  United States Court of Appeals
      for the Federal Circuit
                ______________________

                    WI-LAN, INC.,
                   Plaintiff-Appellant

                           v.

                    APPLE INC.,
               Defendant-Cross Appellant
                ______________________

                 2014-1437, -2014-1485
                ______________________

    Appeals from the United States District Court for the
Eastern District of Texas in Nos. 2:11-cv-00068-JRG,
2:12-cv-00600-JRG, Judge J. Rodney Gilstrap.
                ______________________

               Decided: January 8, 2016
                ______________________

   ROBERT A. COTE, McKool Smith, P.C., New York, NY,
argued for plaintiff-appellant. Also represented by
SAMUEL FRANKLIN BAXTER, Marshall, TX; JASON
BLACKSTONE, RICHTER DARRYL BURKE, SETH R.
HASENOUR, ROSEMARY T. SNIDER, Dallas, TX; DIRK D.
THOMAS, Washington, DC.

    MARK S. DAVIES, Orrick, Herrington & Sutcliffe LLP,
Washington, DC, argued for defendant-cross-appellant.
Also represented by KATHERINE M. KOPP, T. VANN
PEARCE, JR.; BRIAN PHILIP GOLDMAN, San Francisco, CA;
WILL MELEHANI, Irvine, CA; SIDDHARTHA M. VENKATESAN,
2                                   WI-LAN, INC.   v. APPLE INC.



Menlo Park, CA; ANDREW D. SILVERMAN, New York, NY;
ASHLEE N. LIN, MIGUEL JESUS RUIZ, MARK C. SCARSI,
Milbank, Tweed, Hadley & McCloy, LLP, Los Angeles,
CA.
               ______________________

    Before REYNA, WALLACH, and HUGHES, Circuit Judges.
REYNA, Circuit Judge.
    Wi-LAN, Inc. (“Wi-LAN”) is the assignee of U.S. Pa-
tent No. RE37,802 (“’802 patent”), which concerns a
wireless data communication technique called “Multi-
Code Direct-Sequence Spread Spectrum” (MC-DSSS). Wi-
LAN asserts that the patented technique is embodied in
several modern wireless communications standards.
    On February 2, 2011, Wi-LAN sued Apple Inc. (“Ap-
ple”) and other technology companies in the United States
District Court for the Eastern District of Texas for in-
fringing claims 1 and 10 of the ’802 patent by manufactur-
ing and selling products complying with various wide-
area communication standards. A jury found that Apple
did not infringe and that the claims are invalid. The
district court denied Wi-LAN’s motion for judgment as a
matter of law (“JMOL”) and for a new trial with respect to
infringement, but it granted Wi-LAN’s motion for JMOL
of no invalidity.
    Wi-LAN appeals the trial court’s denial of JMOL and
its motion for a new trial on infringement, and Apple
cross-appeals the grant of JMOL of no invalidity. Because
the jury’s verdict of non-infringement was supported by
substantial evidence, we affirm the district court’s denial
of JMOL as to non-infringement. Because the trial court’s
JMOL determination of no invalidity was based on a post-
verdict reconstruction of the claims, we reverse the district
court’s grant of JMOL of no invalidity.
WI-LAN, INC.   v. APPLE INC.                            3



                         I. BACKGROUND
                  A. The Patented Technology
    Wireless communication devices use radio waves to
communicate digital data by modulating the frequency,
amplitude, or phase of those waves according to pre-
established patterns.    Each pattern communicates a
respective “symbol” corresponding to a given combination
of bits. J.A. 3546. Devices that detect the radio waves
can observe and interpret the modulation patterns to
recover the transmitted symbols.
    “Direct-Sequence Spread Spectrum” (DSSS) is a prior
art modulation technique that prevents third parties from
intercepting and interpreting radio communications.
Using DSSS, a radio transmitter “spreads” a signal across
a band of frequencies by multiplying the signal against a
pseudo-random signal called “pseudo-noise.” The pseudo-
noise signal corresponds to a particular code, such that a
receiver with a corresponding code can “invert” (i.e.,
reverse) the spreading to recover the original signal. A
third party scanning the spectrum would detect only what
appears to be natural ambient noise, while the intended
recipient could use the corresponding code to detect and
decode the communication. A drawback of DSSS is that
each communication occupies an entire band of frequency,
which makes it difficult for multiple users to transmit
data simultaneously.
    “Code Division Multiple Access” (CDMA) is another
prior art modulation technique that addresses the band-
width shortcomings of DSSS by allowing multiple users to
transmit on the same band using different spreading
codes. Under CDMA, the signals from the multiple users
form a combined noise-like signal, and each receiver can
use its respective code to recover the communications
intended for it from the combined signal.
4                                 WI-LAN, INC.   v. APPLE INC.



