   United States Court of Appeals
       for the Federal Circuit
                      ______________________

                    IN RE: SAMIR VARMA,
                            Appellant
                     ______________________

                            2015-1502
                      ______________________

    Appeal from the United States Patent and Trademark
Office, Patent Trial and Appeal Board in No. 90/012,366.
        -------------------------------------------------------------------

                         INVESTPIC LLC,
                            Appellant

                                    v.

       INTERNATIONAL BUSINESS MACHINES
        CORPORATION, SAS INSTITUTE INC.,
                     Appellees
              ______________________

                            2015-1667
                      ______________________

    Appeal from the United States Patent and Trademark
Office, Patent Trial and Appeal Board in No. 95/001,939.
                  ______________________

                     Decided: March 10, 2016
                     ______________________
2                                             IN RE: VARMA




   JAY P. KESAN, DiMuroGinsberg PC, McLean, VA,
argued for appellants. Also represented by CECIL E. KEY,
DGKeyIP Group, Tysons Corner, VA; TERESA MARIE
SUMMERS, DiMuroGinsberg PC – DGKeyIP Group, Tysons
Corner, VA.

    FARHEENA YASMEEN RASHEED, Office of the Solicitor,
United States Patent and Trademark Office, Alexandria,
VA, argued for appellee Michelle K. Lee in 2015-1502.
Also represented by ROBERT MCBRIDE, THOMAS W.
KRAUSE.

    JOHN MARLOTT, Jones Day, Chicago, IL, argued for
both appellees in 2015-1667. SAS Institute Inc. also
represented by DAVID B. COCHRAN, Cleveland, OH.

    KENNETH R. ADAMO, Kirkland & Ellis LLP, Chicago,
IL, for appellee International Business Machines. Also
represented by BRENT P. RAY; ARCHIT P. SHAH, Palo Alto,
CA.
                 ______________________

    Before WALLACH, CLEVENGER, and TARANTO, Circuit
                       Judges.
TARANTO, Circuit Judge.
    These two appeals involve U.S. Patent No. 6,349,291,
which names Samir Varma as the inventor and is owned
by InvestPic LLC (collectively, Varma). The patent
describes and claims methods and systems for performing
statistical analyses of investment data. The Patent Trial
and Appeal Board of the Patent and Trademark Office
cancelled certain claims of the ’291 patent in two related
reexamination proceedings—one initiated by Internation-
al Business Machines Corp. and SAS Institute Inc., the
other by SAS alone. IBM v. InvestPic LLC, No. 2015-
1450, 2015 WL 1456097, at *6 (PTAB Mar. 27, 2015); Ex
parte Varma, No. 2014-7760, 2014 WL 7186800, at *7
IN RE: VARMA                                                 3



(PTAB Dec. 16, 2014). Varma’s appeals center on two
claim phrases: (1) a “bias parameter” that “determines a
degree of randomness in sample selection in a resampling
process”; and (2) “a statistical analysis request corre-
sponding to two or more selected investments.” We agree
with Varma that the Board erred regarding both claim
phrases. Correcting the first error, we reverse the cancel-
lation of claims 1–5, 8–16, 19–21, and 24. Correcting the
second error, we vacate the cancellation of claims 22, 23,
25, and 29–31 and remand for further proceedings on
those claims.
                        BACKGROUND
                              A
     The ’291 patent states that many “conventional finan-
cial information sites” on the World Wide Web furnish
information derived from “rudimentary statistical func-
tions [that] are not useful to investors in forecasting the
behavior of financial markets because they rely upon
assumptions that the underlying probability distribution
function (‘PDF’) for the financial data follows a normal or
Gaussian distribution, which is generally false.” ’291
patent, col. 1, lines 24–37. It adds that “the PDF for
financial market data is heavy tailed (i.e., the histograms
of financial market data typically involve many outliers
containing important information)” and that “statistical
measures such as the standard deviation provide no
meaningful insight into the distribution of financial data.”
Id., col. 1, lines 41–47. Conventional “analyses under-
state the true risk and overstate potential rewards for an
investment or trading strategy.” Id., col. 1, line 53–54.
    After those descriptions of deficiencies of conventional
methods, the ’291 patent’s Summary of the Invention
states that “[t]he present invention utilizes resampled
statistical methods for the analysis of financial data,”
which does not necessarily follow a normal probability
distribution. Id., col. 1, line 65, through col. 2, line 3. One
4                                                IN RE: VARMA




