Court Opinion

ID: 6118807
Source: CourtListenerOpinion
Date Created: 2022-02-04 17:00:52.249752+00
Date Added: 2024-06-11T08:22:43.371627
License: Public Domain

Case: 20-2222    Document: 63     Page: 1   Filed: 02/04/2022

   United States Court of Appeals
       for the Federal Circuit
                  ______________________

    CALIFORNIA INSTITUTE OF TECHNOLOGY,
                Plaintiff-Appellee

                             v.

   BROADCOM LIMITED, NKA BROADCOM INC.,
      BROADCOM CORPORATION, AVAGO
     TECHNOLOGIES LIMITED, NKA AVAGO
  TECHNOLOGIES INTERNATIONAL SALES PTE.
           LIMITED, APPLE INC.,
             Defendants-Appellants
            ______________________

                   2020-2222, 2021-1527
                  ______________________

    Appeals from the United States District Court for the
 Central District of California in No. 2:16-cv-03714-GW-
 AGR, Judge George H. Wu.
                  ______________________

                Decided: February 4, 2022
                 ______________________

     KATHLEEN M. SULLIVAN, Quinn Emanuel Urquhart &
 Sullivan, LLP, Los Angeles, CA, argued for plaintiff-appel-
 lee. Also represented by JAMES R. ASPERGER; BRIAN P.
 BIDDINGER, EDWARD J. DEFRANCO, New York, NY; TODD
 MICHAEL BRIGGS, KEVIN P.B. JOHNSON, Redwood Shores,
 CA; DEREK L. SHAFFER, Washington, DC; KEVIN
 ALEXANDER SMITH, San Francisco, CA.
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2            THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

     WILLIAM F. LEE, Wilmer Cutler Pickering Hale and
 Dorr LLP, Boston, MA, argued for defendants-appellants.
 Also represented by LAUREN B. FLETCHER, MADELEINE C.
 LAUPHEIMER, JOSEPH J. MUELLER; STEVEN JARED HORN,
 DAVID P. YIN, Washington, DC; MARK D. SELWYN, Palo
 Alto, CA.
                 ______________________

       Before LOURIE, LINN, and DYK, Circuit Judges.
     Opinion for the Court filed by Circuit Judge LINN.
 Opinion concurring-in-part and dissenting-in-part filed by
                   Circuit Judge DYK.
 LINN, Circuit Judge.
     Broadcom Limited, Broadcom Corporation, and Avago
 Technologies Ltd. (collectively “Broadcom”) and Apple Inc.
 (“Apple”) appeal from the adverse decision of the District
 Court for the Central District of California in an infringe-
 ment suit filed by the California Institute of Technology
 (“Caltech”) for infringement of its U.S. Patents No.
 7,116,710 (“the ’710 patent”), No. 7,421,032 (“the ’032 pa-
 tent”), and No. 7,916,781 (“the ’781 patent”).
      Because the district court did not err in its construction
 of the claim limitation “repeat” and because substantial ev-
 idence supports the jury’s verdict of infringement of the as-
 serted claims of the ’710 and ’032 patents, we affirm the
 district court’s denial of JMOL on infringement thereof.
 We also affirm the district court’s conclusion that claim 13
 of the ’781 patent is patent-eligible but vacate the jury’s
 verdict of infringement thereof because of the district
 court’s failure to instruct the jury on the construction of the
 claim term “variable number of subsets.” We thus remand
 for a new trial on infringement of claim 13 of the ’781 pa-
 tent. We further affirm the district court’s summary judg-
 ment findings of no invalidity based on IPR estoppel and
 its determination of no inequitable conduct. We affirm the
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                      3

 district court’s decision with respect to its jury instructions
 on extraterritoriality. But because Caltech’s two-tier dam-
 ages theory cannot be supported on this record, we vacate
 the jury’s damages award and remand for a new trial on
 damages.
                         BACKGROUND
                   I.   The Caltech Patents
      Caltech’s ’710 and ’032 patents disclose circuits that
 generate and receive irregular repeat and accumulate
 (“IRA”) codes, a type of error correction code designed to
 improve the speed and reliability of data transmissions.
 Wireless data transmissions are ordinarily susceptible to
 corruption arising from noise or other forms of interfer-
 ence. IRA codes help to identify and correct corruption af-
 ter it occurs.
      The encoding process begins with the processing of
 data before it is transmitted. The data consists of infor-
 mation bits in the form of 1’s and 0’s. The information bits
 are input into an encoder, a device that generates code-
 words comprised of parity bits and the original information
 bits. Parity bits are appended at the end of a codeword.
 Codewords are created in part by repeating information
 bits in order to increase the transmission’s reliability.
 When noise or other forms of interference introduce errors
 into the codewords during transmission, the decoder iden-
 tifies these errors and relies on the codeword’s redundant
 incorporation of the original string of information bits to
 correct and eliminate the errors.
     Before Caltech’s patents, error correction codes had al-
 ready incorporated repetition and irregular repetition.
 These codes, however, were less than optimally efficient be-
 cause they were either encoded or decoded in quadratic
 time, which meant that the number of computations
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4             THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 required to correct a given number of bits far exceeded the
 number of bits ultimately corrected.
      In the ’710 and ’032 patents, the IRA codes are linear-
 time encodable and decodable, rather than quadratic. ’710
 patent, col. 2, ll. 6–7 (“The encoded data output from the
 inner coder may be transmitted on a channel and decoded
 in linear time.”); id. col. 2, l. 59 (“The inner coder 206 may
 be a linear rate-1 coder.”); id. col. 3, ll. 25–26 (“An IRA code
 is a linear code.”). Using a linear code means that the re-
 lationship between the bits corrected and the computations
 required is directly proportional. Minimizing the number
 of calculations that an encoder or decoder must perform
 permits smaller, more efficient chips with lower power re-
 quirements.
      The claimed improvement involves encoding the infor-
 mation bits through a process of irregular repetition,
 scrambling, summing, and accumulation. Repeating in-
 putted information bits is necessary to increase the relia-
 bility of data transmissions, and irregular repetition
 minimizes the number of times that information bits are
 repeated. Minimizing the number of times that an infor-
 mation bit is repeated is crucial to the efficiency of the
 claimed inventions because the repetitions impact the de-
 vice’s coding rate or speed, as well as the code’s complexity.
 The fewer repeated bits there are, the fewer number of
 computations that an encoder must perform, which in turn
 permits smaller circuits, decreased power requirements,
 and decreased operating temperatures in devices incorpo-
 rating the circuits.
     The claims and accompanying specifications of the Cal-
 tech patents make clear that each inputted information bit
 must be repeated. The parties agree that every claim at
 issue requires irregular repetition of information bits ei-
 ther explicitly or via the court’s construction. This is so
 even where the irregular repetition is not expressly
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                     5

 required by the claims. For example, the agreed-upon con-
 struction of a Tanner graph in the ’032 patent requires that
 “every message bit is repeated . . . .” J. App’x 33. Further-
 more, the claims and accompanying specifications make
 clear that each bit must be repeated irregularly, stating,
 for example in the ’710 patent, “a fraction of the bits in the
 block may be repeated two times, a fraction of bits may be
 repeated three times, and the remainder of bits may be re-
 peated four times.” ’710 patent, col. 2, ll. 53–58.
      The ‘781 patent discloses and claims a method for cre-
 ating codewords in which “information bits appear in a var-
 iable number of subsets.”        Before trial, Apple and
 Broadcom sought summary judgment that claim 13 was
 unpatentable under 35 U.S.C. § 101. After finding that the
 claims were directed to a patent-eligible subject matter
 (step 1 of Alice 1)—a method of performing error correction
 and detection encoding with the requirement of irregular
 repetition—the court declined to reach whether they con-
 tained an inventive concept (step 2 of Alice). To support
 patentability, Caltech argued that the “variable number of
 subsets” language required irregular information bit repe-
 tition. The district court agreed and adopted and relied on
 Caltech’s interpretation to deny summary judgment of un-
 patentability. No party on appeal challenges this claim in-
 terpretation.
                  II. The Accused Products
     Caltech alleged infringement by certain Broadcom Wi-
 Fi chips and Apple products incorporating those chips, in-
 cluding smartphones, tablets, and computers. The accused
 Broadcom chips were developed and supplied to Apple pur-
 suant to Master Development and Supply Agreements

