., 574 F.3d 1371, 1379-80 (Fed.Cir.2009). A challenge to the sufficiency of a party’s motion for judgment “should be examined in light of the accomplishment of its particular purpose as well as in the general context of securing a fair trial for all concerned in the quest for truth.” MacArthur v. Univ. of Tex. Health Ctr., 45 F.3d 890, 897 (5th Cir.1995). The purpose of a Rule 50 motion is to: 1) alert the Court as to the party’s legal position; and 2) put the opposing party on notice of the moving party’s position as to the insufficiency of the evidence. Blackboard, Inc., 574 F.3d at 1379-80. Apple’s motions for judgment as a matter of law and renewed motions were not limited as Mirror Worlds asserts. Apple repeatedly objected to the adequacy of evidence. supporting Mirror Worlds’ claims, such that neither Mirror Worlds nor the Court could have failed to understand Apple’s positions. Thus, Apple satisfied the procedural requirements for its motions for judgment as a matter of law. SUFFICIENCY OF EVIDENCE FOR INFRINGEMENT Next, the Court addresses whether the record contains sufficient evidence to support the jury’s finding of infringement. The Court first examines the evidence supporting Apple’s direct infringement of the asserted method claims of the '227 and '313 patents and then turns to the evidence supporting Mirror Worlds’ claims of infringement under the doctrine of equivalents as to the '427 patent. The Court’s determination regarding the asserted method claims affects all asserted claims of the '227 and '313 patents, thus is dispositive for these patents. Likewise, the Court’s examination of Mirror Worlds’ equivalency infringement claims addresses limitations that are required by all of the asserted claims of the '427 patent, thus is dispositive of the '427 patent. Accordingly, the Court’s decisions addressing these two issues are case dispositive on all claims for all asserted patents. Direct Infringement of the Asserted Method Claims After the Court dismissed Mirror Worlds’ indirect infringement claims from the case, Mirror Worlds’ claims were restricted to Apple’s direct infringement. *712 Accordingly, the jury’s verdict was limited to Apple’s direct infringement of the '227, '313, and '427 patents by making, using, offering to sell, selling, or importing computers and servers containing Mac OS X 10.4-6. All of the asserted claims from the '227 patent (claims 13 and 22) and the '313 patent (claims 1, 2, 3, 9, and 11) are method claims. At trial, Mirror Worlds alleged that various capabilities of Spotlight, Cover Flow, and Time Machine infringed the asserted method claims. In support, Mirror Worlds relied on the testimony of its expert, Dr. Levy, who described the capabilities of the accused features and concluded they infringed. Apple challenges the sufficiency of evidence that Apple directly infringed by practicing the steps required by the method claims. To practice the claimed steps, Apple contends that a user must interact with the accused Apple computers by accessing and using the accused features of Mac OS X (i.e., Spotlight, Cover Flow, and Time Machine) to perform the claimed steps. Apple claims this is absent from the record. Mirror Worlds first asserts that Apple “automatically” infringes because the accused Spotlight feature is “built into the core” of Apple’s operating systems that “are always on and necessarily practiced by Apple’s computers.” See Docket No. 445 at 3. Mirror Worlds contends that once the operating system is up and running, Spotlight performs the infringing steps “by automatically including every document generated or received by the computer, automatically selecting timestamps, and associating chronological indicators.” Id. Mirror Worlds also relies on exhibition video clips of Apple’s co-founder, Steve Jobs, and press releases that generally refer to “instant” and “automatic” integration of files into Spotlight Store. Taken together, Mirror Worlds contends this demonstrates Apple’s direct infringement. Second, Mirror Worlds argues that Apple’s computer sales containing the accused Mac OS X software supports the jury’s finding of direct infringement of the method claims. Citing Apple’s documents that discuss the accused Spotlight, Cover Flow, and Time Machine features of Mac OS X, Mirror Worlds contends that “Apple’s offers for sale were for the infringing applications, not a computer or software that was merely capable of infringement.” Thus, Mirror Worlds concludes that Apple’s advertisements, highlighting the accused features, is also legally sufficient evidence for the jury to have found direct infringement of the method claims. Id. at 7. Finally, Mirror Worlds argues that it is undisputed that Apple developed and sold the accused products; therefore, it was reasonable for the jury to infer that Apple necessarily tested the accused products and performed the patented steps. Applicable Law To prove infringement, the plaintiff bears the burden of proof to show the presence of every element or its equivalent in the accused device. Lemelson v. United States, 752 F.2d 1538, 1551 (Fed.Cir.1985). “A determination of infringement is a question of fact that is reviewed for substantial evidence when tried to a jury.” ACCO Brands, Inc. v. ABA Locks Mfr. Co., 501 F.3d 1307, 1311 (Fed.Cir.2007). “To infringe a method claim, a person must have practiced all steps of the claimed method.” Finjan, Inc. v. Secure Computing Corp., 626 F.3d 1197, 1206 (Fed.Cir.2010) (citing Lucent Techs, v. Gateway, Inc., 580 F.3d 1301, 1317 (Fed. Cir.2009)). “[A] method claim is not directly infringed by the sale of an apparatus even though it is capable of performing *713 only the patented method. The sale of the apparatus is not a sale of the method. A method claim is directly infringed only by one practicing the patented method.” Joy Techs., Inc. v. Flakt, Inc., 6 F.3d 770, 774-75 (Fed.Cir.1993); Ricoh Co. v. Quanta Computer Inc., 550 F.3d 1325, 1335 (Fed. Cir.2008) (“[A] party that sells or offers to sell software containing instructions to perform a patented method does not infringe the patent under § 271(a).”). Analysis Actual practice of the specific claim steps is required to infringe the asserted method claims. Viewing the record in a light most favorable to Mirror Worlds, there is insufficient evidence that Apple performed the claimed steps and therefore directly infringed the '227 and '313 patents. See Lucent, 580 F.3d at 1317. Mirror Worlds’ reliance on Apple’s sales of computers that contain the accused Mac OS X 10.4-6 software does not prove direct infringement. The law is clear that the sale or offer for sale is insufficient to prove direct infringement of a method claim. See Joy Techs., 6 F.3d at 773 (“The law is unequivocal that the sale of equipment to perform a process is not a sale of the process within the meaning of section 271(a).”). Mirror Worlds attempts to skirt this precedent by alleging that Apple specifically offered the accused methods for sale — citing Apple’s marketing materials and user manuals, which highlight some of the steps required by the method claims. However marketed, Apple’s computer sales containing the accused Mac OS X software do not constitute direct infringement of the method claims without the requisite evidence showing Apple actually performed the claimed steps. See Ricoh Co. v. Quanta Computer Inc., 550 F.3d 1325, 1335 (Fed.Cir.2008) (“we hold that a party that sells or offers to sell software containing instructions to perform a patented method does not infringe the patent under § 271(a)”); see also Finjan, Inc. v. Secure Computing Corp., 626 F.3d 1197, 1205-06 (Fed.Cir.2010) (applying Lucent and reversing the denial of defendants’ motion for judgment as a matter of law of non-infringement of method claims where the record, which included sales of the accused software and hardware containing the accused software, did not contain sufficient evidence to support direct infringement for the asserted method claims); cf. Microsoft Corp. v. AT & T Corp., 550 U.S. 437, 127 S.Ct. 1746, 1753-55, 167 L.Ed.2d 737 (2007) (holding that as a set of instructions, software is not a component of a patented device within the meaning of § 271(f) until it is reduced to a machine-readable copy). Not only is it legally insufficient to show direct infringement of the method claims through Apple’s sales, it is insufficient to merely assume that Apple conducted tests that performed the method while the accused features were under development. Mirror Worlds did not present any evidence of testing. General development alone is insufficient to prove that Apple performed the claimed steps. Mirror Worlds’ arguments that it is reasonable to infer that testing occurred during development of the accused features does not replace the evidence required to prove infringement. See, e.g., Gemtron Corp. v. Saint-Gobain Corp., 572 F.3d 1371, 1380 (Fed.Cir.2009) (criticizing parties’ reliance on unsworn attorney argument as “evidence”). Mirror Worlds’ characterization of the accused features as “automatic” also fails to show that each step of the method claims was performed. Contrary to Mirror Worlds’ contentions, the method claims are not “automatically” infringed by Apple’s computers because of the accused products’ capabilities; rather, the claims require user interaction to perform the *714 steps. For example, the claims require “generating a mainstream of data units and at least one substream,” “receiving data units from other computer systems,” “generating data units in the computer system,” and “responding to a user sliding the cursor or pointer over said displayed stack to display a glance view.” 8 '227 patent at 16:9-25; '313 patent at 15:10-37, 16:14-36. And to show infringement, Mirror Worlds’ expert, Dr. Levy, represented that generating a “substream” requires a user to enter a search query into Spotlight and receive search results (i.e. data units) in response to the query. 