particular resampling method described in the ’291 patent
is the bootstrap method, which estimates the distribution
of data in a pool (sample space) by repeated sampling
from the pool. Id., col. 10, lines 20–38. In a bootstrap
analysis, one way to define a sample space, id., col. 11,
lines 16–17, is by identifying a specific investment or
particular time period, id., col. 12, lines 62–66. The
“bootstrap” samples of data are then drawn “with re-
placement”: samples are repeatedly drawn from that
sample space, and after each drawing, the drawn data
returns to the pool for the drawing of the next sample.
Id., col. 10, lines 60–62; id., col. 11, lines 18–20. Although
samples may be drawn at random, id., col. 10, lines 60–
62, the ’291 patent also describes using a “ ‘bias’ parame-
ter” that “specifies the degree of randomness in the
resampling process,” id., col. 11, lines 55–58. See id., col.
15, lines 52–62; id., col. 16, lines 9–21. The ’291 patent
states that, “[i]n order to perform a resampled statistical
analysis, a query is received from a client,” who “may
specify a number of parameters including an investment
or investments (e.g., a portfolio) to be analyzed, a financial
function, a sample size, a period, a type of plot and a bias
parameter, which controls the randomness of the
resampling process.” Id., col. 2, lines 50–56 (emphasis
added).
    Claim 1, amended during reexamination, is repre-
sentative, for present purposes, of the claims that include
the “bias parameter” limitation:
       1. A method for calculating, analyzing and dis-
    playing investment data comprising the steps of:
      (a) selecting a sample space, wherein the sam-
        ple space includes at least one investment da-
        ta sample;
      (b) generating a distribution function using a
        re-sampled statistical method and a bias pa-
        rameter, wherein the bias parameter deter-
IN RE: VARMA                                               5



        mines a degree of randomness in sample se-
        lection in a resampling process; and,
      (c) generating a plot of the distribution func-
        tion.
InvestPic J.A. 735 (amendment underlined).
    Claim 22, also amended during reexamination, in-
volves a request concerning two or more investments:
      22. A system for providing statistical analysis
   of investment information over an information
   network comprising:
      a financial data database for storing invest-
       ment data;
      a client database;
      a plurality of processors collectively arranged to
        perform a parallel processing computation,
        wherein the plurality of processors is adapted
        to:
        receive a statistical analysis request corre-
          sponding to [a] two or more selected invest-
          ments;
        based upon investment data pertaining to the
         two or more selected investments, perform a
         resampled statistical analysis to generate a
         resampled distribution; and,
        provide a report of the resampled distribu-
         tion.
Varma J.A. 331 (amended version: additions underlined;
bracketed word deleted).
    Claim 29, also amended during reexamination, is an-
other claim involving two or more investments:
6                                               IN RE: VARMA




       29. A system for providing statistical analysis
    of investment information over an information
    network comprising:
        a financial data database for storing invest-
         ment data pertaining to two or more invest-
         ments;
        a front end subsystem for receiving a statistical
          analysis request corresponding to two or more
          selected investments;
        a parallel processor, wherein the parallel pro-
         cessor includes:
        at least one processor for performing resampled
          statistical analysis based upon the statistical
          analysis request.
InvestPic J.A. 742 (amendments underlined).
                            B
    In March 2012, IBM and SAS filed a request for inter
partes reexamination of claims 1–31 of the ’291 patent—
claims lacking the language underlined in the quotations
just above. 1 IBM and SAS argued in the reexamination
request that the claims are anticipated by each of two
prior-art references, Sortino and Barraquand, and in any
event rendered invalid for obviousness by those refer-
ences, with or without additional references.
    Sortino, the reference of primary importance in these
proceedings, discloses using a bootstrap method to gain
better information about the expected returns on an asset,
including the uncertainty associated with the expected
returns, than is given by the mean and standard devia-


    1   IBM and SAS were joined by Algorithmics Inc. in
requesting the inter partes reexamination, but Algorith-
mics is not an appellee in this court.
IN RE: VARMA                                               7



tion of historical data. Sortino speaks of nine asset cate-
gories, one being the Standard & Poor’s 500 index (S&P
500), and describes performing bootstrap analyses on
historical data. As an example, Sortino describes sorting
the data for the S&P 500 into seven economic scenarios
(e.g., deep recession, mild inflation, chaos) and performing
a separate bootstrap analysis on the data from each of the
scenarios. After the separate bootstrap analyses, Sortino
indicates, the user may inject a subjective judgment into a
final set of figures by weighting the results from the seven
scenarios to arrive at a combined distribution for the
asset. For example, if the investor believes there to be “a
2% chance of a deep recession, a 10% chance of a moder-
ate recession, an 8% chance of a stagnant period, a 60%
chance of growth and a 20% chance of moderate inflation,”
InvestPic J.A. 216; Varma J.A. 288, the results of the
separate bootstrap analyses for those five data sets may
be weighted according to the investor’s beliefs to give the
combined distribution. As for Barraquand, that reference
discloses an error-reduction technique (which it calls
“quadratic resampling”), applied to pricing a class of
financial assets and implemented on a parallel processor.
    The examiner granted the request for inter partes
reexamination as to claims 1–5, 8–16, 19–21, and 29–31
in May 2012. The examiner then rejected all of those
claims: claims 1–5, 10–16, 19, and 21 for anticipation by
Sortino; claims 8, 9, 20, and 29–31 for obviousness over
Sortino in view of other references. The examiner found
that “Sortino’s teaching of identification and use of differ-
ent scenarios for analyses” meets the “bias parameter”
limitation (in the unamended claims). InvestPic J.A. 723.
The examiner cited the assertion by IBM and SAS that
InvestPic effectively “want[ed] to ‘rewrite’ the claim
language as ‘wherein the bias parameter determines a
degree of randomness in the selection of samples in a
resampling process’ reading in limitations regarding how
and when the ‘bias parameter’ must operate.” InvestPic
8                                                IN RE: VARMA




