  United States Court of Appeals
      for the Federal Circuit
                ______________________

             ZOLTEK CORPORATION,
                Plaintiff-Appellant

                           v.

                  UNITED STATES,
                  Defendant-Appellee
                ______________________

                      2014-5082
                ______________________

    Appeal from the United States Court of Federal
Claims in No. 1:96-cv-00166-EJD, Judge Edward J.
Damich.
               ______________________

              Decided: February 19, 2016
               ______________________

    DEAN A. MONCO, Wood, Phillips, Katz, Clark & Mor-
timer, Chicago, IL, argued for plaintiff-appellant. Also
represented by JOHN S MORTIMER; MEREDITH MARTIN
ADDY, Katten Muchin Rosenman LLP, Chicago, IL.

    GARY LEE HAUSKEN, Commercial Litigation Branch,
Civil Division, United States Department of Justice,
Washington, D.C., argued for defendant-appellee. Also
represented by DAVID M. RUDDY, JOYCE R. BRANDA, JOHN
FARGO.
                  _____________________
2                                        ZOLTEK CORP.   v. US



Before NEWMAN, CLEVENGER, and MOORE, Circuit Judges.
NEWMAN, Circuit Judge.
     Zoltek Corporation seeks compensation from the
United States for use, with the authorization and consent
of the Departments of the Air Force and Navy, of the
patented method of producing carbon fiber sheet products
as claimed in United States Reissue Patent No. Re 34,162
issued January 19, 1993 (“the ’162 patent”). The ’162
patent is a reissue of U.S. Patent No. 4,728,395, issued
March 1, 1988 to inventor George Boyd and assigned to
Mr. Boyd’s employer Stackpole Fibers Company. The
patent was acquired by Zoltek Corporation with its acqui-
sition of Stackpole in 1988.
Litigation history
    On March 25, 1996, Zoltek filed suit in the United
States Court of Federal Claims (CFC) alleging that the
process used to produce carbon fiber sheet materials for
the B-2 Bomber and the F-22 Fighter Plane infringed the
’162 patent. This is the third appeal in this action. The
factual background is set forth in the prior opinions of the
CFC and this court.
    In the first appeal, this court answered a certified
question to hold that the patentee has no cause of action
against the United States when any step of the patented
method is practiced outside of the United States, as for
the F-22 Fighter. Zoltek Corporation v. United States,
442 F.3d 1345, 1353 (Fed. Cir. 2006) (Plager, J., dissent-
ing) (Zoltek I).
    On remand, the CFC granted Zoltek’s request for
leave to amend its complaint to substitute as defendant
Lockheed Martin, the general contractor for the F-22
Fighter, and then granted Zoltek’s motion to transfer the
count relating to the F-22 Fighter to the United States
District Court for the Northern District of Georgia, where
it was “reasonably plausible” that the court had jurisdic-
ZOLTEK CORP.   v. US                                      3



tion over an infringement suit against Lockheed. Zoltek
Corporation v. United States 85 Fed. Cl. 409, 422 (2009).
On Lockheed’s motion, this aspect was certified for ap-
peal.
    The Federal Circuit then acted en banc (in part) and
reversed its ruling in Zoltek I. This court recognized the
liability of the United States for infringement by acts that
are performed with its authorization and consent. 28
U.S.C. § 1498(a) (“Whenever an invention described in
and covered by a patent of the United States is used or
manufactured by or for the United States without license
of the owner thereof or lawful right to use or manufacture
the same, the owner’s remedy shall be by action against
the United States in the United States Court of Federal
Claims for the recovery of his reasonable and entire
compensation for such use and manufacture.”). By stat-
ute the contractor is immunized from liability. Id. (“use
or manufacture … by a contractor … shall be construed as
use or manufacture for the United States”). This court
dismissed Lockheed as a party, negated the proposed
transfer to Georgia, and remanded to the Court of Federal
Claims for inclusion of counts for infringement with
respect to both the F-22 Fighter and the B-2 Bomber.
Zoltek Corporation v. United States, 672 F.3d 1309, 1311
(Fed. Cir. 2012) (en banc) (Zoltek II).
    On remand, the CFC separated trial of the issues of
validity and infringement, and denied discovery as to
infringement with respect to the F-22 Fighter. Zoltek
sought mandamus from this court concerning these
actions; the petition was denied. In re Zoltek Corporation,
526 F. App’x 956, 957 (Fed. Cir. 2013) (non-precedential).
Trial proceeded in the CFC, limited to validity. The
government challenged the ’162 patent under sections
101, 103, and 112 of Title 35. The CFC sustained patent
eligibility under section 101; that ruling is not appealed.
4                                         ZOLTEK CORP.   v. US



    At trial, each side presented an expert witness, Dr.
Brian Sullivan for the government and Mr. Zsolt Rumy
for Zoltek. The CFC held the asserted claims invalid on
the grounds of obviousness and inadequate written de-
scription. Zoltek Corporation v. United States, No. 96-166
C, 2014 WL 1279152 (Fed. Cl. Mar. 31, 2014) (“CFC Op.”).
Zoltek appeals, arguing that the CFC applied incorrect
laws of written description and obviousness, that the CFC
did not apply the appropriate burdens and standards of
proof, and that the CFC erred in its conclusions.
     Zoltek also argues that the issues were improperly bi-
furcated. We conclude that in the circumstances of this
case, taking note of the government’s official invocation of
state secret privilege, the CFC acted within its discretion
in limiting trial initially to the issues of validity. Howev-
er, as we next discuss, we conclude that the trial court
erred in its judgment of patent invalidity.
The Boyd Invention
     The ’162 patent is directed to a method of manufac-
turing carbon fiber sheet products whose electrical resis-
tivity is pre-selected and value-controlled by the described
method. This method is based on Boyd’s discovery of a
non-linear relationship among the heat treatment condi-
tions, partial carbonization, and surface resistivity 1 of
sheet products.
    The method as claimed in the reissue patent starts
with a previously oxidized and stabilized carbonizable
fiber, a product known in the prior art and commercially
available. This oxidized fiber is then partially carbonized