     1  Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S.
 208 (2014).
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6               THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 negotiated and entered into in the United States. Caltech
 specifically identified as infringing products two encode1·s
 contained in the Broadcom chips-a Richardson-Urbanke
 ("RU") encoder and a low-area ("LA") encoder. In the ac-
 cused encoders, incoming information bits are provided to
 AND gates in the RU encoder or multiplexers in the LA
 encodei·.
      Throughout the ti·ial and on appeal, the parties treated
 AND gates and multiplexers as functionally identical for
 all relevant issues. It thus suffices to describe in detail the
 RU encoder only. In the RU encoder, each information bit
 is simultaneously fed as one input to 972 separate AND
 gates. Each AND gate receives a second input-a "parity-
 check" or "enable" bit of 0 or I-derived from a low-density
 parity check matrix. This matrix is an anay of l 's and O's.
 A low-density parity check matrix is one in which the num-
 ber of l's in the matrix is significantly fewer than the num-
 ber of O's.
     In its brief, Broadcom presents the following table, us-
 ing the example of the functioning of a single AND gate, to
 show how outputs ai·e determined by the two inputs:

      Input 1                Input 2             AND Gate
 (Information Bit)      (Parity-Check Bit)        Output
         0                       0                     0
         0                       1                     0
          1                      0                     0
         1                       1                     1

     For each AND gate, the output of the gate is 1 if both
 inputs (the information bit and the parity-check bit) are l ;
 otherwise, the output is 0. One consequence of this logic is
 that if the parity-check bit is 1 (as shown in rows two and
 four) , then the output is identical to the information-bit in-
 put. If the parity-check bit is 0, the output is 0, regardless
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                    7

 of the value of the input (rows one and three). Throughout
 trial, the parties referred to parity-check bits and enable
 bits interchangeably. Parity-check bits determine the ac-
 tion of the AND gates, which are open/on when the parity-
 check bit is 1 and closed/off when the parity-check bit is 0.
     Caltech sued Broadcom and Apple on May 26, 2016, al-
 leging infringement under 35 U.S.C. § 271 by Broadcom
 wireless chips and Apple products incorporating those
 chips. Both defendants denied that any of the accused de-
 vices infringed Caltech’s patents, and in turn asserted
 counterclaims for declaratory judgment of non-infringe-
 ment, invalidity under 35 U.S.C. §§ 101, 102, 103, and/or
 112, and unenforceability due to inequitable conduct.
                 III.   Pre-Trial Proceedings
      Before trial, Apple filed multiple IPR petitions chal-
 lenging the validity of the claims at issue, relying on vari-
 ous prior art references. The Patent Trial and Appeal
 Board (“PTAB” or “Board”) issued a number of written de-
 cisions, which concluded that Apple failed to show the chal-
 lenged claims were unpatentable as obvious. Before the
 district court, Apple and Broadcom argued that the as-
 serted claims would have been obvious over new combina-
 tions of prior art not asserted in the IPR proceedings.
     The district court granted summary judgment of no in-
 validity, interpreting 35 U.S.C. § 315(e)(2) as precluding
 parties from raising invalidity arguments at trial that they
 reasonably could have raised in their IPR petitions. It also
 denied the motion filed by Apple and Broadcom for sum-
 mary judgment of invalidity under 35 U.S.C. § 101 for the
 ’781 patent. The district court granted Caltech’s summary
 judgment motion as to inequitable conduct, finding no in-
 equitable conduct with respect to Caltech’s failure to dis-
 close Richardson99 during prosecution. The district court
 reasoned that this prior art reference was not but-for ma-
 terial to the PTO’s grant of Caltech’s patents.
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8             THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

     The district court also conducted a Markman hearing
 and initially construed the claim limitation “repeat.” That
 construction is germane to all of the asserted claims. At
 the conclusion of the Markman hearing, the district court
 construed “repeat” to have its plain and ordinary meaning.
 The district court noted that the repeated bits “are a con-
 struct distinct from the original bits from which they are
 created,” but that they need not be generated by storing
 new copied bits in memory.
                    IV Trial Proceedings
         A. Infringement of the ’710 and ’032 Patents
     At trial, Caltech argued that the accused chips in-
 fringed claims 20 and 22 of the ’710 patent and claims 11
 and 18 of the ’032 patent. Both groups of claims explicitly
 require irregular repetition; i.e., repetition of groups of in-
 formation bits an irregular number of times. Claims 20
 and 22 of the ’710 patent depend from claim 15, which
 claims:
     15. A coder comprising: a first coder having an in-
     put configured to receive a stream of bits, said first
     coder operative to repeat said stream of bits irreg-
     ularly and scramble the repeated bits; and a second
     coder operative to further encode bits output from
     the first coder at a rate within 10% of one.
 ’710 patent, col. 8, ll. 1–6. Claims 11 and 18 of the ’032
 patent cover devices for encoding and decoding pursuant to
 a Tanner graph: 2

     2   During claim construction, the parties agreed that
 a Tanner graph is a visual representation of the “con-
 straints that determine the parity bits” created by an IRA
 code. J. App’x 33.
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                             9

    11. A device comprising: an encoder configured to
    receive a collection of message bits and encode the
    message bits to generate a collection of parity bits
    in accordance with the following Tanner graph:

                  ·········/P\
                  •········\p):
                          ·~...~··

                  ·········•18r      I
                        \c} I
                           ·~....•

                  •·····---r3\:
                  . . ...\:8L
                                         c✓.28 U.S.C. §1295(a)(1).
                          DISCUSSION
                   I.   Standard of Review
     Claim construction is reviewed de novo when relying
 on intrinsic evidence. Teva Pharms. USA, Inc. v. Sandoz,
 Inc., 574 U.S. 318, 333 (2015). Infringement and damages
 are reviewed for substantial evidence. Lucent Techs., Inc.
 v. Gateway, Inc., 580 F.3d 1301, 1309, 1324 (Fed. Cir.
 2009). Statutory interpretation is reviewed de novo. Power
 Integrations v. Semiconductor Components Indus., LLC,
 926 F.3d 1306, 1313 (Fed. Cir. 2019). Patent-eligibility un-
 der 35 U.S.C. § 101 is reviewed de novo. Recognicorp, LLC
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                   13