J.A. 721 (emphasis in original). In response, InvestPic
amended the claims. Claims 1 and 11 were amended to
clarify that “the bias parameter determines a degree of
randomness in sample selection in a resampling process.”
InvestPic J.A. 735, 738 (emphasis added). InvestPic also
amended claim 29, on which claims 30 and 31 depend, to
include the language underlined in the block quote above,
including the requirement that the system “receiv[e] a
statistical analysis request corresponding to two or more
selected investments.” InvestPic J.A. 724.
    After entering the claim amendments, the examiner
again rejected claims 1–5, 10–16, 19, and 21 for anticipa-
tion by Sortino and claims 8, 9, 20, and 29–31 for obvi-
ousness over Sortino and other prior art. The examiner
separately rejected claim 29 for anticipation by Bar-
raquand and claims 30–31 for obviousness over Bar-
raquand and other prior art.
    InvestPic appealed to the Board, arguing that Sortino
does not teach a bias parameter that is applied in sample
selection in a resampling process, as required by claims
1–5, 8–16, and 19–21; Sortino does not disclose two or
more investments, as required by claims 29–31; and
Barraquand does not teach a resampling method at all.
The Board affirmed the examiner’s rejection of the claims
for anticipation and obviousness over Sortino. It did not
reach the alternative, Barraquand-based grounds of
rejection of claims 29–31.
     For the requirement of using a bias parameter in
sample selection, the Board found “that Sortino teaches
the application of bias after an initial selection by applica-
tion of the various enumerated scenarios.” InvestPic,
2015 WL 1456097, at *3. For the requirements involving
two or more investments, the Board gave several reasons
for finding that Sortino suggests the ability to analyze two
or more investments. The Board relied on Sortino’s
ability to conduct distinct analyses of different invest-
IN RE: VARMA                                             9



ments seriatim, which it thought sufficed because of “[t]he
absence of a temporal limitation from Owner’s claims
indicating that ‘two or more investments’ are analyzed at
the same time.” Id. The Board also cited the transitional
term “comprising” in claim 29, which indicates that the
claim is open-ended, and the claim’s use of the indefinite
article “a” when introducing “a statistical analysis re-
quest,” which has been construed to mean “one or more.”
Therefore, the Board found that although two requests
would be necessary in the Sortino system to analyze two
or more investments, using “multiple ‘requests’ to analyze
‘two or more investments[ ]’ shows or suggests the claimed
feature.” Id. at *4.
                            C
    In June 2012, after the examiner had granted the re-
quest for inter partes reexamination of claims 1–5, 8–16,
19–21, and 29–31, SAS requested an ex parte reexamina-
tion of claims 22–31 of the ’291 patent. Claims 22–28
claim systems for performing a statistical analysis of
financial data over a network. Claim 22, on which claims
23–28 originally depended, is quoted above. Claim 24,
before amendment, required that the claim 22 statistical
analysis request include a bias parameter. The amended
version of claim 24, now independent, does not involve a
requirement of “two or more” selected investments, but it
does require (as relevant here) that the bias parameter
“determine[ ] a degree of randomness in sample selection
in a resampling process.”
     The examiner granted the request for reexamination
of claims 22–28, then confirmed the validity of claims 26–
28 but rejected claims 22–25 (when lacking the under-
lined language) for obviousness over the combination of
Sortino, Barraquand, and the prior-art patent Maggion-
calda (U.S. Patent No. 6,012,044). Maggioncalda de-
scribes a user interface for a financial advisory system
that operates over a computer network. The examiner
10                                              IN RE: VARMA




determined that “[i]t would have been obvious . . . to use
an interactive computer based financial advisory system,
as taught by Maggioncalda, to perform statistical analysis
of investment options, as taught by Sortino.” Varma J.A.
305–06. Further, the examiner determined that it would
have been obvious to use the parallel-processing computer
system “taught by Barranquand [sic] in order to be able to
perform the calculations more quickly.” Varma J.A. 306.
    Varma then amended claims 22, 24, and 25 by rewrit-
ing claims 24 and 25 in independent form, adding the
above-underlined language regarding “two or more select-
ed investments” to claims 22 and 25, and specifying that
the bias parameter of claim 24 (applicable even to a single
investment) “determines a degree of randomness in
sample selection in a resampling process.” Varma J.A.
331–33. The examiner entered the amendments and
again rejected claims 22–25 for obviousness over Sortino,
Maggioncalda, and Barraquand.
    Varma appealed to the Board, arguing that because
the bias parameter of claim 24 “cannot be construed as
merely biasing in general, or biasing the randomness of
something else outside of sample selection in the
resampling process itself,” Varma J.A. 1005, Sortino does
not disclose the requisite bias parameter. Varma also
argued that Sortino does not teach a resampled analysis
of two or more investments as required by claims 22, 23,
and 25. The Board agreed with the examiner on both
points.
    For claim 24 and its bias-parameter limitation, the
Board found “that claim 24 does not mandate that the
bias parameter be utilized during initial sample selection”
and Sortino suggests a bias parameter by “teach[ing] the
application of bias after an initial selection by application
of the various enumerated scenarios.” Varma, 2014 WL
7186800, at *4. For the other claims and their two-or-
more-investments limitations, the Board found that
IN RE: VARMA                                            11