9/28/10 TT at 116:24-117-21 (Dr. Levy’s testimony of using Spotlight to meet the “substream” limitation of claim 13 of the '227 patent: “So the Court’s definition of a substream is a stream that is a subset of data units or documents yielded by a filter on the screen and the filter identifying certain documents within the screen. Well, that’s just a very good description of a search that we’ve described that selects certain documents out of that mainstream or out of the full set of all the data units on the computer system.”). Dr. Levy testified about Mirror Worlds’ theory of infringement regarding the capability of the accused Mac OS X to perform the claimed steps, but not without user involvement to perform these steps. Thus, the steps required by the method claims are not “automatically” infringed by the accused products. The remaining evidence presented by Mirror Worlds also fails to show that Apple performed the steps required by the claims. Throughout trial, Mirror Worlds continually referenced and played clips of Mr. Jobs demonstrating the Spotlight and Cover Flow features. Both during and after trial, Mirror Worlds asserted the video was evidence of infringement; however, this assertion is unsupported by the record. First, the video did not demonstrate Mr. Jobs performing all of the steps of the claimed method. At best, the video clips highlighted and promoted a few attributes of the accused Spotlight and Cover Flow features and practiced some of the claimed steps. Second, despite representing to the jury that the videos showed Mr. Jobs using the accused products, Mirror Worlds did not establish that the features demonstrated in the videos were actually the features accused of infringement in this case. Common to the industry, Apple has different versions of its software. In this case, Mirror Worlds accuses the Spotlight, Cover Flow, and Time Machine features of Mac OS X 10.4-6. Contrary to Mirror Worlds’ representations, Mr. Jobs’ demonstration of Spotlight in June 2004 and January 2005 were of non-accused software that did not practice all of the steps— Mirror Worlds’ damages expert admitted that there was no evidence of infringement before April 2005 and the June 2004 version used in the video clips of Spotlight “wasn’t infringing.” 9/29/10 p.m. TT at 75:6-11 (“Q. Sir, at that conference in June of 2004, Apple handed out 3,000 copies of the accused infringing software, correct? A. No, that’s not true at all. Q. That software wasn’t infringing? A. It was not.”), 76:19-21; see PX933 (no “main stream,” because 2004 version of Spotlight only found files “some of the time”). Thus, contrary to Mirror Worlds’ contentions, the videos featuring Mr. Jobs fail to meet the evidentiary burden showing the patented method was practiced by Apple. Likewise, Mirror Worlds did not show Apple’s direct infringement through circumstantial evidence. Direct infringement of a method claim can also be proved by circumstantial evidence. See Lucent, 580 F.3d at 1317-18. In Lucent, the jury was *715 presented with circumstantial documentary evidence of infringement — evidence of sales by the defendant with manuals teaching how to perform the claimed method steps. This evidence was supported by explanatory expert testimony. Id. at 1318. This was sufficient evidence for the jury to conclude that, more likely than not, someone had performed the claimed method steps using the accused products. Id. However, this is distinguished from the case at hand. Mirror Worlds did not introduce circumstantial evidence that would support a finding of Apple’s direct infringement. For example, there was neither supplemental documentary evidence nor corresponding testimony (e.g. evidence of Apple’s employees testing the method steps, guides or manuals provided to its employees with supplemental testimony explaining how the limitations are met) that would allow the jury to reasonably conclude that Apple performed the method steps and, therefore, infringed. See Lucent, 580 F.3d at 1318. Nor did Mirror Worlds present documents containing instructions that teach all of the steps of the method claims. Mirror Worlds likewise offered no explanatory testimony matching any documentary evidence to the corresponding claimed steps. Mirror Worlds’ post-trial citations to Apple employees’ testimony — who briefly discuss the development of the accused features — a few email exchanges — which generally acknowledge the accused products were tested — and surveys — which generally acknowledged the accused features — likewise fail to show any Apple employee actually performed all the claimed steps. Thus, Mirror Worlds failed to present even circumstantial evidence of direct infringement for the asserted method claims. See E-Pass Techs., Inc. v. 3Com Corp., 473 F.3d 1213, 1222 (Fed.Cir.2007). At the post-trial hearing, Mirror Worlds stated it is “disingenuous” for Apple to argue that Mirror Worlds failed to prove direct infringement. Mirror Worlds protests that, with Apple’s development, marketing, and testing of the features, it is hard to imagine that Apple and its customers did not use the accused Spotlight, Cover Flow, and Time Machine features of Mac OS X 10.4-6. However, direct infringement of a method claim cannot be determined on speculation, assumptions, or inferences. If it was inconceivable to Mirror Worlds that the accused features were not practiced by Apple, it should have had no difficulty in meeting its burden of proof and in introducing testimony of such use. See E-Pass, 473 F.3d at 1222-23. Mirror Worlds simply failed to present sufficient evidence from which a reasonable jury could find that Apple, or anyone else, practiced each and every step of the claimed methods by using the Spotlight, Cover Flow, and Time Machine features in the accused Mac OS X 10.4-6. While it is important to persuade a jury, it is imperative to present a “legally sufficient evidentiary basis” to support that persuasion. Construing this evidence most favorably to Mirror Worlds, the record does not contain evidence that Apple performed each of the claimed steps in the asserted method claims. Accordingly, no reasonable jury could have concluded that Apple directly infringed claims 13 and 22 of the '227 patent and claims 1, 2, 3, 9, and 11 of the '313 patent. Direct Infringement of the Asserted System Claims In addition to the Court’s dismissal of indirect infringement, the Court also granted judgment as a matter of law specific to the asserted system claims of the '427 patent. The Court ruled that Apple did not literally infringe claims 16 and 18 of the '427 patent, 9/29/10 p.m. TT at 96:25-97:16, and further ruled that Apple’s mobile devices did not infringe claims 16 and 18 of the '427 patent under the doc *716 trine of equivalents. Docket No. 400. These rulings removed the mobile devices from the case. Thus, Mirror Worlds’ infringement claims for the '427 patent were limited to Apple’s alleged direct infringement by the Mac OS X 10.4-6 that use Leopard and Snow Leopard operating systems. At trial, Dr. Levy relied on the doctrine of equivalents to conclude Apple’s Mac OS X infringed the asserted system claims of the '427 patent. Apple argues that Mirror Worlds failed to present sufficient evidence to show the accused Mac OS X infringes the asserted system claims and that the features of Mac OS X do not meet several of the claim limitations. In response, Mirror Worlds argues it presented sufficient evidence to support the jury verdict of infringement and Apple’s evidence of non-infringement was rejected by the jury. Mirror Worlds contends that Dr. Levy explained how each limitation of each asserted claim is found in Apple’s infringing products. Applicable Law To prove literal infringement, the patentee must show that the accused device contains every limitation in the asserted claims. Cybor Corp. v. FAS Techs., Inc., 138 F.3d 1448, 1467 (Fed.Cir.1998) (en banc). To find infringement under the doctrine of equivalents, any differences between the claimed invention and the accused product must be insubstantial. Graver Tank & Mfg. Co. v. Linde Air Prods. Co., 339 U.S. 605, 608, 70 S.Ct. 854, 94 L.Ed. 1097 (1950). The “essential inquiry” in any determination under the equivalents doctrine is whether “the accused product or process contain[s] elements identical or equivalent to each claimed element of the patented invention.” See Warner-Jenkinson Co. v. Hilton Davis Chem. Co., 520 U.S. 17, 40, 117 S.Ct. 1040, 137 L.Ed.2d 146 (1997). One way of proving infringement under the doctrine of equivalents “is by showing on a limitation by limitation basis that the accused product performs substantially the same function in substantially the same way with substantially the same result as each claim limitation of the patented product.” Id. at 39-40, 117 S.Ct. 1040. However, “ ‘[equivalence, in the patent law, is not the prisoner of a formula and is not an absolute to be considered in a vacuum.’ ” Id. at 24-25, 117 S.Ct. 1040 (quoting Graver Tank, 339 U.S. at 609, 70 S.Ct. 854). To support a finding of infringement under the doctrine of equivalents, Mirror Worlds must have presented, on a limitation-by-limitation basis, “particularized testimony and linking argument as to the ‘insubstantiality of the differences’ between the claimed invention and the accused device or process, or with respect to the function, way, result test.” Amgen Inc. v. F. Hoffman-LA Roche Ltd., 580 F.3d 1340, 1382 (Fed.Cir.2009) (quoting Tex. Instruments v. Cypress Semiconductor Corp., 90 F.3d 1558, 1567 (Fed.Cir. 1996)). “Generalized testimony as to the overall similarity between the claims and the accused infringer’s product or process will not suffice.” Tex. Instruments, 90 F.3d at 1567. Particularized testimony is essential, so that a patentee cannot “under the guise of applying the doctrine of equivalents, erase a plethora of meaningful structural and functional limitations of the claim on which the public is entitled to rely in avoiding infringement.” Perkin-Elmer Corp. v. Westinghouse Elec. Corp., 822 F.2d 1528, 1532 (Fed.Cir.1987). These requirements “ensure that a jury is provided with the proper evidentiary foundation from which it may permissibly conclude that a claim limitation has been met by an equivalent.” Comark Commc’ns, Inc. v. Harris Corp., 156 F.3d 1182, 1188 (Fed. Cir.1998). Analysis The Court’s evaluation of Mirror Worlds’ evidence of infringement by equiv *717 alents addresses limitations that are common to all of the asserted claims of the '427 patent and thus dispositive of the '427 patent. With some variation in the claim language, 9 all the asserted claims of the '427 patent require: 1) displaying a cursor or pointer; 2) responding to a user sliding without clicking the cursor or pointer over a displayed stack of document representations; and 3) displaying a glance view of a document when the document representation is touched by the cursor or pointer. 10 At trial, Mirror Worlds’ infringement claims were limited to the doctrine of equivalents for these limitations — alleging the Mac OS X Cover Flow feature practiced the equivalent. 11 Viewing the record in the light most favorable to Mirror Worlds, Mirror Worlds did not present sufficient evidence to allow a reasonable jury to conclude that the asserted claims of the '427 patent were infringed under the doctrine of equivalents. In asserting its infringement claim under the doctrine of equivalents, Mirror Worlds had an obligation to provide the jury with particularized testimony linking Mac OS X to the patents. During the post-trial hearing, Mirror Worlds acknowledged that Dr. Levy’s testimony did not include the “function, way, result test”; however, Mirror Worlds argued that Dr. Levy’s testimony of the “insubstantial differences” between the claims and Cover Flow feature of the accused Mac OS X was sufficient to support the jury verdict. Yet, contrary to Mirror Worlds’ arguments, Dr. Levy failed to specifically describe the “insubstantial differences” to the jury. The following trial excerpts illustrate the insufficiency of Dr. Levy’s testimony under the doctrine of equivalents. First, to demonstrate Cover Flow met the “displaying a cursor or pointer” portion of the *718 claim limitation, Dr. Levy offered general testimony that Cover Flow’s moving stack of document representations over a stationary pointer is equivalent to the claimed moving pointer over a stationary stack: Q. And what is it in the Cover Flow view that you consider to be the equivalent? A. In the Cover Flow view, instead of having a moving pointer and a stationary stack, we have a moving stack and essentially a stationary pointer, because the user knows that he’s looking always at the center here. 9/28/10 p.m. TT at 144:23-145:3. Dr. Levy testified that a cursor or pointer somehow existed “by default” at the center of the display: Q. Dr. Levy, does the Cover Flow display — display a pointer? A. It does not display a literal pointer, but I believe it has the equivalent, because the user always is looking at the center where the glance view is going to pop up, and that is where the cursor or pointer is by default. Id. at 145:11-17; see also id. at 150:24-151:2 ('427 claim 8), 153:3-9 ('427 claim 16), 155:18-20 ('427 claim 25), 158:2-4 ('313 claim 1), 162:12-20 ('313 claim 9). Second, Dr. Levy addressed the “responding to a user sliding without clicking the cursor or pointer over a displayed stack of document representations” and “displaying a glance view of a document” limitations. He testified that with Cover Flow “you don’t have to click on each document in order to get it to move — or pop up in the center. You can achieve that by moving this scroll bar thumb [sic], by dragging it, or you can use a gesture of two fingers across or down a touch pad which will cause the stack to move.” Id. at 146:18-23. Without further specific testimony or linking argument, Dr. Levy surmised that Cover Flow met these claim limitations. Dr. Levy offered no substantive explanation for how or why Mac OS X operates in a similar way to the asserted claims. Instead, Dr. Levy merely repeated the claim language when testifying about the accused Mac OS X Cover Flow features and summarily considered them equivalent. Specifically, Dr. Levy did not offer particularized testimony describing how the differences are insubstantial between Cover Flow’s moving stack of document representations over a stationary pointer and the claimed moving pointer over a stationary stack. At best, Dr. Levy’s testimony summarily addressed the Cover Flow functions but failed to discuss why or how Cover Flow operates in a way that is substantially similar to the claim limitation. Rather, he merely described the Cover Flow attributes and provided no explanation specifically linking any functions to the limitation. 12 For example, Dr. Levy testified that a bathroom scale showed an example of why “the moving stack and the stationary stack are equivalent” by referencing a demonstrative picture of two types of bathroom scales: one scale with a movable pointer and a stationary dial, the other with a moving dial and stationary pointer. Id. at 147:-148:1. Without any further explanation than merely describing the photographs of the scales for the jury, Dr. Levy testified that the scale illustrations were “equivalent in the same way that the Cover Flow and the Gelernter stack are equivalent.” Id. As with his narrative regarding Cover Flow, *719 Dr. Levy made the jump from describing the pictorials of his examples to a conclusion of infringement without making any connection explaining why the exemplar scales were analogous to his infringement theory. While Dr. Levy’s examples were illustrative, they were insufficient to show insubstantial differences between the claims and the accused products. In addition, Mirror Worlds’ infringement theory under the doctrine of equivalents regarding the cursor or pointer vitiates that claim limitation by accusing Apple’s products of functioning in a way that is opposite of what the claim requires. Dr. Levy admitted that Cover Flow does not literally display a cursor or pointer but alleged the equivalent exists “by default” at the area in the center of the display where the glance view pops up. 9/28/10 p.m. TT at 145:11-17. Dr. Levy’s general testimony that Apple’s products do not display a cursor or pointer, while maintaining infringement under the doctrine of equivalents of a claim that requires the display of a cursor or pointer, reads this claim limitation out of the claim. Thus, based on Dr. Levy’s theory of infringement, no reasonable jury could determine the accused Apple products to be insubstantially different from the claimed limitation. See Warner-Jenkinson, 520 U.S. at 39 n. 8, 117 S.Ct. 1040 (“Under the particular facts of a case ... if a theory of equivalence would entirely vitiate a particular claim element, partial or complete judgment should be rendered by the court.”). In its post-trial briefing, Mirror Worlds attempts to distance itself from the “default” pointer Dr. Levy presented at trial by contorting his testimony. Dr. Levy referenced the scroll bar as a way of moving the stack in Cover Flow to meet the “sliding without clicking” limitation, and his “default” pointer theory was used to meet the “displaying a cursor or pointer” limitation. Compare 9/28/10 p.m. TT. at 144:23-145:3, 146:7-23 with 144:11-145; see also Docket No. 398 at 4. Post-trial, Mirror Worlds argues the scroll bar meets the “displaying a cursor or pointer” limitation and argues this theory is distinguished from the “default” pointer theory the Court found legally insufficient due to claim vitiation as to the mobile devices. See Docket No. 400. Specifically, Mirror Worlds contends that unlike the mobile devices, the Cover Flow feature in Mac OS X displays a cursor and a scroll bar. Mirror Worlds argues the pointer or cursor requirement is literally infringed by a black arrow that is displayed on the screen and the scroll bar is the equivalent to the display stack. Using a cursor to manipulate the scroll bar, a user can flip through the display stack. Mirror Worlds now argues, contrary to Dr. Levy’s testimony, that the scroll bar used by Cover Flow in the accused Mac operating systems meets the “displaying a cursor or pointer” limitation. This revised infringement theory is not what Mirror Worlds presented to the jury and likewise fails. Dr. Levy did not testify that the black arrow displayed by the Cover Flow feature in Mac OS X literally met the claim limitation, nor did he testify that the scroll bar is equivalent to the display stack as required by the claims. The record is absent of any particularized testimony equating the scroll bar to the display stack or explanation of the insubstantiality of the differences between the two, and Mirror Worlds cannot rewrite the evidence at trial by its post-trial arguments to justify the jury verdict. As such, the Court rejects this argument. Dr. Levy’s bald recitation of Cover Flow features and references to pictures and demonstratives without supportive reasoning of why the accused devices are substantially similar to the claim limitation is simply legally insufficient. Dr. Levy’s testimony was far from the re *720 quired limitation-by-limitation testimony that specifically links the features of the asserted patents to the accused features in Mac OS X that would provide the jury with substantive evidence to support a finding of infringement by equivalence. To be clear, the Court is not evaluating the weight of Dr. Levy’s testimony or comparing it to Apple’s expert as the jury was entitled to decide what infringement theories to accept or reject. Rather, the Court evaluates the legal sufficiency of the proffered evidence of infringement under the doctrine of equivalents, which requires “particularized testimony and linking argument as to the ‘insubstantiality of the differences’ between the claimed invention and the accused device or process, or with respect to the function, way, result test.” Tex. Instruments, 90 F.3d at 1567. Dr. Levy’s generalized testimony as to the overall similarity between the claims and Mac OS X’s Cover Flow is not “particularized testimony and linking argument” of the “insubstantial differences” that would support a finding of infringement by equivalence. For these reasons, the record lacks sufficient evidence to support the jury’s finding of infringement for the asserted claims of the claims 1, 8, 16, 18, 25 of the '427 patent. 