 v. Nintendo Co., 855 F.3d 1322, 1326 (Fed. Cir. 2017). We
 review patent jury instructions on patent law issues de
 novo, asking if the instructions were legally erroneous and
 prejudicial. Bettcher Indus., Inc. v. Bunzl USA, Inc., 661
 F.3d 629, 638-39 (Fed. Cir. 2011).
      We review a district court’s order denying JMOL under
 the standard applied by the regional circuit. Apple, Inc. v.
 Samsung Electronics Co., Ltd., 839 F.3d 1034, 1040 (Fed.
 Cir. 2016). In the Ninth Circuit, JMOL “is proper when the
 evidence permits only one reasonable conclusion and the
 conclusion is contrary to that of the jury.” See Monroe v.
 City of Phoenix, 248 F.3d 851, 861 (9th Cir. 2001). The
 Ninth Circuit explains that “[t]he evidence must be viewed
 in the light most favorable to the nonmoving party, and all
 reasonable inferences must be drawn in favor of that
 party.” Id. The Ninth Circuit reviews a district court’s de-
 cision to deny JMOL de novo. Id.
                      II. Infringement
                A. The ’710 and ’032 Patents
     Broadcom and Apple argue that the district court erro-
 neously construed “repeat,” contending that the accused
 AND gates and multiplexers do not “repeat” information
 bits in the manner claimed, but instead combine the infor-
 mation bits with bits from a parity-check matrix to output
 new bits reflecting that combination. Broadcom and Apple
 further argue that the AND gates and multiplexers also do
 not generate bits “irregularly,” asserting that they output
 the same number of bits for every information bit. Caltech
 argues in response that expert testimony throughout the
 record establishes that every information bit is repeated an
 irregular number of times. According to Caltech, the jury
 heard testimony explaining that in the RU devices every bit
 in the stream of information bits is fed by wire simultane-
 ously to the information inputs of all 972 AND gates and
 that at any time, at least 3 and up to 12 of those AND gates
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 14          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 will be enabled to repeat that bit at the output of the AND
 gates. We find no error in the district court’s construction
 of the term “repeat” and agree with Caltech that substan-
 tial evidence in the record supports the jury’s verdict on in-
 fringement.
             1. Claim Construction of “repeat”
      The district court construed “repeat” to mean “genera-
 tion of additional bits, where generation can include, for
 example, duplication or reuse of bits” (emphasis added). J.
 App’x 171. Broadcom and Apple argue that that construc-
 tion is inconsistent with the claim language, the specifica-
 tion and the construction given by another judge in a
 different case. 3 Caltech argues in response that the plain
 claim language requiring repeating information bits does
 not require generating new, distinct bits and that the dis-
 trict court was correct in construing the term to not exclude
 the reuse of bits. We agree with Caltech.
     The district court correctly observed that the claims re-
 quire repeating but do not specify how the repeating is to
 occur: “The claims simply require bits to be repeated, with-
 out limiting how specifically the duplicate bits are created
 or stored in the memory.” J. App’x 10. The specifications
 confirm that construction and describe two embodiments,
 neither of which require duplication of bits. The district
 court carefully and fully considered both the language of
 the claims and that of the written description and faithfully
 applied our precedent to reach the construction made dur-
 ing the trial and presented to the jury. We are not

      3  Broadcom and Apple misplace reliance on the con-
 struction of the term “repeat” made on an undeveloped rec-
 ord in the context of a summary judgment motion. See
 California Institute of Technology v. Hughes Communica-
 tions Inc., 35 F. Supp. 3d 1176 (C.D. Cal. 2014).
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                    15

 persuaded that the district court erred in construing the
 term “repeat” and, therefore, affirm the same.
                2.   JMOL on Infringement
      Broadcom and Apple argue that the evidence before the
 jury on infringement permitted only one verdict, namely no
 infringement, and that the district court erred in denying
 JMOL. Broadcom and Apple put forth two rationales for
 noninfringement of the “irregular repeat” requirement, Ap-
 pellant’s Br. 27–31. First, looking at each gate alone and
 commenting on the “repeat” requirement, they argue that
 the AND gate does not “repeat” the inputted information
 bit “because the AND gate’s output depends on not only the
 information bit but also the parity-check-matrix bit.” Ap-
 pellant’s Br. 29. Second, focusing on the “irregular” half of
 “irregular repeat,” they argue that “even if the outputted
 bits could be deemed ‘repeats’ of the information bits,” “any
 repetition is not ‘irregular’ because each information bit
 leads to the same number of outputted bits.” Appellant’s
 Br. 30.
     Caltech argues in response that the jury was provided
 with substantial evidence to support the verdict of infringe-
 ment and that the district court correctly denied JMOL.
 Caltech asserts that the fact that an AND gate doesn’t have
 an information-bit/output match for every information bit
 hardly means that it isn’t repeating any information bit.
 Appellee’s Br. 21–22 (citing J. App’x 3036–38). All that
 matters, according to Caltech, is that sometimes there is
 such a match that qualifies as a “repeat,” so long as each
 and every bit is repeated at least once. Caltech argues that
 Broadcom ignores ample expert testimony, which the jury
 could credit, that sometimes an AND gate repeats an infor-
 mation bit and that, taking the 972 AND gates together,
 the carefully designed parity-bit table/matrix meant that
 “the products output and store information bits between
 two and twelve times.” Appellee’s Br. 22. Caltech asserts
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 16          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 that, considering the system as a whole, each information
 bit is in fact repeated, and they are not all repeated the
 same number of times. We agree with Caltech.
      Caltech’s expert, Dr. Matthew Shoemake began his tes-
 timony with reference to the exemplary table reproduced
 above. See J. App’x 3036–38. He explained that in the par-
 ity-check-bit-equals-1 situation (second and fourth rows of
 the table), the output bit is a “repeat” of the information-
 bit input. Where the parity-check bit is 1, the gate affirm-
 atively enables the information bit to be duplicated as the
 output bit. That is a “repeat.” That is so, he explained,
 because the information bit in that situation “flows
 through” to appear again in the output. He also addressed
 the one other situation where the output bit is identical to
 the information bit, namely, in the first row of the above
 table, where both the information bit and the parity-check
 bit are 0, and so is the output. Despite the identity of the
 information bit and the output bit, he explained, that situ-
 ation does not involve a “repeat.” A 0 parity-check bit turns
 every information bit (0 or 1) into a 0 output, so the output
 bit in that situation tells one nothing about the information
 bit. Since the whole point of this encoding scheme is to use
 outputs that give information about the information bits, a
 0 parity-check bit does not produce a “repeat” even when
 the information-bit input and the output are the same.
 Broadcom’s expert, Dr. Wayne Stark, expressly recognized
 that this was exactly what Dr. Shoemake said in his testi-
 mony. J. App’x 3956 (“He said it’s a repeat only if the ena-
 ble [parity-check] signal is a one and it’s not a repeat if an
 enable [parity-check] symbol is a zero.”).
     Dr. Shoemake also explained to the jury that “flow
 through” means that the information bit is repeated at the
 output gate. See, e.g., J. App’x 2810, 2812, 3017–19. When
 the information bit “flows through” to the output gate be-
 cause the parity-check bit is 1, that’s a repeat, both accord-
 ing to the expert’s usage and a plain understanding of the
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                     17

 word “repeat.” See, e.g., J. App’x 3038. When the infor-
 mation bit is not allowed to flow through (because the par-
 ity-check bit is 0), that’s not a repeat (even though both the
 information bit and the output bit are 0). 4
     In explaining the operation of the RU encoder itself, Dr.
 Shoemake testified that it contains “972 mac_reg modules
 [AND gates], and the information bits are connected to
 every single one of them.” J. App’x 2831. He further testi-
 fied that: “[D]epending on which information bit it is, 3 to
 12 of these gates are enabled which then allows 3 to 12 …
 [information bits] to flow through 3 to 12 times and since
 that number varies, there’s irregular repetition,” J. App’x
 3034-35; “[W]hat really happens in the accused products,
 the tables tell you how many times should information bit
 number one be repeated. And the tables I've mentioned
 several times that they allow information bits, and I should
 force information bits to be repeated between 3 and 12
 times,” J. App’x 3080; and “[T]he information bit starts off
 in one location in the chip, and then it’s connected to 972
 distinct locations so it can be irregularly repeated in this
 architecture.” J. App’x 3018.
     Dr. Shoemake’s position was consistent throughout his
 testimony: the physical connection of the first inputs of all
 972 AND gates for simultaneous receipt of the information
 bit stream and the connection of the parity-bit system to
 the other inputs of the AND gates to selectively enable 3 to
 12 of those gates at any time together implement irregular