Sortino suggests the ability to analyze two or more in-
vestments. As in the inter partes reexamination, the
Board noted that the claims use the transitional term
“comprising” and the indefinite article “a” in the claim
term “a statistical analysis request,” and on that basis it
found “that a system such as that disclosed by Sortino,
that may utilize multiple ‘requests’ to analyze ‘two or
more investments,’ shows or suggests the claimed fea-
ture.” Id. at *3. The Board also observed that the exam-
iner “note[d] that Sortino discloses analysis of the S&P
500 index, which comprises 500 underlying stocks (or
investments).” Id. at *2.
    Varma appeals under 35 U.S.C. § 141(b), challenging
the Board’s rejection of claims 1–5, 8–16, 19–25, and 29–
31. We have jurisdiction under 28 U.S.C. § 1295(a)(4)(A).
                       DISCUSSION
    Where there is no dispute about findings or evidence
of facts extrinsic to the patent, we review de novo the
Board’s determination of the broadest reasonable inter-
pretation of the claim language. Straight Path IP Grp.,
Inc. v. Sipnet EU S.R.O., 806 F.3d 1356, 1360 (Fed. Cir.
2015). We review the Board’s anticipation determination
for substantial evidence. In re Rambus, Inc., 753 F.3d
1253, 1256 (Fed. Cir. 2014). We review the Board’s ulti-
mate obviousness determination de novo and underlying
factual findings for substantial evidence. Belden Inc. v.
Berk-Tek LLC, 805 F.3d 1064, 1073 (Fed. Cir. 2015).
                            A
    Varma’s first challenge is to the Board’s understand-
ing of the bias parameter required by claims 1–5, 8–16,
19–21, and 24. For the inter partes reexamination, as it
comes to us, dependent claims 2–5, 8–10, 12–16, and 19–
21 rise or fall with independent claims 1 and 11. For the
ex parte reexamination, claim 24 is the sole claim before
us presenting this issue.
12                                             IN RE: VARMA




    As a threshold matter, we reject the suggestion that
Varma’s claim-construction position on the key point
involving the bias-parameter limitations is new on appeal
and therefore should be disregarded. Varma consistently
asserted to the examiner and the Board the meaning of
the bias parameter limitation asserted here—that the
bias parameter must be applied to the selection of sam-
ples from a sample space, as distinguished from the
creation of a sample space or the post-sampling combina-
tion of results calculated separately from the separate
sampling analyses of distinct sample spaces. See, e.g.,
InvestPic J.A. 759–60, 1245–47, 1372–75; Varma J.A.
355–60, 1035–36.
    On the merits, we agree with Varma that there is only
one reasonable meaning of the claim language, considered
alone and in light of the specification: the bias parameter
is used in selecting samples from the sample space, not in
creating a sample space, and not in making arithmetic
combinations of statistical measures previously calculated
from separate, resampled analyses. The claim language
makes this clear. It explicitly states that the bias param-
eter “determines a degree of randomness in sample selec-
tion in a resampling process.” InvestPic J.A. 735–42;
Varma J.A. 331–32. Claim 1 clearly differentiates be-
tween “selecting a sample space,” which occurs in step (a),
and “sample selection,” which occurs in step (b). The bias
parameter is applied in sample selection in step (b), not in
step (a)’s creation of a sample space. And “sample selec-
tion” is complete before any process of taking calculated
statistical results of several distinct sampling processes
and combining those measures in a preferred way.
    The specification reinforces the distinctions that are
clear in the claim language. The specification first de-
scribes the bootstrap process generally: “In step 920, a
sample space x is selected. In step 925, a statistical func-
tion based on the sample space data is computed . . . . In
step 930, bootstrap samples . . . are generated from the
IN RE: VARMA                                              13