13 Infringement Conclusion For the reasons stated above, the Court GRANTS Apple’s Renewed Motion for Judgment as a Matter of Law for Apple’s direct infringement of the '227, '313, and '427 patents. Although Apple’s motion for judgment raises additional arguments regarding the sufficiency of evidence for other claim limitations, the grounds set forth above are case dispositive; therefore, the Court need not address these additional challenges. WILLFULNESS To establish willful infringement, Mirror Worlds was required to “show by clear and convincing evidence” that (1) Apple “acted despite an objectively high likelihood that its actions constituted infringement of a valid patent,” and (2) “[the] objectively defined risk ... was either known or so obvious that it should have been known to the accused infringer.” In re Seagate Tech, 497 F.3d 1360,1371 (Fed. Cir.2007). Because the record lacks sufficient evidence to support the jury’s finding of infringement, the Court further vacates the jury’s finding of willfulness. Accordingly, the Court GRANTS Apple’s Renewed Motion for Judgment as a Matter of Law for no willful infringement of the '227, '313, and '427 patents. DAMAGES The scope of Mirror Worlds’ case and Apple’s potential liability exposure changed during the course of trial. At the onset of trial, Mirror Worlds accused Apple’s operating systems contained in its computers and mobile devices of both direct and indirect infringement and sought aggregate damages totaling $625 million for infringement of all three patents (the “patent portfolio”). 9/29/10 p.m. TT at 15:25-16:14. Mirror Worlds’ expert, Mr. Bratic, based the damages calculation on a hypothetical negotiation as set forth in Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F.Supp. 1116 (S.D.N.Y.1970). Mirror Worlds’ damages theory was based on the accused features of the patent portfolio, and Mirror Worlds did not present evidence of damages on a “per patent” basis. 9/29/10 p.m. TT at 44:12-47:7, 50:25-52:5. For the royalty base, Mr. Bratic used the revenue from the sales of the Apple *721 products that contained the accused Mac OS X 10.4-6 Spotlight, Cover Flow, and Time Machine features. 9/29/10 p.m. TT at 19:10-22:15. While Apple offers a software upgrade with the accused features, it does not sell the features separately, nor does it attribute specific portions of its revenue to the features of its operating system. Id. at 39:19-40:9; 43:9-45:16, 51:10-52:5. Mirror Worlds’ royalty base not only included the revenue from sales of the software upgrade, it included revenue from hardware sales as well — Mac desktops, portables, servers, iPods, iPhones, and iPads that contained the accused operating system — totaling $72 billion dollars. Id. at 19:10-22:15. Mr. Bratic opined that the hypothetical negotiation would have occurred in April 2005, and he applied a royalty rate of 8.8% for the software product sales and 0.81% for the hardware sales. Id. at 35:20-36:4, 39:19-40:9. This resulted in a royalty of $11.26 or 8.81% of the $129 operating system upgrade. Id. at 44:12-45:16. Mr. Bratic then applied the $11.26 royalty to the price of a Mac computer (approximately $1200), to arrive at a 0.81% hardware royalty rate. Id. At the end of Mirror Worlds’ case-in-chief, the Court granted Apple’s motion for judgment as a matter of law that Mirror Worlds had not presented any evidence of indirect infringement on any of the patents-in-suit. The Court also granted judgment as a matter of law that Apple’s mobile products did not infringe literally or under the doctrine of equivalents. Thus, the case was then limited to only Apple’s direct infringement by its computers using Mac OS X 10.4-6, which use the accused Spotlight, Cover Flow, and Time Machine features. Following the Court’s ruling that removed the mobile devices from the case, Mr. Bratic was recalled and testified that if the “iPhone, iPad, and iTunes” were removed from the case, the total aggregate damages requested by Mirror Worlds would be reduced by approximately 50 percent — approximately $300 million. 9/30/10 p.m. (pt. 2) TT at 83:1-5. However, Mr. Bratic did not adjust his damages calculations after dismissal of Mirror Worlds’ indirect infringement claims. After the close of evidence, Apple re-urged its motion for judgment as a matter of law for no direct infringement of the asserted method claims of the '227 and '313 patents, which if granted would have only left the '427 patent in the case. The Court expressed serious concern whether Mirror Words had met its evidentiary burden for the method claims for the '227 and '313 patents. However, the Court decided to allow the '227 and '313 patents to go to the jury, informing the parties that the Court would consider the motion post verdict. 10/1/10 TT at 11:14-21. In an attempt to provide Mirror Worlds with a basis for a damages award if the Court granted a post-trial motion for judgment as a matter of law dismissing the '227 and '313 patents, the Court revised the verdict form to provide separate damage findings for each patent. Id. at 15:9-16; Docket No. 409 at 2. The Court specifically asked Mirror Worlds if there was sufficient evidence of record to support a per-patent damage award for the '427 patent if the '227 and '313 patents were dismissed. Mirror Worlds responded it “didn’t have a clue.” 14 Id. at 13:3-14:1. The Court then *722 gave both parties the opportunity to reopen the record for additional damages testimony to establish damages on a per-patent basis. Id. at 15:21-16:11. Mirror Worlds declined the Court’s offer. 15 Id. at 23:20-21. The Jury’s Verdict During closing argument, Mirror Worlds’ counsel, consistent with Mr. Bratic’s testimony, argued that if the jury found any one of the patents infringed, Mirror Worlds was entitled to approximately $300 million in damages. Because infringement of any one of the patents resulted in infringement of the patented features — which Mr. Bratic said supported an approximately $300 million award- — ■ Mirror Worlds asked the jury to award approximately $300 million if it found even one of the patents infringed. Likewise, using a demonstrative verdict form, Mirror Worlds’ counsel wrote approximately $300 million next to each of the '427, '227, and '313, and patents: 16 Okay. So this is the verdict form. This is what I think.... [Mirror Worlds’ counsel writes in damages of $322, 336, and 320 million for each of the patents-in-suit] Now, these are the damage numbers, and I’ll talk to you more about these, but you remember the Judge told you that the — the iPods are out; that’s all been resolved. So what that means is that the numbers that Mr. Bratic — you remember I got him up at the very last and I said, if you take the i’s [iPhone, iPad, iTunes, iPod] out, what do you have, and he said about 50 percent. These are the allocations that I thought were appropriate based on what I heard Bratic say, but in each instance, it’s about 50 percent of that 6-1/4 [$625 million] that Bratic told you about during his testimony, and that still means that [Apple is] making $25 million every day. Id. at 92:11-93:24. However, in Apple’s closing arguments, its counsel apparently misunderstood Mirror Worlds’ request and stated that Mirror Worlds was asking for $300 million for each patent, which added together would award close' to a “billion dollars.” Id. at 123:3-6. In rebuttal closing argument, Mirror Worlds’ counsel clarified for the jury that it was not asking for a billion dollars — rather, it was asking the jury to award $300 million if it found any one of the patents infringed: These are the Judge’s questions. He wants damage numbers for each separate patent. That doesn’t mean we’re going to get a billion dollars. That just means the Judge wants to know why you believe or if you believe what the value of the reasonable royalty for each patent. The reason these numbers made sense to me is, they were all infringed at the same time. They would have all been part of the same hypothetical negotiation. The numbers are a little different, based on the different products; but that’s up to you. I think they’re all around 300, 300-and-a-quar- *723 ter apiece, if you believe that we were, in fact, the victim of patent infringement. Id. at 132:18-133:8 (emphasis added). Presumably, Mirror Worlds made this argument to ensure that it would still be entitled to $300 million even if the Court, or jury, found one or more of the patents invalid or non-infringing. Following deliberation, the jury found the patents-in-suit valid and infringed and listed damages of $208.5 million on the lines provided for each patent. Docket No. 409. Accordingly, and consistent with the record established at trial, the Court evaluates the sufficiency of evidence to support the jury’s award of $208.5 million. Mirror Worlds’ Post-Trial Arguments Despite Mirror Worlds’ representation to the jury that it was only entitled to approximately $300 million, Mirror Worlds now asserts it is entitled to aggregate the $208.5 million answer for each patent, totaling $625.5 million. Specifically, Mirror Worlds requests: 1) entry of the total damages of $625.5 million awarded by jury’s verdict; 2) prejudgment interest on the awarded damages; 3) damages for Apple’s infringement from the date of the verdict through the date of entry of final judgment; 4) ongoing royalties for Apple’s continued infringement after final judgment; 5) enhanced damages; 6) grant of attorneys’ fees and experts’ fees; 7) grant of costs; and (8) grant of post judgment interest. 