     4    Caltech’s Red Brief incorrectly cited this example
 as representing a repeat. Red. Br. 21. This was evidently
 error, given that it directly contracted the directly cited
 pages of Dr. Shoemake’s testimony. This error does not,
 however, change the fact that Caltech correctly identified
 the substantial trial testimony on which the jury could base
 its decision.
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 18          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 repetition. Dr. Shoemake explained that this is exactly
 what one sees when one looks at the “overall architecture”
 (“whole architecture”), not each gate alone. J. App’x 3031,
 3035, 3038. As he specifically testified:
      Q: Your position, your opinion . . . is that that
      branch wire creates 972 repeat bits within the
      meaning of the claims in the Caltech patents; cor-
      rect?
         A: So based on my analysis, this wire going
         to the Mac rag modules and the AND gates
         under control of the tables that are stored
         in the RU encoder actually allows the infor-
         mation bits to flow through [a] different
         number of times. It’s always 3 to 12 times
         for a particular information bit. And so [i]n
         my analysis, this is exactly how the RU en-
         coder is implementing irregular repetition
         of information bits.
 J. App’x 3019 (emphasis added).
     For the foregoing reasons, substantial evidence sup-
 ports the jury’s verdict of infringement of the ’710 and ’032
 patents. We are not persuaded that the record before the
 jury permits only a verdict of no infringement. We there-
 fore affirm the district court’s denial of JMOL.
                     B. The ‘781 Patent
                     1. Patent Eligibility
     Broadcom and Apple contend that claim 13 is not pa-
 tent eligible under 35 U.S.C. § 101. Broadcom and Apple’s
 briefing on this issue was cursory and relied solely on an
 argument that claim 13 is ineligible because it depends on
 mathematical operations. Caltech contends that the ’781
 patent is directed to a patent-eligible method of performing
 error correction and detection encoding with the require-
 ment of irregular repetition. It asserts that the claim
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                     19

 limitation “variable number of subsets” requires irregular
 information bit repetition.
     The mere fact that Caltech’s claim employs a mathe-
 matical formula does not demonstrate that it is patent in-
 eligible. See Diamond v. Diehr, 450 U.S. 175, 187 (1981)
 (“[A] claim drawn to subject matter otherwise statutory
 does not become nonstatutory simply because it uses a
 mathematical formula, computer program, or digital com-
 puter.”). Claim 13 does not claim a mathematical formula
 as such. It claims more than a mathematical formula be-
 cause it is directed to an efficient, improved method of en-
 coding data that relies in part on irregular repetition. This
 alleged improvement is not patent ineligible simply be-
 cause it employs a mathematical formula.
                      2. Infringement
     Broadcom and Apple argue that even if claim 13 is di-
 rected to patent eligible subject matter, the infringement
 verdict as to claim 13 cannot stand. As discussed above,
 the parties agree that claim 13 requires irregular repeti-
 tion, but dispute whether the district court erred in refus-
 ing to instruct the jury that the ’781 patent’s “variable
 number of subsets” limitation requires irregular repetition.
 The district court’s sole ground for refusing to instruct the
 jury of the interpretation the parties and the court reached
 during summary judgment was to avoid “confus[ing] the
 record on this issue.” J. App’x 207. This was error and
 requires remand for a new trial on infringement. Sulzer
 Textil A.G. v. Picanol N.V., 358 F.3d 1356, 1366 (Fed. Cir.
 2004) (“[I]t is the duty of trial courts in patent cases in
 which claim construction rulings on disputed claim terms
 are made . . . to inform jurors both of the court's claim con-
 struction rulings on all disputed claim terms and of the ju-
 ry's obligation to adopt and apply the court's determined
 meanings[.]”). On remand, the district court must instruct
 the jury as to the proper construction of the claim limita-
 tion “variable number of subsets.”
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 20          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

                III. Validity and IPR Estoppel
     Apple and Broadcom contend that the district court
 erred in granting summary judgment of no invalidity, bar-
 ring them from presenting an invalidity case at trial on the
 ground of statutory estoppel. In the district court proceed-
 ings, the parties challenged the patents’ invalidity, relying
 on grounds the PTAB did not address in its earlier insti-
 tuted IPR decisions. The district court nonetheless held
 that these challenges were barred by estoppel because Ap-
 ple and Broadcom were aware of the prior art references at
 the time they filed their IPR petitions and reasonably could
 have raised them in those petitions even if they could not
 have been raised in the proceedings post-institution.
     Before the district court, Broadcom and Apple brought
 counterclaims seeking declaratory judgment of invalidity
 under § 103. The district court’s summary judgment or-
 ders disposed of the parties’ affirmative defenses as well as
 their counterclaims. We therefore consider whether this
 ruling was erroneous and review the grant of summary
 judgment de novo. Synopsys, Inc. v. Mentor Graphics
 Corp., 839 F.3d 1138, 1146 (Fed. Cir. 2016).
      When IPR proceedings result in a final written deci-
 sion, 35 U.S.C. § 315(e)(2) precludes petitioners from rais-
 ing invalidity grounds in a civil action that they “raised or
 reasonably could have raised during that inter partes re-
 view.” Shaw Industries Group, Inc. v. Automated Creel
 Systems, Inc., 817 F.3d 1293, 1300 (Fed. Cir. 2016) (empha-
 sis added). In Shaw, this court held that IPR “does not
 begin until it is instituted.” Id. If IPR “does not begin until
 it is instituted,” grounds raised in a petition (or that rea-
 sonably could have been raised in a petition) were neces-
 sarily not raised “during the IPR.” Id. Only the grounds
 actually at issue in the IPR were raised, or reasonably
 could have been raised in the IPR. Thus, estoppel did not
 bar the petitioner in Shaw from presenting a petitioned-
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                   21