sample space using a resampling process.” ’291 patent,
col. 11, lines 16–20 (emphases in original). The sample
space, therefore, is created before the resampling process,
and bootstrap samples are generated from the sample
space. The specification then describes a bootstrap pro-
cess using the bias parameter. The sample space is
created in step 1115. See id., col. 12, lines 60–66 (“In
particular, in step 1115, a sample space is determined
using the sample_size parameter received in step 1105.
Because financial database 150d may store samples for
investments for many different time periods, in step 1115,
a set of relevant samples for the resampled statistical
analysis requested by the client 105 is determined.”)
(emphases in original). The bias parameter is applied in
step 1135, after the creation of the sample space. Id., col.
14, lines 5–10 (“In step 1135, the bias parameter received
in step 1105 is analyzed. If no bias is selected (i.e., bias=
–1 and data is to be selected randomly), control passes to
step 1045 (‘no’ branch of step 1035). If bias<>0, in step
1040, a bias initialization algorithm is performed as
described in detail below.”).
     The particular descriptions of use of a bias parameter
confirm the point: the samples that produce a single
resampling analysis are all drawn from a given sample
space, with the bias parameter determining selection of
each particular sample. “The ‘bias’ parameter is a deci-
mal value that is either –1 or between 0 and 1 . . . .” Id.,
col. 11, lines 55–56. “A value of –1 indicates that the
resampling process should be conducted purely random-
ly.” Id., col. 11, lines 58–59. When “the ‘bias’ parameter
is between 0 and 1, sampling is performed so that b% of
the samples are ‘up’ days and 1−b% of the samples are
‘down’ days, where b=bias. Thus, if b=1, only ‘up’ days
will be selected and if b=0 only ‘down’ days are selected.”
Id., col. 11, lines 59–64. In the described algorithm for
the process, “the sample space is separated into two sets,
a first set including only ‘up’ days and a second set includ-
14                                            IN RE: VARMA




ing only ‘down’ days.” Id., col. 16, lines 10–15. Each
sample is drawn from either one set or the other based on
whether a randomly generated number between 0 and 1
is or is not less than the bias parameter (between 0 and
1); the distribution of samples, therefore, depends on
where between 0 and 1 the bias parameter is set. Id., col.
16, lines 15–22. In this process, the bias parameter
controls how samples are selected from the sample space
to produce a resampling result for that sample space; it
does not change the definition of the sample space itself.
    The process leading to the amendments of claims 1,
11, and 24 further supports this reading of the bias pa-
rameter. In the inter partes reexamination, when the
examiner initially rejected the claims, he stated that
Varma’s arguments about the bias parameter were effec-
tively “ ‘rewrit[ing]’ the claim language as ‘wherein the
bias parameter determines a degree of randomness in the
selection of samples in a resampling process’ reading in
limitations regarding how and when the ‘bias parameter’
must operate.” InvestPic J.A. 721 (emphasis in original).
Varma then proposed amendments to add “in sample
selection,” amendments “essentially and helpfully sug-
gested by the Examiner.” InvestPic J.A. 749. Based on
the amended claim language, Varma specifically argued
the distinction between “bias in the selection of sample
space to do resampling from” and “selection of samples
from that sample space, for example, once that space had
been selected.” InvestPic J.A. 749–50 (emphases omitted).
In the ex parte reexamination, Varma amended claim 24
in the same manner and for the same reasons.
    Given the proper understanding of the bias-parameter
limitation, the Board’s rejection of claims 1–5, 8–16, 19–
21, and 24 must be reversed. The Board’s rulings in both
reexamination proceedings rely solely on Sortino for this
limitation, “find[ing] that Sortino teaches the application
of bias after an initial selection by application of the
various enumerated scenarios.”        InvestPic, 2015 WL
IN RE: VARMA                                             15



1456097, at *3; Varma, 2014 WL 7186800, at *4. But
Sortino does not teach or suggest biasing how samples are
selected from a defined sample space to arrive at a
resampling-based measure for that sample space.
     Sortino allows for the introduction of bias in two
ways: (1) by sorting the data into seven economic scenari-
os to perform separate bootstrap analyses of each scenar-
io; and (2) weighting the individual results of the separate
bootstrap analyses for the seven scenarios to produce a
combined distribution. Neither option biases the selection
of samples in the resampling process as required by the
claims. First, Sortino is clear that once a scenario is
created, all selection of samples from that scenario is
random, not biased. InvestPic J.A. 214 n.4 (“All of the
monthly returns for a given asset in a given scenario were
entered into a file. Twelve monthly returns were random-
ly selected from this file and combined to make a single
annual return. This procedure was repeated 200 times
with replacement to generate the underlying distribution
for a given asset in a given scenario.”); Varma J.A. 286
n.4. Second, the post-bootstrap weighting of scenarios
similarly does not change the selection of samples from a
sample space, and therefore is not the result of the appli-
cation of a bias parameter within the meaning of the ’291
patent. And none of the expert declarations, all of which
were submitted before the clarifying claim amendments,
supports finding that Sortino biases the selection of
samples from the sample space when performing a
resampling process.
    Finally, we note that the Board did not find, and we
have not been shown, that Sortino’s process—which sorts
data into seven economic scenarios, performs a random
bootstrap analysis on each individual scenario, and then
allows for arithmetic combination of measures separately
derived for each of the scenarios—is mathematically equal
to applying a bias in choosing samples from a sample
space to create bootstrap samples. We therefore need not
16                                              IN RE: VARMA