    The ’802 patent discloses a “multi-code” variation of
DSSS (MC-DSSS), which enhances throughput by permit-
ting a single transmitter to utilize multiple codes simul-
taneously. ’802 patent col. 1 l. 66 – col. 2 l. 5. The
specification describes two embodiments, corresponding to
Figures 1 and 4 respectively.




The embodiment of Figure 1 includes: (1) a converter 10
for converting a stream of data symbols into multiple sets
WI-LAN, INC.   v. APPLE INC.                              5



of N data symbols each, (2) a computing means 12 that
operates on the sets of data symbols to produce “modulat-
ed data symbols corresponding to an invertible random-
ized spreading of the stream of data symbols” and (3) a
combiner 14 for combining the modulated data symbols
for transmission. Id. Fig. 1, col. 4 ll. 1–7. The computing
means modulates each data symbol using a respective
DSSS code, which may be derived using a series of math-
ematical transforms, as shown in Figure 3. Id. col. 4 ll. 7–
12, col. 4 ll. 29–34. The patent lists a dozen exemplary
mathematical transforms, including the complex “ran-
domizer transform” of Figure 8. Id. col. 4 l. 66 – col. 5 l.
12. In the alternative embodiment of Figure 4, the com-
puting means modulates the N data symbols by applying
the transforms directly to the N data symbols rather than
indirectly via the DSSS codes. Id. col. 4 ll. 38–43.
    Asserted claim 1 recites a transceiver for transmitting
data using three components:
      1. A transceiver for transmitting a first stream
         of data symbols, the transceiver comprising:
      a converter for converting the first stream of
         data symbols into plural sets of N data sym-
         bols each;
      first computing means for operating on the plu-
          ral sets of N data symbols to produce modu-
          lated data symbols corresponding to an
          invertible randomized spreading of the first
          stream of data symbols; and
      means to combine the modulated data symbols
        for transmission.
The claimed transceiver includes a “converter” for con-
verting a stream of data symbols into multiple sets of data
symbols, where each set includes N symbols. Second, the
transceiver includes a “computing means” for operating
on the sets to produce “modulated data symbols corre-
6                                   WI-LAN, INC.   v. APPLE INC.



sponding to an invertible randomized spreading” of the
original data symbols. Finally, the transceiver includes a
“means to combine the modulated data symbols for
transmission.” Asserted claim 10, which depends on
claim 1, adds means for receiving and decoding the data
symbols.
                  B. Procedural History
     The district court held a Markman hearing and issued
two claim constructions relevant to this appeal. J.A. 18.
First, the district court construed “modulated data sym-
bols” to mean “data symbols that have been spread by a
spreading code.” J.A. 62. In doing so, the court rejected
Apple’s argument that the modulated data symbols must
be randomized, explaining that “randomization is a
desirable feature that is addressed by other claim lan-
guage, such as the term ‘invertible randomized spread-
ing,’ which appears in Claim 1 . . . .” Id. Second, the
district court adopted the parties’ agreed construction of
“first computing means.” The parties agreed that the
limitation is a means-plus-function element subject to 35
U.S.C. § 112 ¶6, and that the corresponding structure is
“element 12 of Figures 1 and 4, columns 2:6–10, 2:36–40,
2:58–62, 4:2–12, and 4:35–44, and equivalents thereof.”
J.A. 73. The agreed upon construction matched the
construction of the same term issued by a different court
in previous litigation between the parties. WI-LAN, Inc.
v. Acer, Inc., No. 2:07-CV-473-TJW, Dkt. No. 469 (E.D.
Tex. May 11, 2010) (“Acer”). In that case, the court had
rejected Wi-LAN’s proposal to construe the “first compu-
ting means” as additionally encompassing the exemplary
transforms disclosed at col. 4 l. 66 – col. 5 l. 12, including
the complex randomizer of Figure 8, because the trans-
forms related to how the pseudo-noise is generated rather
than to any structure in the computing means. J.A. 1362,
1364. Wi-LAN agreed to the Acer construction of the
“first computing means” in this case and did not seek a
WI-LAN, INC.   v. APPLE INC.                             7