 for, non-instituted ground in future proceedings because
 the petitioner could not reasonably have raised the ground
 during IPR. Id. Shaw was followed in HP Inc. v. MPHJ
 Technology Investments, LLC, 817 F.3d 1339, 1347–48
 (Fed. Cir. 2016). At the time Shaw was decided, the PTAB
 often instituted review on less than all the grounds raised
 in a petition, which left some grounds unadjudicated on the
 merits. Before Shaw, we had held in Synopsys, Inc v. Men-
 tor Graphics Corp., 814 F.3d 1309, 1314–15 (Fed. Cir.
 2016), that the PTAB’s final decision need not address
 every claim raised in a petition. Under such circum-
 stances, we concluded that Congress could not have in-
 tended to bar later litigation of the issues that the PTAB
 declined to consider.
      After Shaw, several district courts concluded that
 Shaw does not allow a petitioner to avoid estoppel as to all
 arguments that could have been raised in the petition. See,
 e.g., SiOnyx, LLC v. Hamamatsu Photonics K.K., 330 F.
 Supp. 3d 574, 602 (D. Mass. 2018) (determining that estop-
 pel applies to grounds not included in a petition that the
 petitioner reasonably could have raised); Cobalt Boats,
 LLC v. Sea Ray Boats, Inc., Case No. 15-cv-21, 2017 WL
 2605977, at *3 (E.D. Va. June 5, 2017) (same); Biscotti Inc.
 v. Microsoft Corp., Case No. 13-cv-1015, 2017 WL 2526231,
 at *7 (E.D. Tex. May 11, 2017) (same); Douglas Dynamics,
 LLC v. Meyer Prods. LLC, Case No. 14-cv-886, 2017 WL
 1382556, at *5 (W.D. Wis. Apr. 18, 2017) (same); Parallel
 Networks Licensing, LLC v. IBM Corp., Case No. 13-cv-
 2072, 2017 WL 1045912, at *12 (D. Del. Feb. 22, 2017)
 (same); Oil-Dri Corp. of Am. v. Nestle Purina Petcare Co.,
 Case No. 15-cv-1067, 2017 WL 3278915, at *8 (N.D. Ill.
 Aug. 2, 2017) (“[W]hile it makes sense that noninstituted
 grounds do not give rise to estoppel because a petitioner
 cannot—to no fault of its own—raise those grounds after
 the institution decision, when a petitioner simply does not
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 22          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 raise invalidity grounds it reasonably could have raised in
 an IPR petition, the situation is different.”).
      Other district courts read Shaw differently, focusing on
 Shaw’s discussion of the “during the IPR” language in
 § 315(e)(2). See, e.g., Koninklijke Philips N.V. v. Wangs All.
 Corp., Case No. 14-cv-12298, 2018 WL 283893, at *4 (D.
 Mass. Jan. 2, 2018) (“It would seem, then, that the phrase
 “inter partes review” . . . refers only to the period of time
 after review is instituted, and, therefore, the estoppel pro-
 vision does not apply to arguments that the petitioner only
 ‘raised or reasonably could have raised’ in its petition ra-
 ther than after institution of review.”); Verinata Health,
 Inc. v. Ariosa Diagnostics, Inc., Case No. 12-cv-5501, 2017
 WL 235048, at *3 (N.D. Cal. Jan 19, 2017) (“The [Shaw]
 court chose instead to interpret the IPR estoppel language
 literally, plainly stating that only arguments raised or that
 reasonably could have been raised during IPR are subject
 to estoppel.”); Intellectual Ventures I LLC v. Toshiba Corp.,
 221 F. Supp. 3d 534, 553–54 (D. Del. 2016) (holding that
 although exempting nonpetitioned grounds from estoppel
 “confounds the very purpose of this parallel administrative
 proceeding, the court cannot divine a reasoned way around
 the Federal Circuit’s interpretation in Shaw”).
     After Shaw, in SAS Institute, Inc. v. Iancu, 138 S. Ct.
 1348 (2018), the Supreme Court made clear both that there
 is no partial institution authority conferred on the Board
 by the America Invents Act and that it is the petition, not
 the institution decision, that defines the scope of the IPR.
 See id. at 1357–58 (“[T]he statute tells us that the peti-
 tioner’s contentions, not the Director’s discretion, define
 the scope of the litigation . . . There is no room in this
 scheme for a wholly unmentioned ‘partial institution’
 power that lets the Director select only some challenged
 claims for decision.”). Given the statutory interpretation
 in SAS, any ground that could have been raised in a peti-
 tion is a ground that could have been reasonably raised
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                   23

 “during inter partes review.” Thus, the Supreme Court’s
 later decision in SAS makes clear that Shaw, while per-
 haps correct at the time in light of our pre-SAS interpreta-
 tion of the statute cannot be sustained under the Supreme
 Court’s interpretation of related statutory provisions in
 SAS.
     The panel here has the authority to overrule Shaw in
 light of SAS, without en banc action. To be sure, SAS did
 not explicitly overrule Shaw or address the scope of statu-
 tory estoppel under § 315(e)(2). But the reasoning of Shaw
 rests on the assumption that the Board need not institute
 on all grounds, an assumption that SAS rejected. Even in
 the Ninth Circuit, which has one of the stricter approaches
 to panel overruling, see Henry J. Dickman, Conflicts of
 Precedent, 106 Va. L. Rev. 1345, 1350–51 (2020), “the is-
 sues decided by the higher court need not be identical in
 order to be controlling. Rather, the relevant court of last
 resort must have undercut the theory or reasoning under-
 lying the prior circuit precedent in such a way that the
 cases are clearly irreconcilable,” Miller v. Gammie, 335
 F.3d 889, 900 (9th Cir. 2003) (en banc). We approved that
 higher standard in Troy v. Samson Manufacturing Corp.,
 758 F.3d 1322, 1326 (Fed. Cir. 2014), and conclude that
 that standard is satisfied in this case.
     Accordingly, we take this opportunity to overrule Shaw
 and clarify that estoppel applies not just to claims and
 grounds asserted in the petition and instituted for consid-
 eration by the Board, but to all claims and grounds not in
 the IPR but which reasonably could have been included in
 the petition. 5 In a regime in which the Board must

     5  In this case, SAS was decided while IPR proceed-
 ings remained pending before the Board. Accordingly, we
 need not decide the scope of preclusion in cases in which
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 24          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 institute on all grounds asserted and the petition defines
 the IPR litigation, this interpretation is the only plausible
 reading of “reasonably could have been raised” and “in the
 IPR” that gives any meaning to those words.
     It is undisputed that Apple and Broadcom were aware
 of the prior art references that they sought to raise in the
 district court when Apple filed its IPR petitions. Despite
 not being included in any of Apple’s IPR petitions, the con-
 tested grounds reasonably could have been included in the
 petitions, and thus in the IPR. We affirm the district
 court’s decision barring Apple and Broadcom from raising
 invalidity challenges based on these prior art references.
                  IV. Inequitable Conduct
     We turn next to the district court’s grant of Caltech’s
 summary judgment motion of no inequitable conduct.
 Generally, inequitable conduct requires a showing that un-
 disclosed prior art was but-for material to the PTO’s deci-
 sion of patentability. Therasense, Inc. v. Becton, Dickinson
 and Co., 649 F.3d 1276, 1291 (Fed. Cir. 2011). Prior art is
 but-for material if the PTO would have denied a claim had
 it known of the undisclosed prior art. Id. Prior art is not
 but-for material if it is merely cumulative. Regeneron
 Pharms., Inc. v. Merus N.V., 864 F.3d 1343, 1350 (Fed. Cir.
 2017) (citing Dig. Control Inc. v. Charles Mach. Works, 437
 F.3d 1309, 1319 (Fed. Cir. 2006)).
     Broadcom and Apple on appeal have limited their ar-
 gument to the district court’s conclusion that Richardson99
 was not shown to be but-for material to patentability. The
 district court found that Richardson99 was merely cumu-
 lative of Luby97 and Luby98—references the PTAB consid-
 ered in IPR proceedings upholding the patents’ validity—

 the Board declined to institute on all grounds and issued
 its final written decision pre-SAS.
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                     25