17 Curiously, Mirror Worlds now requests judgment for aggregate damages of $625.5 million, not withstanding Mr. Bratic’s testimony and counsel’s representations to the jury and the Court that its total $625.5 million damages model was reduced by 50 percent. See 9/30/10 p.m. (pt. 2) TT at 83:1-5 (Mr. Bratic testified that removal of the “iPhone, iPad, and iTunes” reduced damages by- 50 percent). Applicable Law “A district court’s duty to remit excessive damages is a procedural issue, not unique to patent law.” Imonex Servs., Inc. v. W.H. Munzprufer Dietmar Trenner GMBH, 408 F.3d 1374, 1380 (Fed. Cir.2005). In the Fifth Circuit, a decision on remittitur and new trial is within the sound discretion of the trial court. See Thompson v. Connick, 553 F.3d 836, 865 (5th Cir.2008). The standard is highly deferential, and damages are set aside “only upon a clear showing of excessiveness.” i4i Ltd. v. Microsoft Corp., 598 F.3d 831, 857 (Fed.Cir.2010) (cert, granted — U.S. -, 131 S.Ct. 647, 178 L.Ed.2d 476 (2010)) (quoting Duff v. Werner Enters., Inc., 489 F.3d 727, 730 (5th Cir.2007)). An excessive award exceeds the “maximum amount calculable from the evidence.” Carlton v. H.C. Price Co., 640 F.2d 573, 579 (5th Cir.1981). A patentee is entitled to damages for infringement under 35 U.S.C. § 284 (“Upon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.”). The burden of proving damages falls on the patentee. Dow Chem. Co. v. Mee Indus., Inc., 341 F.3d 1370, 1381 (Fed.Cir.2003). There are two alternative categories of infringement compensation: the patentee’s lost profits and the reasonable royalty the patentee would have received through arms-length bargaining. See Lucent, 580 F.3d at 1324. *724 To ascertain the reasonable royalty, patentees commonly consider a hypothetical negotiation, in which the asserted patent claims are assumed valid, enforceable, and infringed, and attempt to ascertain the royalty upon which the parties would have agreed had they successfully negotiated an agreement just before infringement began. Id. at 1324-25; Georgia-Pacific Corp., 318 F.Supp. at 1120; see also Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1554 n. 13 (Fed.Cir.1995) (en banc). Calculation of a reasonable royalty requires determination of two separate and distinct amounts: 1) the royalty base, or the revenue pool implicated by the infringement and 2) the royalty rate, or the percentage of that pool “adequate to compensate” the plaintiff for the infringement. See Cornell Univ. v. Hewlett-Packard Co., 609 F.Supp.2d 279, 286 (N.D.N.Y.2009). The entire market value rule “recognizes that the economic value of a patent may be greater than the value of the sales of the patented part alone.” See King Instruments Corp. v. Perego, 65 F.3d 941, 951 n. 4 (Fed.Cir.1995). “The entire market value rule allows a patentee to assess damages based on the entire market value of the accused product [if] the patented feature creates the ‘basis for customer demand’ or ‘substantially create[s] the value of the component parts.’ ” Uniloc USA, Inc. v. Microsoft Corp., 632 F.3d 1292, 1318 (Fed.Cir.2011) (citing Lucent, 580 F.3d at 1336; Rite-Hite, 56 F.3d at 1549-50). “[T]he patentee ... must in every case give evidence tending to separate or apportion the defendant’s profits and the patentee’s damages between the patented feature and the unpatented features, and such evidence must be reliable and tangible, and not conjectural or speculative,” or show that “the entire value of the whole machine, as a marketable article, is properly and legally attributable to the patented feature.” Uniloc, 632 F.3d at 1318 (citing Garretson v. Clark, 111 U.S. 120, 121, 4 S.Ct. 291, 28 L.Ed. 371 (1884)); see also Lucent, 580 F.3d at 1336-37. For minor patent improvements, a patentee cannot justify using the entire market value of an accused product simply by asserting a low enough royalty rate. Uniloc, 632 F.3d at 1319-20 (rejecting contrary interpretation of Lucent, 580 F.3d at 1338-39); see Garretson, 111 U.S. at 121, 4 S.Ct. 291. Although a reasonable royalty analysis “necessarily involves an element of approximation and uncertainty,” Unisplay, S.A. v. Am. Elec. Sign Co., 69 F.3d 512, 517 (Fed. Cir.1995), the Court must ensure that the jury verdict is supported by sufficient evidence. Sufficiency of Evidence to Support the Jury’s Damages Award of $208.5 Million Separate and apart from the sufficiency of evidence regarding infringement, there is insufficient evidence to support the jury’s $208.5 million damages award. The jury was charged with determining whether Apple directly infringed the patents-in-suit and Apple’s liability for such infringement. The '227 and '313 Method Patents First addressing the '227 and '313 patents, from which only method claims were asserted, Apple’s liability was limited to its use of the patented method since the Court had granted judgment of no indirect infringement. Thus, Mirror Worlds was only entitled to recover damages that resulted from Apple’s direct infringement. However, Mirror Worlds’ infringement theory was based on Apple’s sales, and Mirror Worlds did not present sufficient evidence to allow the jury to determine liability resulting from Apple’s own use (direct infringement) of the methods in the '227 and '313 patents. Apple’s sales cannot be used to determine damages for Apple’s direct infringe *725 ment of the method claims. As explained above, a sale or offer for sale is insufficient to prove direct infringement of a method claim — sale of the apparatus is not the sale of the method — and thereby irrelevant in calculating liability for direct infringement. See Joy Techs., 6 F.3d at 774-75; see also Embrex Inc. v. Service Eng’g Corp., 216 F.3d 1343, 1350 (Fed.Cir.2000) (where experimental testing performed by defendant’s employees formed the evidentiary basis for direct infringement of a method claim, but the record lacked evidence showing testing likewise formed the basis of the damages award, the award was reversed and remanded to determine damages based on defendant’s infringing uses of the patent). Accordingly, because Apple’s sales or offers for sale do not infringe the asserted method patents, they cannot be the basis for damages. See Gen. Motors Corp. v. Devex Corp., 461 U.S. 648, 654-55, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983) (upon a finding of infringement, the patentee is entitled to full compensation for damages “suffered as a result of the infringement”). Even after the Court’s rulings at the close of Mirror Worlds’ case-in-chief that removed indirect infringement from the case, Mirror Worlds did not supplement its damages evidence. Mirror Worlds did not present any evidence of a reasonable royalty based solely on Apple’s own use of the patented methods. Thus, Mirror Worlds left the jury without an adequate basis to award damages for Apple’s direct infringement of the method claims. Therefore, the evidentiary record is insufficient to support the jury’s damage awards for the '227 and '313 patents, even if there had been sufficient evidence to support the jury’s finding of infringement. The '427 Patent Likewise, the record lacks sufficient evidentiary basis to support the jury’s damages award for Apple’s direct infringement of the '427 patent. Since the asserted claims of the '427 patent were system claims the jury could properly include Apple’s sales or offers for sale in determining its damages award. However, the evidence is insufficient to show how inclusion of sales for the system claims of the '427 patent, but not the method claims of the '227 and '313 patents, affected Mr. Bratic’s damages calculation. During trial, Mr. Bratic evaluated the damages as to Mirror Worlds’ patent portfolio rather than on a per-patent basis. Mr. Bratic’s only testimony separating the damages by patents was limited to the timing of the hypothetical negotiation: [I]f you assume the '227 patent is a valid patent and has been infringed, then the date of first infringement and the HN, hypothetical negotiation, occurs in April 2005, and the damages of 625 million in royalties. If you assume that the '227 patent is not a valid patent or has not been infringed, and we’re only dealing with the '313 patent and the '427 patent, then we have to have a separate hypothetical negotiation September 2006 using the same methodology I just walked through with you but different royalty rates, and you end up with a — royalties due of $748 million. 