construction that explicitly included the additional struc-
ture.
    At trial, Apple argued that it did not infringe because
claim 1 requires randomizing the data symbols before
combining them, and that Apple’s products perform these
steps in the reverse order (the “ordering requirement”).
Claim 1 recites that the computing means must “produce
modulated data symbols corresponding to an invertible
randomized spreading” and that the converter must
“combine the modulated data symbols.” Apple argued
that because “the modulated data symbols” refers back to
the earlier-recited “modulated data symbols correspond-
ing to an invertible randomized spreading,” the data
symbols to be combined must have already been random-
ized. J.A. 13. The parties agreed that Apple’s products
randomize the data symbols only after combining them.
    Apple also argued that claims 1 and 10 are invalid be-
cause several prior art publications, including a 1989
paper by Sasaki, 1 anticipated the asserted claims. J.A.
10,334. The parties agreed that the prior art references
taught randomizing the modulated data symbols using
real multipliers (i.e., using a “real randomizer”) rather
than using complex multipliers (i.e., using a “complex
randomizer”). 2 J.A. 1059 at 194:21–25; J.A. 1058 at
190:21–191:4. Apple’s invalidity arguments consequently
rested on the proposition that “the Court’s claim construc-



    1   Shingenobu Sasaki & Gen Marubayashi, A Study
on the Code of Sequence for Parallel Spread-Spectrum
Data Transmission, Inst. of Electronics, Info., and
Commc’n. Engineers (IEICE) Technical Report, Vol. 89,
no. 265 (Oct. 1989).
    2   Complex multipliers are hardware structures that
can multiply complex numbers, whereas real multipliers
can multiply only real numbers.
8                                 WI-LAN, INC.   v. APPLE INC.



tion told us what the first computing means is, and it
didn’t say complex randomizer.” J.A. 1059 at 195:5–11.
    The jury found claims 1 and 10 of the ’802 patent in-
valid and not infringed. J.A. 362, 364. Wi-LAN moved for
JMOL on both issues, and for a new trial on non-
infringement. J.A. 1197. Wi-LAN argued that the court’s
claim constructions precluded the ordering requirement
underlying Apple’s non-infringement defense. J.A. 11-15.
Wi-LAN also argued that the prior art did not anticipate
the asserted claims because the prior art did not random-
ize using complex multipliers, which Wi-LAN argued the
asserted claims require. J.A. 5.
    The district court upheld the jury’s finding of non-
infringement, and reversed on invalidity. J.A. 16. Re-
garding non-infringement, the district court held that the
ordering requirement was consistent with the court’s
claim constructions and that a reasonable jury could have
found non-infringement under those constructions. J.A.
14. Regarding invalidity, the district court determined
that, although its construction of computing means “does
not specifically provide for a complex multiplier,” a com-
plex multiplier was nevertheless necessary because
“expert witnesses from both sides agreed that complex
multipliers are part of the structure of the ‘first compu-
ting means’ as taught by the ’802 patent.” J.A. 9–10. It
was undisputed that such multipliers were absent from
the prior art.
    Wi-LAN appeals the denial of JMOL on non-
infringement. Apple cross-appeals the grant of JMOL on
no invalidity.
                II. STANDARDS OF REVIEW
   In reviewing a district court’s rulings on motions for
JMOL or for a new trial, we apply regional circuit law.
Seachange Int’l, Inc. v. C-COR, Inc., 413 F.3d 1361, 1367–
WI-LAN, INC.   v. APPLE INC.                              9