decide whether such a showing, if made, would matter to
the analysis. Cf. Zenith Labs., Inc. v. Bristol-Myers
Squibb Co., 19 F.3d 1418, 1423 (Fed. Cir. 1994) (all claim
elements must be proved to be met, even if the required
evidence is scientifically redundant).     Therefore, we
conclude that Sortino does not disclose a bias parameter
that operates on the selection of samples from a sample
space in a resampling process.
                             B
    Varma also challenges the Board’s understanding of
“a statistical analysis request corresponding to two or
more selected investments,” as required by claim 22 (and
claims 23 and 25) and claim 29 (and claims 30–31).
InvestPic J.A. 742–43; Varma J.A. 331–33. As with the
bias-parameter limitation, we reject the suggestion that
Varma’s claim-construction position on the key point
involving this claim limitation is new in this appeal. On
this point, the interpretation of the claims that Varma
asserts here is consistent with the meaning it asserted to
the examiner and the Board in the reexamination pro-
ceedings—that the statistical analysis requested is one
that covers two or more investments. See, e.g., InvestPic
J.A. 761–64, 1262–63, 1390–92; Varma J.A. 336–40,
1006–13.
    In finding this claim limitation met by Sortino, the
Board rejected Varma’s position. The Board implicitly
relied on two related but different interpretations. In
Interpretation 1, the claim phrase embraces a request
that calls for a statistical analysis of a single investment.
Thus, the Board reasoned that Sortino is covered by the
claim even if “two requests would be necessary in the
Sortino system to accomplish an analysis of ‘two or more
investments.’ ” InvestPic, 2015 WL 1456097, at *3; Var-
ma, 2014 WL 7186800, at *2. In Interpretation 2, the
claim phrase embraces a request that calls for statistical
analyses of at least two investments, but each analysis
IN RE: VARMA                                            17



may be an analysis of a single investment, and the single-
investment analyses may take place seriatim. Thus, the
Board agreed with the examiner that there is no “tem-
poral limitation from [the] claims indicating that ‘two or
more investments’ are analyzed at the same time.” In-
vestPic, 2015 WL 1456097, at *3; Varma, 2014 WL
7186800, at *2. We conclude that both interpretations are
unreasonable.
    The error of Interpretation 1 is plain from the claim
phrase at issue. The phrase requires “a statistical analy-
sis request corresponding to two or more selected invest-
ments.” InvestPic J.A. 742–43; Varma J.A. 331–33. That
language on its face excludes Interpretation 1. A single
request must correspond to at least two investments.
     The Board relied on the claims’ use of “comprising” as
the transitional term, but that term does not support
Interpretation 1. Although the transitional term “com-
prising” indicates that the claim is open-ended, the term
does not render each limitation or phrase within the claim
open-ended. See Dippin’ Dots, Inc. v. Mosey, 476 F.3d
1337, 1343 (Fed. Cir. 2007); Spectrum Int’l, Inc. v. Ste-
rilite Corp., 164 F.3d 1372, 1380 (Fed. Cir. 1998). “Com-
prising” means that the claim can be met by a system that
contains features over and above those specifically re-
quired by the claim element, but only if the system still
satisfies the specific claim-element requirements: the
claim does not cover systems whose unclaimed features
make the claim elements no longer satisfied. Thus, here,
a claim-covered system may receive more than one re-
quest, but it must in particular be adapted to receive “a
request” that itself corresponds to two or more selected
investments.
    The Board also cited the indefinite article “a” before
“statistical analysis request” to support Interpretation 1.
But while “a” sometimes is non-restrictive as to number,
permitting the presence of more than one of the objects
18                                            IN RE: VARMA




following that indefinite article, context matters even as
to whether the word has that meaning. See Harari v. Lee,
656 F.3d 1331, 1341 (Fed. Cir. 2011). And here the ques-
tion is not whether there can be more than one request in
a claim-covered system: there can. Rather, the question is
whether “a” can serve to negate what is required by the
language following “a”: a “request” (a singular term) that
“correspond[s]” to “two or more selected investments.” It
cannot. For a dog owner to have “a dog that rolls over and
fetches sticks,” it does not suffice that he have two dogs,
each able to perform just one of the tasks. In the present
case, no matter how many requests there may be, no
matter the variety of the requests the system may receive,
the system must be adapted to receive a request that
itself corresponds to at least two investments. 2




     2   The language here is non-technical, and nothing
in the words after “request,” based on ordinary usage or
context or other intrinsic evidence, implies or even tends
to suggest a plurality of requests. In this respect, the
phrase is different from “a contact hole for source wiring
and gate wiring connection terminals” in Eidos Display,
LLC v. AU Optronics Corp., 779 F.3d 1360, 1365–68 (Fed.
Cir. 2015), where both the technical context and intrinsic
evidence made clear that there could not be a single hole
for all the connection terminals. The phrase at issue here
also differs from an example used in Eidos: “I am going to
create an electric car for the United States and United
Kingdom.” Id. at 1365. That phrase itself suggests that
the “car” referred to is a design that would naturally
embrace the necessary country-specific variations in
implementation. In the present case, there is no contex-
tual or intrinsic-evidence basis for inferring from the
words that come after “request” that the singular term
embraces a plurality in some sense.
IN RE: VARMA                                            19