9/29/10 p.m. TT at 61:22-62:10. Likewise, removing the revenue from the sales relating to the '227 and '313 patents would have affected Mr. Bratic’s evaluation and determination of the reasonable royalty. Since Mirror Worlds accused the Leopard and Snow Leopard operating systems of infringing the '227, '427 and '313 patents and the Tiger operating system of infringing the '227 patent, at the very least, Mirror Worlds would need to account for removing sales of the Tiger operating system (Mac OS X 10.4). As such, there is insufficient evidence to determine how Mr. Bratic would have re-evaluated his dam *726 ages calculation for the asserted system claims of the '427 patent. Mirror Worlds’ “Reasonable Royalty” Analysis Moreover, Mirror Worlds presented a fatally flawed reasonable royalty analysis. First, Mirror Worlds did not present a legally sound justification for its royalty base. Mirror Worlds used both software and hardware incorporating the accused Mac OS X 10.4-6 to calculate a $72 billion royalty base. This included revenues from sales of software upgrades, iTunes, Macs (desktops, portables, and servers), iPods, iPhones, and iPads that contained the accused operating systems. Id. at 19:10— 22:15. However, Mirror Worlds argues it did not rely on the entire market value rule, thus the rule does not does not apply to its damages calculation. Mirror Worlds further contends that because Mr. Bratie started with the smallest saleable units in his damages calculation, it need not perform an entire market value rule analysis. Id. at 52:1-54:15. Despite Mirror Worlds’ protestations that the entire market value rule does not apply, it undisputedly used the entire market value of the accused commercial products in calculating its royalty base — and the accused products contain several features, both accused and non-accused. Therefore, Mirror Worlds must show the connection between the accused commercial products, which form its royalty base, and the patented features. Accordingly, at trial Mirror Worlds was obligated to show that the Spotlight, Cover Flow, and Time Machine features create the “basis for customer demand” or “substantially create[s] the value of the component parts” in the accused software and hardware products that contain Mac OS X 10.4-6. See Uniloc, 632 F.3d at 1318. At trial, Mirror Worlds presented consumer surveys and emails indicating customer demand for an upgrade to the Tiger operating system, which includes over 200 features. See 9/29/10 TT at 52:9-56:24; see also Ex. No. DX 851. Mr. Bratie presented an email that lists Spotlight as a “Key Tiger feature,” and 23% of customers surveyed ranked Spotlight as the “[m]ost beneficial Tiger feature.” See 9/29/10 TT at 52:9-56:24; see also Ex. No. DX 851. Mr. Bratie also discussed a customer email regarding the positive feedback Apple received about adding the Spotlight feature to the Tiger operating system. See 9/29/10 TT at 52:9-56:24; PX 983. The survey and emails only addressed Spotlight — the remaining accused Mac OS X operating features, Cover Flow and Time Machine, were not included. Thus, there is no evidence these features similarly drove customer demand. Moreover, the survey and emails were not tied to any of the accused hardware devices (e.g. eMac, MacBook, MacBook Air, MacBook Pro, Mac mini, iMac, Mac Pro, iBook, PowerBook, Power Mac, and PowerPC), thus there is no indication that Spotlight drove customer demand for the hardware products. While the surveys indicated Spotlight generally related to customer demand for Tiger, which had over 200 features, the surveys cannot simply be translated to encompass Apple’s various hardware, all which have exponentially more features with varying attributes that are unaccounted for. Likewise, the evidence only pertained to the Tiger operating system, it did not address the accused Leopard and Snow Leopard operating systems, and Mirror Worlds did not present any evidence that would indicate Spotlight continues to drive customer demand in the Leopard and Snow Leopard operating systems as well. Thus, the record lacks sufficient evidence that a jury could reasonably rely on to find customer demand of the Spotlight features created the “basis for customer demand” or “substantially create[s] the value of the component parts” *727 for the software and hardware revenues used in the royalty base. Uniloc, 632 F.3d at 1318. As Mirror Worlds is not entitled to use the entire market value of the accused products, it was obligated to properly apportion the royalty base to address the accused features, which it did not do. See 9/29/10 TT at 56:25-61:16. The law is clear, courts “do not allow consideration of the entire market value of accused products for minor patent improvements simply by asserting a low enough royalty rate.” Uniloc, 632 F.3d at 1320. Apportionment cannot be achieved by the mere downward adjustment of the royalty rate in a purported effort to reflect the relative value of the accused features because doing so fails to remove the revenues associated with the non-accused features from the revenue base. Id. (clarifying Lucent and rejecting the argument that “the entire market value of the products may appropriately be admitted if the royalty rate is low enough”). Thus, Mirror Worlds cannot simply apply “haircuts” adjusting the royalty rate to apportion damages, and thereby justify the jury award, because the entire market value of the accused products has not been shown to be derived from the patented contribution. Uniloc, 632 F.3d at 1320-21. Second, Mirror Worlds also failed to present a legally sound justification for its royalty rate. Mirror Worlds did not present evidence that would support a 8.8% running royalty on software or 0.81% running royalty for hardware. For example, Mr. Bratic did not explain why Apple, in the hypothetical negotiation, would agree to a running royalty. Nor did Mr. Bratic account for Apple’s license agreements relating to “graphical user interface technology,” which did not award similar royalties. See DX1085; DX0392; DX0393; DX0394; DX0398; DX0419; DX0420; DX0636. And while Mr. Bratic calculated the rate “leaving a lot of meat on the bone for Apple” he did not explain why the accused Spotlight, Cover Flow, and Time Machine features would be in such demand, or so frequently used, to command a 8.8% running royalty on software or 0.81% running royalty for hardware. See 9/29/10 TT at 39:19-40:15; see also Lucent, 580 F.3d at 1326-27. Therefore, the evidentiary record is insufficient to support the jury’s damage awards for the '427 patent, even if there had been sufficient evidence to support the jury’s finding of infringement. For these reasons, the record lacks substantial evidence to support the jury’s award of damages. The Court GRANTS Apple’s request for Judgment as a Matter of Law to vacate the jury’s damages award. Based on the findings of non-infringement set forth above, the Court DENIES AS MOOT Apple’s motion in the alternative for a new trial or remittitur. INVALIDITY Apple argues it presented clear and convincing evidence that all claims of the patents-in-suit are invalid as anticipated and obvious under 35 U.S.C. §§ 102, 103. Apple generally cites the numerous prior art references admitted at trial, arguing that “every asserted claim is rendered obvious over at least the following primary references and/or combinations of the following systems: (1) the ‘Piles’ system, as described in at least U.S. Patent No. 6,243,-724, to Mander et al.; (2) the ‘Workscape’ system, as described in U.S. Patent No. 5,499,330 to Lucas et al.; (3) the Lifestreams system as described in ‘The “Lifestreams” Approach to Reorganizing the Information World,’ YALEU/DCS/TR-1070 (‘TR-1070’); and (4) Retrospect software, as described in the 1993 and 1995 Retrospect Manuals.” Apple makes no other specific arguments regarding the patents’ *728 validity; rather, Apple submits three exhibits of claim charts that provide the entirety of its invalidity arguments. In response, Mirror Worlds argues that Apple’s invalidity case was defective because (1) Apple’s expert applied a different claim construction for invalidity than he did for infringement and (2) Apple did not sufficiently compare the prior art to the claim elements. Applicable Law In order to show that it is entitled to judgment as a matter of law on its affirmative defense of invalidity, Apple must prove the essential elements of that defense to a virtual certainty. ClearValue, Inc. v. Pearl River Polymers, Inc., 735 F.Supp.2d 560, 577 (E.D.Tex.2010) (citing Bank of La. v. Aetna U.S. Healthcare Inc., 468 F.3d 237, 241 (5th Cir.2006) (“For a defendant to obtain summary judgment on an affirmative defense, it must establish beyond dispute all of the defense’s essential elements.”)). A patent claim is invalid as obvious “if the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art.” KSR Int’l Co. v. Teleflex Inc., 550 U.S. 398, 406, 127 S.Ct. 1727, 167 L.Ed.2d 705 (2007). A patent is invalid as anticipated if “the invention was patented or described in a printed publication in this or a foreign country ... more than one year prior to the date of the application for patent in the United States.” 35 U.S.C. § 102(b). Although § 102 refers to “the invention” generally, the anticipation inquiry proceeds on a claim-by-claim basis. See Hakim v. Cannon Avent Group, PLC, 479 F.3d 1313, 1319 (Fed.Cir.2007). The single prior art reference must expressly or inherently disclose each claim limitation to anticipate a claim. Finisar, 523 F.3d at 1334. Additionally, the reference must “enable one of ordinary skill in the art to make the invention without undue experimentation.” In re Gleave, 560 F.3d 1331, 1334 (Fed.Cir.2009). Analysis Apple presented its theories of invalidity to the jury, and the jury was free to disbelieve Apple’s experts. In its post-trial briefing regarding anticipation and obviousness, Apple fails to specifically address how the prior art invalidates the patents-in-suit or how the weight of the evidence was against the jury’s validity determination. Instead of providing concise arguments with supporting evidence that highlights its positions, Apple instead attaches hundreds of pages of claim charts with generalized assertions that the prior art “either anticipate or render obvious, individually or in combination, each and every asserted claim.” Docket No. 432 at 22. It is Apple’s burden, not the Court’s, to piece together and present an invalidity defense. Apple failed to show that it is entitled to judgment as a matter of law on invalidity, and Dr. Levy’s testimony in this regard is sufficient evidence to support the jury’s finding of no anticipation or obviousness. 