68 (Fed. Cir. 2005). The district court here sits in the
Fifth Circuit.
    The Fifth Circuit “reviews a motion for judgment as a
matter of law de novo, applying the same legal standard
as did the trial court.” Ford v. Cimarron Ins. Co., 230 F.3d
828, 830 (5th Cir. 2000) (internal citations omitted). The
Fifth Circuit “grants great deference to a jury’s verdict
and will reverse only if, when viewing the evidence in the
light most favorable to the verdict, the evidence points so
strongly and overwhelmingly in favor of one party that
the court believes that reasonable jurors could not arrive
at any contrary conclusion.” Dresser-Rand Co. v. Virtual
Automation Inc., 361 F.3d 831, 838 (5th Cir. 2004). The
Fifth Circuit “review[s] the district court's decision on a
motion for a new trial for an abuse of discretion.” Holly-
brook Cottonseed Processing, L.L.C. v. Am. Guarantee &
Liab. Ins. Co., 772 F.3d 1031, 1034 (5th Cir. 2014). “The
standard for the district court to grant a new trial is
whether the verdict is against the great weight of the
evidence.” Whitehead v. Food Max of Miss., Inc., 163 F.3d
265, 270 (5th Cir. 1998).
     Anticipation and infringement (both literal and under
the doctrine of equivalents) are questions of fact, which
we review for substantial evidence when tried to a jury.
TI Grp. Auto. Sys. (N. Am.), Inc. v. VDO N. Am., L.L.C.,
375 F.3d 1126, 1133 (Fed. Cir. 2004). Claim construction
is a legal issue that may be based on underlying findings
of fact. Teva Pharm. USA, Inc. v. Sandoz, Inc., 135 S. Ct.
831, 841 (2015). We therefore review a court’s construc-
tions de novo and any underlying factual findings based
on extrinsic evidence for clear error. Id.

                         III. DISCUSSION
                     A. Non-Infringement
    On appeal, Wi-LAN challenges the district court’s de-
nial of JMOL on non-infringement on the grounds that
10                                  WI-LAN, INC.   v. APPLE INC.



the district court’s claim constructions precluded the
ordering    requirement      underlying     Apple’s    non-
infringement defense. Wi-LAN argues that the district
court expressly rejected the ordering requirement at claim
construction when it refused to construe “modulated data
symbols” as necessarily randomized. J.A. 62. Wi-LAN
argues that, even with the ordering requirement, Apple’s
products would still infringe under the doctrine of equiva-
lents because it is undisputed that the different orderings
produce mathematically identical results.
    Claim construction begins with the words of the
claim, which “must be read in view of the specification, of
which they are a part.” Phillips v. AWH Corp., 415 F.3d
1303, 1312–15 (Fed. Cir. 2005) (en banc); Vitronics Corp.
v. Conceptronic, Inc., 90 F.3d 1576, 1582 (Fed. Cir. 1996).
Although courts are permitted to consider extrinsic evi-
dence, like expert testimony, such evidence is generally of
less significance than the intrinsic record. Phillips, 415
F.3d at 1317 (citing C.R. Bard, Inc. v. U.S. Surgical Corp.,
388 F.3d 858, 862 (Fed. Cir. 2004)). Extrinsic evidence
may not be used “to contradict claim meaning that is
unambiguous in light of the intrinsic evidence.” Id. at
1324.

    The text of the asserted claims requires randomizing
the modulated data symbols before combining them.
Claim 1 recites a computing means that “produce[s]
modulated data symbols corresponding to an invertible
randomized spreading” and a means to combine that
“combine[s] the modulated data symbols.” Subsequent
use of the definite articles “the” or “said” in a claim refers
back to the same term recited earlier in the claim. Bald-
win Graphic Sys., Inc. v. Siebert, Inc., 512 F.3d 1338, 1342
(Fed. Cir. 2008). The term “the modulated data symbols”
therefore refers back to the randomized data symbols
produced by the computing means in the second claim
element. Because the modulated data symbols in the
second element are randomized upon being produced,
WI-LAN, INC.   v. APPLE INC.                            11