    While the language of the “a statistical analysis re-
quest” phrase itself makes clear the unreasonableness of
Interpretation 1, it is other claim language—specifically,
language in claim 22 (found also in claim 25)—that makes
Interpretation 2 unreasonable as an understanding of the
“a statistical analysis request” phrase. Claim 22 requires
that the plurality of processors be adapted not only to
“receive a statistical analysis request corresponding to
two or more selected investments,” but also to do these
additional things: “based upon investment data pertain-
ing to the two or more selected investments, perform a
resampled statistical analysis to generate a resampled
distribution; and provide a report of the resampled distri-
bution.” Varma J.A. 331 (emphases added). The refer-
ence to “the two or more selected investments” is to the
immediately preceding “a statistical analysis request”
language. A single resampled statistical analysis must be
performed based on data pertaining to those two or more
investments. A single resampled distribution must be
generated by that analysis, and the single distribution
must be reported. The interlocking of singulars in that
language makes it unmistakable that at least two invest-
ments must be the subject of each statistical analysis that
is the subject of the request in the claim phrase at issue.
For those reasons, the language of claims 22 and 25
precludes Interpretation 2 for those claims.
    Similar language is not found in claim 29, the lone
claim in the inter partes reexamination that raises the
“two or more selected investments” issue. But the princi-
ple that the same phrase in different claims of the same
patent should have the same meaning is a strong one,
overcome only if “it is clear” that the same phrase has
different meanings in different claims. Fin Control Sys.
Pty, Ltd. v. OAM, Inc., 265 F.3d 1311, 1318 (Fed. Cir.
2001); see Digital-Vending Servs. Int’l, LLC v. Univ. of
Phoenix, Inc., 672 F.3d 1270, 1275 (Fed. Cir. 2012); Amer-
ican Piledriving Equip., Inc. v. Geoquip, Inc., 637 F.3d
20                                             IN RE: VARMA




1324, 1333 (Fed. Cir. 2011); PODS, Inc. v. Porta Stor, Inc.,
484 F.3d 1359, 1366 (Fed. Cir. 2007). IBM and SAS have
not pointed to, and we do not see, anything in the lan-
guage of claim 29, or the specification or prosecution
history, that provides the required basis for giving the
phrase in claim 29 a meaning different from the meaning
of the same phrase in claims 22 and 25. And we do not
see why the same-meaning principle is inapplicable here
just because the amended versions of the claims were
introduced in two different reexamination proceedings
(about three weeks apart): claim 29 in the inter partes
reexamination on March 15, 2013; claims 22 and 25 in the
ex parte reexamination on April 5, 2013. If allowed, the
claims would be claims within a single patent.
    The amendment history of the claims reinforces the
conclusion that Interpretation 2 is unreasonable: Varma
specifically argued against that interpretation in both
proceedings based on the language at issue. After the
unamended claims 29–31 were rejected in the inter partes
reexamination, Varma amended claim 29 to add “corre-
sponding to two or more selected investments.” InvestPic
J.A. 742. In doing so, Varma invoked that language to
distinguish Sortino, arguing that “all of [Sortino’s] anal-
yses were based upon a single asset at a time.” InvestPic
J.A. 766. Similarly, Varma amended claims 22 and 25 in
the ex parte reexamination in response to the examiner’s
rejections based on the examiner’s implicit adoption of
Interpretation 2: the examiner found that a request step
in Sortino was “implicit, or at least obvious, because
various analyses on S&P 500 were actually performed.”
Varma J.A. 305.         Varma added the two-or-more-
investments limitation and argued that “Sortino disclosed
a statistical analysis request corresponding only to a
single investment or asset category.” Varma J.A. 337
(emphasis in original).
    We conclude that the Board relied on unreasonable
interpretations of claim language in claims 22, 23, 25, and
IN RE: VARMA                                              21



29–31. The proper remedy, we also hold, is to vacate the
Board’s rejections of those claims for reconsideration of
anticipation and obviousness under the correct claim
construction.
    In the appeal from the ex parte reexamination, the
Director of the PTO argues that we may affirm even
under the correct claim construction based on the obser-
vation by the Board and examiner that Sortino performs
an analysis of the S&P 500 index and the S&P 500 index
corresponds to 500 underlying securities. IBM and SAS
do not make this argument (as to claim 29) in the inter
partes reexamination appeal. We reject the Director’s
position. There is no basis for treating the single index
investment (bought by investors as a single investment)
as two or more investments in the assets whose values
define the value of the index investment.
     Sortino treats the S&P 500 index as a single asset,
and it nowhere provides an analysis of the securities
underlying the S&P 500 index. IBM and SAS themselves
note that Sortino “describes the S&P 500 index as merely
one exemplary investment.” Brief for Appellees IBM
Corp. and SAS Institute Inc. at 52, InvestPic LLC v. IBM
(No. 2015-1667). In his expert declaration, Dr. Sortino
stated that the analysis shown in his paper “bootstrapped
the whole S&P portfolio, not the lowest level underlying
individual securities (e.g., specific stocks, bonds, futures,
etc.) within the portfolio,” further noting that “this dis-
tinction may seem subtle or even trivial, but it in fact has
important practical implications.” Varma J.A. 781 ¶ 21.
Dr. Savage made a similar point, describing “an asset
category such as an S&P Index Fund [a]s itself an asset.”
Varma J.A. 730 ¶ 17. There is no identified record basis
for a contrary understanding.         Because the S&P 500
index is consistently treated as a single asset, Sortino’s
analysis of the S&P 500 index alone cannot meet the two-
or-more-investments claim limitation.
22                                              IN RE: VARMA