 noting Apple and Broadcom’s pleadings, interrogatory re-
 sponses, and briefs failed to distinguish Luby’s disclosed ir-
 regular repetition from Richardson99’s.          Apple and
 Broadcom did not argue at the summary judgment stage
 that Richardson99 was different from Luby such that it
 was not merely cumulative. The district court rejected the
 arguments as to Richardson99 because the Appellants
 failed to put Caltech on notice of an independent inequita-
 ble conduct theory based on alleged differences between
 Richardson99 and Luby.
     The district court’s decision was not an abuse of discre-
 tion. We therefore affirm the grant of summary judgment
 of no inequitable conduct.
                         V. Damages
     Caltech presented to the jury a two-tier reasonable roy-
 alty model based on simultaneous hypothetical negotia-
 tions with Broadcom and Apple in December 2009.
 Broadcom and Apple generally argue that the damages
 judgement cannot be sustained because Caltech’s damages
 model impermissibly applied two separate hypothetical ne-
 gotiations for Broadcom and Apple for sales of the same
 chips; because Caltech’s royalty rates were derived from
 non-comparable settlements—without apportionment and
 based on improperly excluded expert opinions and unre-
 lated “black box” calculations; and because Caltech’s dam-
 age model improperly included extraterritorial sales.
     Caltech argues in response that the damages judgment
 properly rests on separate running-royalty rates for each
 defendant, that the district court’s rulings on admissibility
 and exclusion of evidence were not an abuse of discretion
 and that the damages were based entirely on United States
 sales.
     We find no error in the district court’s jury instructions
 relating to extraterritoriality. But because Caltech’s two-
 tier damages theory is legally unsupportable on this
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 26          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 record, the damages award is vacated and the case is re-
 manded for a new trial on damages.
                    A. Extraterritoriality
     Apple and Broadcom argue that the damages verdict
 improperly included extraterritorial sales from Broadcom’s
 international affiliates. They argue that the district court
 erroneously instructed the jury on extraterritoriality for
 two reasons. First, they argue that the district court erro-
 neously declined to instruct the jury of a presumption
 against extraterritorial application of United States laws.
 We see no error. The relevant presumption is whether a
 law applies extraterritorially. See WesternGeco LLC v.
 ION Geophysical Corp., 138 S.Ct. 2129, 2134, 2136 (2018).
 But the dispute here is not whether infringement laws ap-
 ply domestically or extraterritorially—there is no dispute
 that the laws apply only domestically. Rather, the dispute
 between the parties is whether the relevant transactions
 here were domestic or extraterritorial in nature. The pre-
 sumption against extraterritorial application is thus inap-
 plicable. As Caltech correctly argues, the district court
 expressly instructed the jury that Caltech had the burden
 of proving that infringement occurred in the United States.
 J. App’x 184–85 (instructing the jury that “An allaged in-
 fringer is liable for direct infringement of a claim if the pa-
 tent holder proves by a preponderance of the evidence that
 the infringer, without the patent holder’s authorization,
 imports, offers to sell, sells, or uses [the accused products]
 within the United States,” and explaining the factors for de-
 termining whether a sale occurs in the United States).
 This was a proper and sufficient jury instruction with re-
 spect to the applicable burdens on the territoriality of the
 sales at issue.
     Second, Apple and Broadcom argue that the district
 court erroneously instructed the jury that the “sales cycle
 leading to design wins” could trigger a United States sale.
 Apple and Broadcom argue that Halo recognized a
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                       27

 categorical prohibition against treating such a sales cycle
 as a domestic sale. See Halo Elecs., Inc. v. Pulse Elecs.,
 Inc., 831 F.3d 1369, 1378 (Fed. Cir. 2016), on remand from
 579 U.S. 93 (2016). Halo held that “pricing and contracting
 negotiations in the United States alone do not constitute or
 transform those extraterritorial activities into a sale
 within the United States for purposes of § 271(a).” Id. It
 held that this was so “when substantial activities of a sales
 transaction, including the final formation of a contract for
 sales encompassing all essential terms as well as the deliv-
 ery and performance under that contract, occur entirely
 outside the United States.” Id. This is not a blanket hold-
 ing that design wins arising out of a sales cycle can never
 be domestic transactions. Indeed, the district court noted
 that a design win meeting these criteria, such that “sub-
 stantial activities of a sales transaction . . . occurs entirely
 outside the United States” would not constitute a sale
 within the United States. J. App’x 185. The district court’s
 jury instruction emphasized the key question of whether
 there were such substantial activities in the United States,
 an instruction that Apple and Broadcom do not contest.
 See also Carnegie Mellon U. v. Marvell Tech. Grp., Ltd., 807
 F.3d 1283, 1308 (Fed. Cir. 2015). There is no error in the
 district court’s permissive instruction.
            B. Caltech’s Two-Tier Damage Model
     Caltech presented its damage theory to the jury
 through two experts, Dr. Catherine Lawton and Dr. David
 Teece. They opined that Caltech would have engaged in
 two simultaneous hypothetical negotiations, one with
 Broadcom at the “chip level” and one with Apple at the “de-
 vice level.” Those negotiations would have excluded from
 Broadcom’s hypothetical chip license any Broadcom chips
 incorporated into Apple products sold in the United States
 and treated those identical chips as being subject to Apple’s
 separate hypothetical device license at a vastly different
 royalty rate. Both of Caltech’s experts testified that sepa-
 rate chip-level and device-level negotiations would have
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 28          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 been proper, rather than a single hypothetical negotiation
 for all of the accused chips, because both defendants were
 separate infringers and there would be no “cross-talk” be-
 tween them as they each engaged in their own hypothetical
 negotiation.
     The district court considered the opinions of Caltech’s
 experts and, over Broadcom and Apple’s objection, permit-
 ted Caltech to present that theory to the jury. In doing so,
 the district court observed that “[p]atent owners will some-
 times seek damages from accused infringers at different
 levels in the supply chain, and so long as they do not at-
 tempt to obtain a double recovery to violate other legal
 principles like patent exhaustion, they are free to do so.” J.
 App’x 225. In ruling in Caltech’s favor, the district court
 saw no concern over double recovery because Broadcom
 and Apple were different companies and because the ex-
 perts’ opinions carved out of the Broadcom hypothetical ne-
 gotiation chips sold to Apple. But in the absence of some
 evidence that companies in the positions of Broadcom and
 Apple would engage in such separate negotiations and in
 the absence of additional facts that might justify separate
 and different treatment of the same chips at different lev-
 els of the supply chain, the mere fact that Broadcom and
 Apple are separate infringers alone does not support treat-
 ing the same chips differently at different stages in the sup-
 ply chain and does not justify submitting such a two-tier
 damage theory to the jury. It is generally recognized that
 in the usual case, “a direct infringer or someone who in-
 duced infringement should pay the same reasonable roy-
 alty based on a single hypothetical negotiation analysis.”
 LaserDynamics, Inc. v. Quanta Comput., Inc., 694 F.3d 51,
 76 (Fed. Cir. 2012).
     Caltech argued that separate royalty rates at different
 levels of the supply chain are proper because the reasona-
 ble royalty inquiry focuses on the amount of value that the
 patent technology adds to a product, citing Ericsson, Inc. v.
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED                     29

 D-Link Sys., 773 F.3d 1201, 1226 (Fed. Cir. 2014). The dis-
 trict court concluded that Broadcom and Apple’s products
 were different and therefore possessed different values
 simply because Broadcom and Apple were “different com-
 panies at different levels in the supply chain.” J. App’x 226.
 But to reach that conclusion without more ignores estab-
 lished precedent to the effect that, in the absence of a com-
 pelling showing otherwise, a higher royalty is not available
 for the same device at a different point in the supply chain.
 As we previously held, “a reasonable royalty is not to be
 separately calculated against each successive infringer.
 Once full recovery is obtained from one infringer with re-
 spect to a particular infringing device, at most nominal ad-
 ditional damages may be awarded against another with
 respect to the same device.” Stickle v. Heublein, Inc., 716
 F.2d 1550, 1562 (Fed. Cir. 1983). Moreover, “[a] party is
 precluded from suing to collect damages from direct in-
 fringement by a buyer and user of a product when actual
 damages covering that very use have already been col-
 lected from the maker and seller of that product.” Glenayre
 Elecs., Inc. v. Jackson, 443 F.3d 851, 864 (Fed. Cir. 2006).
     The district court cited but distinguished those cases
 as only applying to damages calculations against two de-
 fendants involving overlapping royalty bases, a situation
 not existing here based on Caltech’s expert’s exclusion of
 chips sold to Apple from the royalty base considered for
 Broadcom. But that exclusion in this case is wholly con-
 trived, lacks any basis of fact and is contrary to the custom-
 ary way patent infringement disputes are ordinarily
 resolved. It is well settled that a reasonable royalty is what
 a willing licensor and a willing licensee would have agreed
 to at a hypothetical negotiation just before infringement
 began. See Carnegie Mellon Univ. v. Marvell Tech. Grp.,
 807 F.3d 1283, 1303-1304 (Fed. Cir. 2015). Here, there is
 nothing in the record to suggest that Broadcom and Apple
 would have been willing to negotiate in this artificial way
 rather than to more conventionally negotiate a single
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 30          THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED

 license at a single rate for the same chips. Neither of Cal-
 tech’s experts offered any factual basis to conclude that
 Broadcom and Apple would have been willing to engage in
 separate negotiations leading to vastly different royalty
 rates for the same chips. The district court’s views to the
 contrary and its limiting of the Stickle and Glenayre cases
 to situations involving double recovery were misplaced and
 erroneous. Caltech’s two-tier damages theory is legally un-
 supportable on this record.
                             ***
     We need not and do not address Broadcom and Apple’s
 indemnification argument, or their argument that the hy-
 pothetical negotiations would have been held not with Cal-
 tech but by its exclusive licensee, Inforon. Nor do we
 address Broadcom and Apple’s argument based on small-
 est-saleable-patent-practicing-unit, or the sufficiency of
 the evidence as to the domestic or extraterritorial charac-
 ter of Broadcom’s sales.

                         CONCLUSION
     For the foregoing reasons, we affirm the district court’s
 construction of the claim limitation “repeat.” We affirm the
 district court’s denial of JMOL on infringement of the as-
 serted claims of the ’710 and ’032 patents. We affirm the
 district court’s conclusion that claim 13 of the ’781 patent
 is patent-eligible but vacate the jury’s verdict of infringe-
 ment thereof and remand for a new trial. We affirm the
 district court’s summary judgment findings of no invalidity
 based on IPR estoppel and no inequitable conduct. We af-
 firm the district court’s jury instructions relating to extra-
 territoriality, but vacate the jury’s damage award and
 remand for a new trial on damages.
      AFFIRMED IN PART, VACATED IN PART, AND
                   REMANDED.
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 THE CALIFORNIA INSTITUTE v. BROADCOM LIMITED               31

                           COSTS
 Each party shall bear its own costs.
Case: 20-2222    Document: 63     Page: 32   Filed: 02/04/2022

    United States Court of Appeals
        for the Federal Circuit
                  ______________________

     CALIFORNIA INSTITUTE OF TECHNOLOGY,
                 Plaintiff-Appellee

                             v.

    BROADCOM LIMITED, NKA BROADCOM INC.,
       BROADCOM CORPORATION, AVAGO
      TECHNOLOGIES LIMITED, NKA AVAGO
   TECHNOLOGIES INTERNATIONAL SALES PTE.
            LIMITED, APPLE INC.,
              Defendants-Appellants
             ______________________

                   2020-2222, 2021-1527
                  ______________________

    Appeals from the United States District Court for the
 Central District of California in No. 2:16-cv-03714-GW-
 AGR, Judge George H. Wu.
                  ______________________

 DYK, Circuit Judge, concurring-in-part and dissenting-in-
 part.
      While I join Discussion sections II.B.1, III, and IV of
 the majority opinion, I respectfully disagree with the ma-
 jority’s holding that substantial evidence supports the
 jury’s verdict of infringement of the asserted claims of the
 ’710 and ’032 patents and would reverse the district court’s
 denial of JMOL of no literal infringement. I would simi-
 larly reverse the denial of JMOL rather than remand for a
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 2              THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED

 new trial with respect to the infringement of the ’781 pa-
 tent.
                               I
     No matter how novel an invention is, it is the patent’s
 claims that “determine what the invention is,” as well as
 the bounds of the patent owner’s rights to that invention’s
 “exclusive use.” Motion Picture Patents Co. v. Universal
 Film Mfg. Co., 243 U.S. 502, 510 (1917). Patent owners are
 limited by the language in the claims, and “can claim noth-
 ing beyond them.” Id. (quoting Keystone Bridge Co. v.
 Phoenix Iron Co., 95 U.S. 274, 278 (1877)). It is the patent
 owner’s burden to show that “the properly construed claim
 reads on the accused device exactly.” CommScope Techs.
 LLC v. Dali Wireless Inc., 10 F.4th 1289, 1295 (Fed. Cir.
 2021) (quoting Engel Indus., Inc. v. Lockformer Co., 96 F.3d
 1398, 1405 (Fed. Cir. 1996)). Denial of JMOL of no literal
 infringement must be reversed when plaintiffs “fail[] to
 present evidence proving that the [accused device] meets
 the district court’s construction of [a] claim term.”
 CommScope, 10 F.4th at 1295. Such a failure occurs when
 expert testimony “points to the result . . . rather than the
 specific mechanism claimed to achieve that result,” id. at
 1297, or when expert testimony is merely “cursory,”
 Alexsam, Inc. v. IDT Corp., 715 F.3d 1336, 1341–42 (Fed.
 Cir. 2013). Here, no showing of literal infringement has
 been made that can support the jury’s infringement verdict
 under the district court’s claim construction, which is not
 challenged by Caltech.
                              II
     Before trial, the district court held a Markman hearing
 to construe the term “repeat,” an essential limitation in all
 of the asserted claims of the three patents. Caltech advo-
 cated for the term’s plain and ordinary meaning. Apple
 and Broadcom proposed a narrower construction, contend-
 ing that “repeat” should be construed as “creating a new bit
 that corresponds to the value of an original bit (i.e., a new
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 THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED                     3

 copy) by storing the new copied bit in memory. A reuse of
 a bit is not a repeat of a bit.” J.A. 9. The district court
 rejected this construction because reusing bits by “selecting
 the bits for use without necessarily storing them at a spe-
 cific location in computer memory” could satisfy the claim
 limitation. J.A. 10. The district court nonetheless noted
 that the “claim language . . . makes clear that ‘repeated
 bits’ are a construct distinct from the original bits from
 which they are created.” Id. Ultimately, the district court
 adopted the term’s plain and ordinary meaning, concluding
 that no further construction was required.
      Following the Markman hearing, the parties continued
 to dispute what exactly the plain and ordinary meaning of
 “repeat” entailed. As a result, at trial, as permitted by
 precedent, 1 the district court revisited and clarified its ear-
 lier claim construction ruling, instructing the jury that the
 ’710 and ’032 patents’ claimed repetition requires the “gen-
 eration of additional bits, where generation can include, for
 example, duplication or reuse of bits.” J.A. 171. The criti-
 cal question, therefore, is whether there is substantial evi-
 dence that the accused devices cause “generation of
 additional bits.” Unfortunately, in denying the appellants’
 post-trial JMOL motion, the district court provided no
 analysis of how Caltech established infringement, relegat-
 ing this question to a footnote which said only that

     1    It is within the district court’s discretion to “engage
 in a rolling claim construction, in which the court revisits
 and alters its interpretation of the claim terms as its un-
 derstanding of the technology evolves.” See, e.g., Jack
 Guttman, Inc. v. Kopykake Enters., 302 F.3d 1352, 1361
 (Fed. Cir. 2002) (citing Sofamor Danek Grp., Inc. v. DePuy–
 Motech, Inc., 74 F.3d 1216, 1221 (Fed. Cir. 1996)); Col-
 legeNet, Inc v. ApplyYourself, Inc., 418 F.3d 1225, 1233–34
 (Fed. Cir. 2005).
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 4              THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED

 “Defendants’ arguments that the verdict was not supported
 by substantial evidence also remain unpersuasive.” J.A.
 206.
     The panel majority does not identify or rely on a reuse
 theory to uphold the jury’s verdict. Rather, the majority
 concludes that infringement of the repeat limitation was
 supported by expert testimony that “the [AND] gate affirm-
 atively enables the information bit to be duplicated as the
 output bit. That is a ‘repeat’ . . . because the information
 bit in that situation ‘flows through’ to appear again in the
 output.” Maj. Op. at 16 (emphasis added). But there is in
 fact no such expert testimony. To the contrary—consistent
 with its claim construction position, Caltech’s expert testi-
 fied that the claims do not “require that the repeat has to
 be done by duplicating information bits,” J.A. 2858, and
 Caltech argued to this court on appeal that “repetition does
 not require duplication,” Appellee’s Br. 18.
     To be sure, Caltech is correct that duplication is not re-
 quired to satisfy the repeat limitation. But the problem for
 Caltech (and for the majority) is that Caltech never estab-
 lished that the accused devices generate “additional bits,”
 as required by the district court’s claim construction. The
 infringement theory presented at trial explained that the
 accused devices work as follows: information bits are input
 into the accused devices, those bits travel down branched
 wires to the inputs of 972 AND gates, and three to twelve
 of those AND gates will be open for each information bit,
 thus outputting the bits a different number of times. For
 this theory to satisfy Caltech’s burden, Caltech was re-
 quired to establish where, when, and how additional bits
 were generated.
     One possibility—presented by Caltech’s counsel—was
 that additional bits were generated by branching at the in-
 puts. During closing arguments, Caltech told the jury
 “That’s how you repeat bits, with a voltage along wires . . .
 how else would you repeat bits? How else would you do it?”
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 THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED                  5

 1/28 Tr. 90:20–91:9. But the record does not support a the-
 ory that the branched wires generate additional bits. Cal-
 tech’s experts testified merely that the bits are “connected
 to” the AND gates by branched wires, without explaining
 whether or how that connection generated additional bits.
 J.A. 2831. Apple and Broadcom presented unrefuted ex-
 pert testimony that the branched wire connection involves
 simultaneously sending the same bit—not an additional
 bit—to the inputs of AND gates. Caltech’s expert did not
 testify to the contrary, and in fact declined to testify that
 branching generates additional bits.
     Q. Branch wire creates repeat bits?
     ...
     THE COURT: I’ll allow him to answer the question
     if he understands it.
     THE WITNESS: That question I did not under-
     stand. I didn’t think it was well formed.
     BY MR. MUELLER: Q. The branch wire in the
     Broadcom chips in your view creates repeat bits
     within the meaning of the claims; correct?
     ...
     THE WITNESS: In my analysis the branch wire is
     being used in conjunction with the tables and these
     and gates to implement irregular repetition.
 J.A. 3019–20. There is no substantial evidence supporting
 an infringement verdict based on branching.
    Caltech’s separate theory to establish that the accused
 devices generate additional bits was the “flow through”
 theory, supported, according to the majority, by expert tes-
 timony that “the information bit ‘flows through’ to the out-
 put gate [when] the parity-check bit is 1,” and that the flow
 through bit constitutes “a repeat, both according to the ex-
 pert’s usage and a plain understanding of the word.” Maj.
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 6              THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED

 Op. at 16–17. The majority identifies record evidence
 where Caltech’s expert summarily testified that the AND
 gates repeated information bits when the gates are ena-
 bled, J.A. 2842; J.A. 3080, and where the expert concluded
 that the AND gates were “generating additional bits at
 their output,” J.A. 4162. This cursory and conclusory tes-
 timony cannot satisfy Caltech’s burden.
     Caltech’s own expert testimony as to how an AND gate
 functions forecloses concluding that the AND gates gener-
 ate additional bits. Throughout trial, Caltech’s expert con-
 sistently testified that an AND gate “act[s] like a switch . . .
 allowing the information bits to flow through . . . or not.”
 J.A. 3016–17; see also J.A. 3031 (“[E]nable one allows the
 AND gate to act like a switch. So enable would close the
 switch and allow the one to come out.”); J.A. 3030 (“[T]he
 AND gate has two inputs. One of them is the enable that
 allows the switch to open or close.”); J.A. 3031 (“Enable zero
 is like the switch not allowing the information bit to flow
 through.”). If an enabled AND gate merely allows the same
 information bit that already exists at the input of an AND
 gate “to come out,” J.A. 3031, or to “flow through,” this does
 not remotely establish how the AND gate output generates
 additional information bits. Under the explanation that
 Caltech repeatedly presented, one information bit comes in
 and one information bit comes out—no additional bit ap-
 pears anywhere. Flow through, with a 1:1 ratio of input
 bits to output bits as described by Caltech’s experts, cannot
 satisfy the generation of additional bits limitation required
 by the district court’s claim construction.
     Caltech’s remaining theory submits that the accused
 devices generate additional bits when the branched wires
 are combined with the AND gates. The majority believes
 that “the physical connection of the first inputs of all 972
 AND gates . . . and the connection of the parity-bit system
 to the other inputs of the AND gates to selectively enable 3
 to 12 of those gates . . . together implement irregular repe-
 tition.” Maj. Op. at 17. Neither the majority’s opinion,
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 THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED                   7

 Caltech’s briefs, and most importantly, Caltech’s experts,
 explain why the combination of these two non-infringing
 components results in infringement. The district court
 therefore erred in denying JMOL of no literal infringe-
 ment.
                              III
     At trial, Caltech also presented a doctrine of equiva-
 lents case to the jury. In a footnote to its JMOL decision,
 the district court found that it was “not necessary” to ana-
 lyze Apple and Broadcom’s challenge to the doctrine of
 equivalents arguments, J.A. 206, and the majority here
 similarly does not address such a theory. There is no basis
 to sustain the verdict on a doctrine of equivalents theory.
     To prevail, Caltech had the burden of proving equiva-
 lence “between the elements of the accused product or pro-
 cess and the claimed elements of the patented invention,”
 Warner-Jenkinson Co. v. Hilton Davis Chem. Co., 520 U.S.
 17, 21 (1997), by showing that “the accused device contains
 an element that is not ‘substantially different’ from any
 claim element that is literally lacking,” Kraft Foods, Inc. v.
 Int’l Trading Co., 203 F.3d 1362, 1371 (Fed. Cir. 2000) (cit-
 ing Warner-Jenkinson, 520 U.S. at 40).
     Caltech’s appellate brief devoted only one and a half
 pages to this issue, citing to eight pages of trial testimony
 in which its expert asserted that the differences between
 the accused chips and the claim limitations were insub-
 stantial. At trial, Dr. Shoemake testified that because the
 claims do not “require repeating with any type of specific
 circuitry,” any differences in the method Broadcom’s chips
 used to accomplish the “overall goal” of the claims were in-
 substantial. J.A. 2856–58.
    But even if no specific circuitry is required, Dr. Shoe-
 make never explained why a bit flowing through to the out-
 put of an AND gate is substantially similar to the claimed
 device that generates additional bits. This is reminiscent
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 8              THE CALIFORNIA INSTITUTE   v. BROADCOM LIMITED

 of the insufficient, “[g]eneralized testimony” proscribed by
 Texas Instruments Inc. v. Cypress Semiconductor Corp., 90
 F.3d 1558, 1567 (Fed. Cir. 1996), and it cannot satisfy Cal-
 tech’s burden to provide “particularized testimony and
 linking argument as to the ‘insubstantiality of the differ-
 ences’ between the claimed invention and the accused de-
 vice or process . . . on a limitation-by-limitation basis,” id.
 There was no basis for the jury to find infringement under
 the doctrine of equivalents.
    I would reverse the district court’s denial of JMOL and
 enter judgment of non-infringement for Broadcom and Ap-
 ple.