those same modulated data symbols in the third element
have already been randomized before they are combined.
The text of the claim thus requires producing randomized
symbols and then combining those randomized symbols.
    The ordering requirement described above is con-
sistent with the specification. Every embodiment dis-
cussed in the specification randomizes the data symbols
before combining them. For instance, Figures 1 and 4
both show combining as the final step, after computing
means 12 operates on (i.e., spreads and randomizes) the
data symbols. No disclosure in the specification depicts or
discusses the possibility of combining before randomizing.
The intrinsic record is therefore clear that the asserted
claims cover only structure that randomizes data symbols
in parallel before combining them for transmission.
    Contrary to Wi-LAN’s argument, the district court did
not explicitly reject the ordering requirement at claim
construction. The district court rejected only Apple’s
argument that the unmodified term “modulated data
symbols” must necessarily refer to randomized data
symbols. J.A. 59–62. The district court did so only be-
cause the randomization requirement “is addressed by
other claim language, such as the term ‘invertible ran-
domized spreading.’” J.A. 59–62. Even though generic
“modulated data symbols” do not have to be randomized,
the recited “modulated data symbols corresponding to an
invertible randomized spreading” do have be randomized.
Because “the modulated data symbols” refers back to
these already-randomized symbols, the claims impose the
disputed ordering requirement. As the district court
reiterated in its JMOL order, nothing in its construction
precludes the ordering requirement. J.A. 14.
    Wi-LAN also argues that the ordering requirement is
inconsistent with dependent claim 4, which Wi-LAN
contends places the “means to combine” between the
12                                WI-LAN, INC.   v. APPLE INC.



spreading and the randomizing steps.        We disagree.
Claim 4 recites:
      4. The transceiver of claim 1 in which the first
         computing means comprises:
      a transformer for operating on each set of data
         symbols to generate modulated data sym-
         bols as output, the modulated data symbols
         corresponding to spreading of each data
         symbol over a separate code selected from a
         set of more than one and up to M codes,
         where M is the number of chips per code;
         and
      means to combine the modulated data symbols
        for transmission.
Claim 4 thus recites that the first computing means
includes both a transformer for spreading the symbols
and a means to combine the symbols. This configuration
does not preclude the recited transformer, or any other
component of the first computing means, from also ran-
domizing the data symbols before they are combined.
Claim 4 is therefore consistent with an interpretation of
claim 1 that requires a structure that randomizes the
symbols before combining them.
    In summary, the intrinsic record requires that the
symbols be modulated according to an invertible random-
ized spreading before being combined for transmission.
Because Apple’s products do not randomize the symbols
before combining them, the structure of those products is
not identical to the disclosed structure, and Apple there-
fore does not infringe the asserted claims.
    Wi-LAN argues that even if claim 1 requires a struc-
ture that randomizes before combining, structure that
performs these steps in the reverse order nevertheless
infringes under the doctrine of equivalents because the
WI-LAN, INC.   v. APPLE INC.                              13



resulting output of the two orderings is mathematically
identical.
    We have recognized that the doctrine of equivalents
may be applied to a means-plus-function limitation to
afford that limitation a somewhat broader scope of equiv-
alents than it would otherwise receive under § 112 ¶6.
Ring & Pinion Serv. Inc. v. ARB Corp., 743 F.3d 831, 835
(Fed. Cir. 2014). Because the record contains no indica-
tion that the doctrine of equivalents is inapplicable here
and because Apple has not so argued, we analyze in-
fringement under that doctrine.
     Infringement under the doctrine of equivalents re-
quires the patentee to prove that the accused device
contains an equivalent for each limitation not literally
satisfied. Catalina Mktg., 289 F.3d at 812. An element in
the accused product is equivalent to a claimed element if
the differences between the two elements are “insubstan-
tial” to one of ordinary skill in the art. Warner–Jenkinson
Co. v. Hilton Davis Chem. Co., 520 U.S. 17, 40 (1997).
    Substantial evidence supports the jury’s verdict that
the order difference between Apple’s products and the
claimed invention is not insubstantial. 3 Apple’s expert,
Dr. Acampora, testified that the processor in Apple’s
products is “not equivalent structure” to the recited
“computing means.” J.A. 1052 at 167:6–7. He explained
that the two structures are “fundamentally different
because the order [of randomizing and combining] is
wrong.” J.A. 1054 at 174:20–22. Dr. Acampora elaborat-



    3   Though the verdict form did not include a sepa-
rate question specific to the doctrine of equivalents, J.A.
361, the district court instructed the jury on that doctrine,
J.A. 384–387, and the verdict is therefore one of no in-
fringement, either literally or under the doctrine of equiv-
alents.
14                                  WI-LAN, INC.   v. APPLE INC.