9/30/10 p.m. (part 2) TT at 60:1-72:19. The jury’s verdict is not against the weight of the evidence; therefore, the Court DENIES Apple’s request for Judgment as a Matter of Law that the patents-in-suit are invalid. INEQUITABLE CONDUCT Apple asserts the applicants’ and prosecuting attorney’s submission of false statements, false declarations, and concealment of prior art demonstrate a pattern of deceptive intent that is grounds for a finding of inequitable conduct. Apple argues that the applicants failed to properly identify prior art by misrepresenting its availability and that the inventors and their attor *729 ney submitted false declarations relating to inventorship. Apple also contends there were other material prior art references that the applicants knew of but failed to disclose to the Patent Office. Applicable Law “Inequitable conduct resides in failure to disclose material information, or submission of false material information, with an intent to deceive, and those two elements, materiality and intent, must be proven by clear and convincing evidence.” Kingsdown Med. Consultants, Ltd. v. Hollister Inc., 863 F.2d 867, 872 (Fed.Cir. 1988); see also Praxair, Inc. v. ATMI, Inc., 543 F.3d 1306, 1313 (Fed.Cir.2008). Because an actual “intent to deceive” is required, “[mistake or negligence, even gross negligence, does not support a ruling of inequitable conduct.” Abbott Labs. v. Sandoz, Inc., 544 F.3d 1341, 1353 (Fed.Cir. 2008). A court only has discretion to invalidate a patent for inequitable conduct after a showing of both materiality and intent to deceive. Id. When examining intent, the alleged conduct must be “viewed in light of all the evidence, including evidence indicative of good faith.” Kingsdown, 863 F.2d at 876. However, when a “failure to disclose” is alleged, intent to deceive may be inferred when 1) highly material information is withheld, 2) the applicant knew of the information and knew or should have known of the materiality of the information, and 3) the applicant has not provided a credible explanation for the withholding. Praxair, 543 F.3d at 1313-1314. Analysis First, Apple’s arguments center around representations regarding the availability of the Yale Technical Report 1070 (“TR-1070”), dated April 1995, entitled “The ‘Lifestreams’ Approach to Reorganizing the Information World.” DX0004 at 0344-54, 0384-85. TR-1070 was co-authored by the inventors of the '227 patent, Dr. David Gelernter and Eric Freeman. Apple contends that if it was available, and indeed a printed publication under § 102(b), it would have been material prior art. In the Information Disclosure Statement (“IDS”), the applicants stated that TR-1070 was not publicly available: This Technical Report [TR-1070] was stored at Yale University in the files of Christopher Hatchell, an Administrative Associate, whose tasks included distribution of this Technical Report. According to Mr. Hatchell’s records and to the best of his knowledge, this Technical Report was not distributed outside of the Department of Computer Science at Yale. Further, the list containing bibliographic information about the Technical Report from which the technical report number was determined, is kept in a locked file in the Office of Computer Science at Yale University. DX0004 at 0384-85. To demonstrate the report was publicly available, Apple references an internet archiving website and presented evidence that the inventors made TR-1070 available on the Computer Science Department’s website at Yale. DX1126 at 0049, 0117. In addition, Yale administrative employees testified that copies of technical reports were made available upon request; however, hard copies of the reports were generally kept locked in either a cabinet or locked in a department office. 10/8/10 TT at 22:20-28:1; 37:22-42:9. The prosecuting attorney testified that he did not believe TR-1070 was publicly available, and therefore he did not believe it was a material reference. Even though he concluded TR-1070 was not material, he intended to inform the Patent Office of the document and thus included it in the IDS. 10/8/10 TT at 46:24-52:15. *730 Although there is conflicting evidence regarding the availability of TR-1070, the Court is not persuaded that the prosecuting attorney or the inventors believed TR-1070 was a printed publication at the time the statement was made in the IDS. The evidence indicates Technical Reports were generally under “lock and key” and supports the prosecuting attorney’s conclusion that TR-1070 was not a printed publication under § 102(b). As the Court finds the prosecuting attorney’s reasoning sound, and his testimony credible, the totality of evidence supports a conclusion that the prosecuting attorney and the applicants were candid with the Patent Office about TR-1070. Weighing the materiality of the statements made regarding TR-1070 with the lack of intent, the Court does not find this evidence meets the clear and convincing burden to prove inequitable conduct. Second, Apple argues the inventors and their attorney submitted false declarations of inventorship. Yale’s Patent Policy required University employees to assign their patents to the school. DX0793 at ¶ 6. The '227 patent originally named Yale student, Mr. Freeman, as the sole inventor. DX0004 at 0056-57. Citing the prior art references in the application, the examiner noted that “the record appears to indicate that David Gelernter should be included as an inventor.” Id. at DX0065; see also DX0065-68. The applicants subsequently filed an Amendment adding Dr. Gelernter, with a declaration that asserted that the correction “is necessitated by amendment of the claims.” Apple contends this constitutes inequitable conduct because the first declaration intentionally misrepresented inventorship, and the second declaration misrepresented the reason for the correction because the amendments did not necessitate a change of inventor-ship. However, Dr. Gelernter testified that there was no deceptive intention on his part. 9/27/10 p.m. TT 144:9-146:21. Although the prosecuting attorney testified he did not have a specific recollection of the statements made in the declaration, he also testified that it was his typical practice to investigate such statements before submitting them to the Patent Office. 10/8/10 TT at 44:6-46:23. While representations regarding inventorship are material to patentability, the Court does not find the declarations were filed with deceptive intent. See PerSeptive Biosystems, Inc. v. Pharmacia Biotech, Inc., 225 F.3d 1315, 1321 (2000). The evidence does not indicate that the patentees or the prosecuting attorneys intentionally presented falsehoods or omissions to the Patent Office, and the Court finds Mr. Gelernter’s and the prosecuting attorney’s testimony credible. Weighing the materiality of the statements regarding inventor-ship with the lack of intent, the Court does not find this evidence meets the clear and convincing burden to prove inequitable conduct. Finally, Apple argues the inventors were aware of prior art references they did not disclose to the Patent Office. Apple argues that in December 1999 Mr. Freeman’s dissertation and other publications described the Piles prior art reference (9/27/10 pm 127:18-128:23; DX0375 at 0002; DX0789 at 0015, 0172; DX0641), but the applicants did not disclose Piles to the Patent Office until June 2003 after receiving a Notice of Allowance for a related patent. DX0385. Apple also contends the inventors concealed the existence of Yale Technical Report 1054 entitled, “The Lifestreams Software Architecture.” DX0794 at 0002. Although Apple does not have a copy of TR-1054, as it was not produced in this case, Apple contends it was likely material prior art. Apple summarily argues that the Piles reference is “highly” material without providing support for this conclusion, and Apple failed to present any evidence of the *731 inventors’ deceptive intent. Likewise, Apple’s arguments regarding TR-1054 are based on conjecture, and there is no evidence of deceptive intent. Weighing the materiality of the references with the lack of intent, the Court does not find this evidence meets the clear and convincing burden to prove inequitable conduct. Accordingly, the Court DENIES Apple’s Motion for a Finding of Inequitable Conduct (Docket No. 433) and DENIES Apple’s Motion Regarding Mirror Worlds’ Waiver of Privilege for Documents Listed on the December 9, 2010 Privilege Log (Docket No. 465). CONCLUSION While a jury’s collective wisdom should always be honored as to disputed factual issues, it is equally true that the party with the burden of proof must present sufficient evidence as to each and every element required in its cause of action. This is often a painstaking task — especially in a complex patent case — -but it is important. Perhaps it is even more important in patent cases where the jury must consider multilayered claims and interconnected arguments. The jury often relies on the representations of parties, who bear the burden of being accurate and complete and living up to the representations they make to the jury. No matter how attractive a party paints the facade of its case, it is worthless without the requisite foundational support. It is the Court’s job to inspect that foundation, and where it has not been properly laid under the law, to set aside the verdict to protect the reliability of our jury system. In this case, Mirror Worlds may have painted an appealing picture for the jury, but it failed to lay a solid foundation sufficient to support important elements it was required to establish under the law. Accordingly, the