    On the other hand, we do not reverse the cancellation
of the claims that involve this claim limitation. One
reason is that paragraphs 20 and 22 of Dr. Sortino’s
declaration raise a question—which we do not answer—
about whether the prior-art Sortino article might teach or
suggest a single resampling analysis of at least two as-
sets. To be sure, in the Sortino article itself, the figures
relate only to a single asset category, the S&P 500 index;
and the article states that the “statistics support our
earlier claims about the shape of uncertainty for the S&P
500 and these results held for all nine asset categories
studied,” with no statement as to carrying out any single
bootstrap analysis of at least two asset categories togeth-
er. InvestPic J.A. 216; Varma J.A. 288. But in his decla-
ration, Dr. Sortino said the following, seemingly about the
work supporting his article:
     The asset allocation model we developed at this
     time and which was marketed to a number of
     firms used stocks and bonds from different coun-
     tries. In both cases it is important to estimate the
     correlations between the asset categories and cre-
     ate a variance-covariance matrix. While we esti-
     mated covariance and correlation between the
     asset categories (e.g., stocks, bonds) we did not
     want to, need to, and did not, estimate the much
     more complex correlation and covariance relation-
     ships between all the underlying individual secu-
     rities (individual stocks, bonds or other financial
     instruments within the portfolios).
InvestPic J.A. 294–95 ¶ 20; Varma J.A. 780–81 ¶ 20
(emphasis in original). Dr. Sortino added that “for asset
allocation we only needed to measure the covariance
between the overall asset categories (e.g., the entire S&P,
Japan, etc.).” InvestPic J.A. 295 ¶ 22; Varma J.A. 781
¶ 22 (emphasis in original).
IN RE: VARMA                                            23



    The Board did not rely on those paragraphs of the
Sortino declaration. InvestPic, 2015 WL 1456097, at *3–
4; Varma, 2014 WL 7186800, at *2–3. We will not ad-
dress in the first instance the meaning and legal signifi-
cance of those passages, or whether reliance on them at
this stage is procedurally appropriate. We leave such
questions to the Board on remand. See Ariosa Diagnostics
v. Verinata Health, Inc., 805 F.3d 1359, 1366–67 (Fed.
Cir. 2015).
    Varma also challenges the adequacy of the Board’s
analysis regarding the obviousness rejections of claims 22,
23, 25, and 29–31. We do not address that challenge,
because we are independently vacating and remanding for
the Board to reconsider those claims in light of the proper
claim construction. We also do not address the examiner’s
alternative grounds of rejection of claims 29–31 based on
Barraquand. The Board stated that it was not reaching
those grounds. InvestPic, 2015 WL 1456097, at *6.
Whether to reach to those grounds, and, if so, whether
they are sound, are determinations to be made in the first
instance by the Board on remand.
                            C
     Varma challenges the Board’s understanding of
“resampled statistical analysis,” a term that appears in
all claims at issue. 3 Varma suggests that the term refers
to “a statistical analysis using resampling of data involv-
ing multiple investments for multiple time periods,
wherein the interrelationships in the financial data are
preserved.” Brief for Appellant, InvestPic LLC at 35,
InvestPic LLC v. IBM (No. 2015-1667); Brief for Appel-



   3     Claims 1–5 and 8–10 use the term “re-sampled
statistical method,” but Varma treats the terms as equiv-
alent. Brief for Appellant, InvestPic LLC at 35, InvestPic
LLC v. IBM (No. 2015-1667).
24                                            IN RE: VARMA




lant, Samir Varma at 37, In re Varma (No. 2015-1502).
That proposed construction goes far beyond the language
supposedly being construed, which refers to a statistical
technique that indisputably may be used for analysis
outside the financial context altogether and, indeed, may
be used for single-investment analysis, as many of the
patent claims at issue here make clear. We reject Var-
ma’s narrowing construction of “resampled statistical
analysis.”
                       CONCLUSION
    We reverse the Board’s rejection of claims 1–5, 8–16,
19–21, and 24. We vacate the Board’s rejection of claims
22, 23, 25, and 29–31 and remand for further proceedings
regarding those claims.
     Costs awarded to InvestPic in No. 2015-1667.
     REVERSED IN PART, VACATED IN PART, AND
                  REMANDED