ed that even though the different orderings produce
mathematically equivalent results, they require structur-
ally different hardware pipelines to implement:
     [T]he order in which these multiplications are
     done, the spreading and the randomization, does
     matter, because it – it affects the number of – the
     number of multipliers, the number of transistors
     that are needed on the circuitry. In one case, you
     need a lot more circuitry than you need in the sec-
     ond case. So that order really does matter. This is
     a design consideration. And the number of – the
     amount of circuitry that is needed is important,
     because these circuits, first of all, will take up
     space on the silicon, on the chip itself, and the
     more complicated and larger that chip becomes, in
     general, the more power-hungry it becomes. And
     in the cellular field, actually two things are very
     precious: Bandwidth spectrum and battery. So
     anything you do to reduce the power drain is use-
     ful, even if it’s only a little bit.
J.A. 1034 at 93:22–94:13.
    Wi-LAN counters that the structural differences Dr.
Acampora described were insubstantial, and it points to
Dr. Acampora’s testimony that in a configuration such as
that found in Apple’s products, changing the order of
operations would save as few as twenty transistors out of
the millions found on the chip. J.A. 1053–54. Wi-LAN
argues that such a slight modification is insubstantial
and therefore cannot support a finding of non-
equivalence.
    Though Wi-LAN’s argument has merit, we find it in-
sufficient to disturb the jury’s verdict on substantial
evidence review. On cross-examination Dr. Acampora
testified that one should not consider the magnitude of
structural differences with respect to the entire chip, but
only with respect to the portion of the chip used to per-
WI-LAN, INC.   v. APPLE INC.                              15



form the relevant functionality. J.A. 1054 at 173:10–14.
He testified that because that portion of the chip contains
only a few hundred transistors, a savings of “20 out of a
few hundred transistors” is “a big deal in wireless com-
munications.” Id. Moreover, Dr. Acampora testified that,
as parallelism increases, the differences in hardware
requirements between the two designs could be orders of
magnitude greater than the twenty transistors discussed
in his cross-examination. J.A. 1033–34 at 91:19–93:11. It
was therefore reasonable for the jury to credit Dr.
Acampora’s testimony and to conclude that a person of
ordinary skill would have found the design differences not
insubstantial.
     For the foregoing reasons, the jury’s verdict is neither
unreasonable nor against the great weight of the evi-
dence. The district court’s denial of JMOL respecting
non-infringement was therefore proper and its denial of a
new trial on the issue was not an abuse of discretion. We
affirm the district court’s denials of both motions.
                          B. Invalidity
    The district court vacated the jury’s verdict of invalid-
ity because a reasonable jury should have understood that
the first computing means must randomize the symbols
using complex multipliers while the prior art used only
real multipliers. J.A. 5. While acknowledging that its
construction “does not specifically provide for a complex
multiplier,” the district court nevertheless found such a
component required because “throughout the trial, both
sides took the position that the complex multiplier found
in Figure 8 was necessarily included in the Court’s con-
struction.” J.A. 8–9.
    On appeal, Apple argues that the district court’s post-
verdict addition of a complex multiplier requirement was
a new claim construction, which the district court may not
issue at the JMOL stage. We agree.
16                                  WI-LAN, INC.   v. APPLE INC.



    “[I]t is too late at the JMOL stage to argue for or
adopt a new and more detailed interpretation of the claim
language and test the jury verdict by that new and more
detailed interpretation.” Hewlett-Packard Co. v. Mustek
Sys., Inc., 340 F.3d 1314, 1321 (Fed. Cir. 2003). At the
JMOL stage, the question for the trial court is limited to
whether substantial evidence supports the jury’s verdict
under the issued construction. Id.
     Here, the jury was instructed that the “first compu-
ting means” is the structure corresponding to “elements
12 of Figures 1 and 4, columns 2:6–10, 2:36–40, 2:58–62,
4:2–12, 4:35–44, and equivalents thereof.” J.A. 73. As the
district court acknowledged, this construction “does not
specifically provide for a complex multiplier.” J.A. 9. In
fact, nothing in the cited portions of the specification
refers to Figure 8 or even mentions complex multipliers.
J.A. 7. Instead, the portion of the specification dealing
with Figure 8 and the other exemplary transforms (i.e.,
col. 4 l. 66 – col. 5 l. 12) is absent from the construction.
This absence is particularly conspicuous given that in
Acer, Wi-LAN had sought and failed to obtain a construc-
tion that included the omitted material, and that it sub-
sequently consented to the omission in this case. When
tested by the construction the court provided, it was
reasonable for the jury to conclude that the “first compu-
ting means” need not include the complex multiplier of
Figure 8.
    Wi-LAN argues that the trial court’s JMOL order was
based, not on an impermissible reconstruction, but on a
permissible clarification of the existing construction. Wi-
LAN echoes the district court’s conclusion that expert
testimony from both sides established that the complex
multiplier of Figure 8 was implicit within the construc-
tion. Wi-LAN notes that Apple’s expert, Dr. Acampora,
agreed that “the randomizer transform in Figure 8 is part
of the transforms that are in Figure 4 and Figure 1 of the
patent.” Therefore, Wi-LAN argues, the district court’s
WI-LAN, INC.   v. APPLE INC.                             17