Court rejects Mirror Worlds’ case as to infringement and damages, while affirming it as to validity and inequitable conduct. Upon consideration of the parties’ arguments and the evidence of record established at trial, the Court GRANTS Apple’s Renewed Motion for Judgment as a Matter of Law, Motion for New Trial and Motion for Remittitur Pursuant to Federal Rules of Civil Procedure 50 and 59 as to Apple’s direct infringement of the '227, '313, and '427 patents, DENIES the motion as to invalidity, and DENIES AS MOOT the request for a new trial or remittitur; DENIES Apple’s Motion for a Finding of Inequitable Conduct and Good Cause to Re-Open the Record for a Bench Trial (Docket No. 433); DENIES Mirror Worlds’ Motion for (1) Entry of Judgment, (2) Prejudgment Interest, (3) Post Verdict and Prejudgment Damages, (4) Post Judgment Royalties, (5) Enhanced Damages, (6) Attorneys’ and Experts’ Fees, (7) Costs, and (8) Post Judgment Interest (Docket No. 435); GRANTS Apple’s Motion to Strike the October 29, 2010 Declaration of Walter Bratic and Documents Not in Evidence (Docket No. 446); and DENIES Apple’s Motion Regarding Mirror Worlds’ Waiver of Privilege for Documents Listed on the December 9, 2010 Privilege Log (Docket No. 465). All other pending motions not previously resolved are DENIED AS MOOT. So ORDERED. Footnotes [1] The Court previously addressed Apple’s request to reopen the record (Docket No. 433) granting leave to submit its inequitable conduct exhibits and testimony not offered at trial. See Docket No. 461. The Court's order setting time limits was clear that trial times were to apply to all issues including those before the jury and to the Court. See Docket No. 387. Trial includes all issues, jury and non-jury, upon which a judgment could be based. In every patent case it has tried, it has been this Court’s practice to allow the parties to present inequitable conduct evidence, that is not otherwise relevant to jury issues, at the end of each trial day after the jury is discharged. This is for the convenience of the witnesses and so the Court may hear the evidence at the same time and in the context of the other jury related evidence presented at trial. Apple failed to properly allocate its time and resources within the time the Court allotted for trial and, for whatever reason, misconstrued the time allocations. To complete the record, the Court reopened the record so the Court had all of the evidence before it when considering Apple's inequitable conduct defense. [2] Mirror Worlds did not proceed to trial on the 6,768,999 patent. See Docket No. 353. [3] The '427 patent issued from a divisional of application Ser. No. 09/398,611, now the '318 patent, which is a continuation of application Ser. No. 08/673,255, now the '227 patent. [4] The Court defined “stream” as "a time-ordered sequence of documents that functions as a diary of a person or an entity’s electronic life and that is designed to have three main portions: past, present, and future.” Docket No. 302 at 10. [5] The accused "Tiger” Operating System refers to Mac OS X 10.4 Tiger or Mac OS X Server V10.4 Tiger. The accused "Leopard” and “Snow Leopard” Operating Systems refer to 1) Mac OS X 10.5 Leopard, 2) Mac OS X Server V10.5 Leopard, 3) Mac OS X 10.6 Snow Leopard, and 4) Mac OS X Server V10.6 Snow Leopard. [6] The Court found claims 1, 5, 6, 9-12, 25, 26, and 29 of the '227 patent invalid as indefinite. Docket Nos. 178, 302. [7] Mirror Worlds did not offer any evidence that anyone, Apple’s customers or otherwise, actually performed the patented steps. While Mirror Worlds’ expert, Dr. Levy, testified about the attributes and capabilities of the accused Spotlight, Cover Flow, and Time Machine features, he did not testify that anyone else performed all of the steps in the asserted method claims. Nor did Dr. Levy testify that he actually performed the claimed steps. Likewise, Mirror Worlds offered no documentary evidence (e.g. instructions, manuals, or user guides) that instructed others to practice the patented steps. Mirror Worlds also failed to provide any corresponding testimony tying any documentation to the method steps or explanation of how Apple instructed users to perform each of the claim limitations. As such, no reasonable jury could conclude Apple was liable for indirect infringement. Accordingly, the Court ruled that, as a matter of law, Mirror Worlds had not proven that Apple induced or contributorily infringed any claims. 9/29/10 p.m. TT at 96:25-97:16; see Lucent, 580 F.3d at 1317-23; see also Cross Med. Prods., Inc. v. Medtronic Sofamor Danek, Inc., 424 F.3d 1293, 1312 (Fed.Cir.2005) ("In order to succeed on a claim of contributory infringement, in addition to proving an act of direct infringement, plaintiff must show that defendant knew that the combination for which its components were especially made was both patented and infringing and that defendant’s components have no substantial non-infringing uses.”) (internal quotations omitted); Manville Sales Corp. v. Paramount Sys., Inc., 917 F.2d 544, 553 (Fed.Cir.1990) (plaintiff has the burden of showing that the alleged infringer’s actions induced infringing acts and that it knew or should have known its actions would induce actual infringement). [8] The Court defined a "data unit" as "an item of information of significance to the user that the user considers as a unit.” Docket No. 302 at 37. [9] The asserted independent claims of the '427 patent have insubstantial differences in the wording of this limitation: Claim 1 of the '427 patent requires: “displaying a cursor or pointer and responding to user-controlled sliding without clicking of the cursor over said displayed stack to display a glance view of a document whose document representation is currently touched by the cursor or pointer;” Claim 8 of the '427 patent requires: "displaying a cursor or pointer and responding to user-controlled sliding without clicking of the cursor or pointer over the displayed document representations to display at least a glance view of a document whose document representation is currently touched by the cursor or pointer;” Claim 16 of the '427 patent requires: “displaying a cursor or pointer and responding to a user sliding without clicking the cursor or pointer over a portion of a displayed document representation to display the glance view of the document whose document representation is touched by the cursor or pointer;” Claim 25 of the '427 patent requires: "displaying a cursor or pointer and responding to a user sliding without clicking the cursor or pointer over said displayed stack of document representations to display the glance view of the document whose document representation is currently touched by the cursor.” [10] With some variation, the method claims of the '313 patent similarly require these limitations. Claim 1 of the '313 patent also requires the same limitations as the '427 patent; however, claim 9 requires "responding to a user sliding the cursor or pointer over said displayed stack," but it does not require "sliding without clicking.” Likewise, claim 11, which depends from claim 9, does not require "sliding without clicking.” [11] Dr. Levy acknowledged that moving a cursor over the accused Cover Flow display did not produce an infringing response that would literally meet the claim limitation. 9/28/10 p.m. TT at 145:11-17 (Dr. Levy's testimony that Cover Flow does not literally display a cursor or pointer); see also 9/29/10 a.m. TT at 29:1-21 (Dr. Levy's testimony regarding a video demonstration of the operation of Cover Flow (DX1043 Clip 6): “Q. Does that demonstrate infringement right there, that black cursor passing over the stack? A. The black cursor does not.”). [12] In its post-trial briefing, Mirror Worlds contends that the demonstratives used at trial also depict infringement; however, it is the obligation of the testifying expert to reduce the demonstrative to words and testify accordingly. However useful, pictorials are conclusory and cannot be used as a substitute for the rigorous comparison of the claims to the accused products that is required to prove infringement by equivalents. [13] For the same reasons, the record lacks sufficient evidence to support a finding of infringement for the asserted method claims of the '313 patent. [14] Specifically, the Court asked: Court: Do you believe that the damages can be apportioned between those two groups of patents? Mirror Worlds: I think — and I don’t want this to sound flip, but I think the jury can do whatever they want. Court: I’m talking about as a matter of law. I know the jury can do whatever they— Mirror Worlds: I don’t have a clue, Judge. I mean, all I know is— Court: That's an honest answer. 10/1/10 TT at 13:4-13. [15] After the parties had time to consider the Court’s offer to re-open the record, Mirror Worlds chose to stand on the evidence already presented at trial: Court: All right. Did the parties have an opportunity to decide whether you wish to have — to present any additional testimony? Mirror Worlds: We don't believe it's necessary, Your Honor. Court: Okay. 10/1/10 TT at 23:15-22. [16] Mirror Worlds’ counsel did not state on the record the specific numbers he wrote on the demonstrative, nor was a copy of this demonstrative offered for the Court’s records. However, in Apple’s closing, counsel repeated the numbers written on the demonstrative for the record, noting that Mirror Worlds had written "322, 336, 320” for the three patents. 10/1/10 TT at 123:3-6. [17] With its post trial briefing, Mirror Worlds attached an additional declaration from Mr. Bratic that contains information and arguments that were not presented at trial. The Court GRANTS Apple’s Motion to Strike the October 29, 2010 Declaration of Walter Bratic and Documents Not in Evidence (Docket No. 446).