clarification at JMOL only made explicit what was al-
ready implicit in the original construction.
    We have recognized that a trial court may “adjust
constructions post-trial if the court merely elaborates on a
meaning inherent in the previous construction.” Mfor-
mation Techs., Inc. v. Research in Motion Ltd., 764 F.3d
1392, 1397 (Fed. Cir. 2014). For example, in Cordis Corp.
v. Boston Scientific, the district court construed the term
“undulating” to mean “rising and falling in waves,” but
clarified in granting JMOL that the plural “waves” could
not be met by a single “U” shape. 658 F.3d 1347, 1355–57
(Fed. Cir. 2011) (emphasis added). We held that clarifica-
tion permissible because it only “made plain . . . what
should have been obvious to the jury.” Id. at 1356.
     This is not a case, however, where the inclusion of an
implicit component should have been obvious to the jury.
Contrary to the district court’s characterizations of the
expert testimony, the parties clearly did not agree that
the claims required complex randomization. Dr. Acampo-
ra made clear that “the Court’s claim construction told us
what the first computing means is, and it didn’t say
complex randomizer.”       J.A. 1059 at 195:9–11.       Dr.
Acampora’s entire invalidity theory rested on the premise
that the claims do not require complex randomization. He
testified that, “Sasaki does not show complex randomiz-
ing, just randomizing.” J.A. 1059 at 196:4–5; see also J.A.
1059 at 194:21–25 (“[Sasaki] does not use a complex
randomizer.”); J.A. 1058 at 190:21–191:4. Despite the
absence of the complex randomizer, Dr. Acampora testi-
fied repeatedly that the Sasaki reference discloses the
first computing means because it discloses invertible
randomized spreading using real randomizers. J.A. 1037
at 106:19–21; J.A. 1037 at 107:10–12; J.A. 1038 at 111:11-
13. The district court’s characterization of Dr. Acampo-
ra’s testimony as requiring a complex randomizer is
clearly at odds with that witness’s testimony. And even
had Dr. Acampora opined that the invention’s computing
18                                 WI-LAN, INC.   v. APPLE INC.



means required a complex multiplier, the jury was in-
structed that it was “not required to accept that opinion,”
and that “it is solely up to you to decide whether to rely
upon that opinion or not.” J.A. 373. Dr. Acampora’s
testimony did not require a reasonable jury to conclude
that a complex multiplier was necessary.
    In sum, the district court’s JMOL of no invalidity was
based on a reconstruction of the claims that went far
beyond clarifying a meaning inherent in the construction
or making plain what should have been obvious to the
jury. Instead, the post-verdict reconstruction altered the
scope of the original construction and undermined Apple’s
invalidity case post-verdict.
    The only other argument Wi-LAN raised at JMOL re-
specting invalidity was that Apple’s expert had failed to
perform a structural comparison of the claimed structure
and the prior art. J.A. 5, 1197. The district court rejected
that argument, and Wi-LAN has not appealed that rejec-
tion. J.A. 7. Because the complex multiplier requirement
was the only other basis on which the district court could
have vacated the jury’s invalidity verdict, and because we
reject that basis here, we reverse.
                     IV. CONCLUSION
    For the reasons stated above, we affirm the district
court’s denial of JMOL and of a new trial with respect to
non-infringement, and we reverse the district court’s
grant of JMOL of no invalidity.
 AFFIRMED-IN-PART AND REVERSED-IN-PART
                          COSTS
     No costs.