    1   Throughout these proceedings, the terms resistivi-
ty and resistance were often used interchangeably. The
correctness of these usages is not at issue.
ZOLTEK CORP.   v. US                                      5



in accordance with the relationship discovered by Boyd, to
produce a partially carbonized fiber whose sheet products
have the desired pre-selected surface electrical resistance.
    This method permits production of carbonized sheets
of pre-selected and uniform electrical resistance, and thus
uniform pre-selected insulating properties. The ’162
specification states that theretofore carbon fiber sheets
having specified surface electrical resistance were availa-
ble only by including other materials, such as glass or
aluminum filaments, with the carbonized fibers. ’162
patent, col.1 ll.49–60.
     Patent Figure 4 shows the foundation discovery of re-
sistivity as a function of carbonizing temperature:




    The lower curve represents the volume resistivity for
single fibers at the carbonizing temperature, and upper
curves A and B show surface resistivities for one half
6                                        ZOLTEK CORP.   v. US



ounce per square yard and one ounce per square yard
sheet products incorporating the designated partially
carbonized fibers. The patent describes and exemplifies
the preparation of fibers having the preselected partial
carbonization, and the production of sheet products hav-
ing the desired electrical properties. Id., col.4 ll.19–23
(“[T]he temperature-resistivity of the single carbonized
fiber is translated into the preselected desired surface
resistance of the resultant partially carbonized fiber sheet
product produced with such fibers.”).
    It is not disputed that the non-linear relationship
shown in Figure 4, and its application to achieve the
results described in the ’162 patent, were not previously
known. The government’s expert, Dr. Sullivan, stated to
be one of the nation’s preeminent experts with a “thirty-
year career in research and design relating to carbon fiber
science,” U.S. Br. 22, testified that his calculations per-
taining to his reproduction of the Figure 4 curve were
based on data that were not in the prior art and were
selected retrospectively. No reference showed the rela-
tionship between volume or surface-resistivity of carbon
fiber sheet products and treatment temperature of carbon
fibers.
    The CFC held claims 1–22 and 33–38 of the reissue
patent invalid on two grounds, (1) that they did not meet
the written description requirement, and (2) that the
claimed invention would have been obvious to a person of
ordinary skill in this field at the time of the invention.
                             I
                  Written Description
     The claimed method is summarized in reissue claim 1,
shown as in the reissue patent, with deletions from the
original claim in brackets and additions in italics—for
these changes are the basis of the CFC’s ruling of invalid-
ity on the ground of inadequate written description:
ZOLTEK CORP.   v. US                                      7



   1. A method of manufacturing a plurality of dif-
   ferent value controlled resistivity carbon fiber
   sheet products employing a carbonizable fiber
   starting material; said method comprising [oxidiz-
   ing and stabilizing the carbonizable fiber starting
   material at an elevated temperature of the order
   of 220 degrees Centigrade to effect molecular ar-
   omatic rearrangement of the fibers,] selectively
   partially carbonizing [the] previously oxidized and
   stabilized fiber starting material for a predeter-
   mined period in an oxygen free atmosphere within
   a furnace at [a] selected temperature values with-
   in a temperature range from 370 degrees Centi-
   grade to about 1300 degrees Centigrade by
   soaking the stabilized fiber starting material at
   the selected temperature for the predetermined
   period of time to provide a [desired] preselected
   known volume electrical resistivity to the partially
   carbonized fibers corresponding to that volume
   electrical resistivity value required to provide the
   preselected desired surface resistance value for the
   finished sheet products, and thereafter processing
   the partially carbonized fibers into [desired elec-
   trical resistivity] homogeneous carbon fiber sheet
   products [having the form of non-woven paper or
   woven or knitted fabric sheet products] having the
   preselected desired surface electrical [resistivi-
   ties] resistances.
    The CFC held that the original patent did “not sup-
port the elimination of the oxidation and stabilization
step” from the reissued claims, and that this rendered the
claims “invalid for lack of written description.” CFC Op.
at *20-21. The CFC explained that the reissue “imper-
missibly broadens the patented process by reducing the
number of steps required for infringement.” Id. at *21.
The CFC stated that “although the step is found in the
reissue patent, its elimination from the claimed process
8                                          ZOLTEK CORP.   v. US



goes beyond the written description of the invention in the
original ’395 patent.” Id. at n.10 (emphasis in original).
    The elimination of the preparation of the starting ma-
terial broadened the reissue. However, a broadening
reissue is not improper if filed within two years of issu-
ance. A patentee is entitled to a reissue “enlarging the
scope of the claims,” when, as here, the reissue applica-
tion is filed “within two years from the grant of the origi-
nal patent.” 35 U.S.C. § 251(d).
    The CFC also held that the broadened claim is not
supported in the specification, holding that it is irrelevant
that the omitted oxidizing and stabilizing step is fully
described in the specification as well as being in the prior
art. The CFC held that the preparation of the known
starting material must be included in the claim, that it is
insufficient that the reissue claim requires that these
steps be performed, and that whether these steps were
known to the prior art is “irrelevant to the question of
whether the written description requirement is satisfied.”
CFC Op. at *19.
    There was no argument as to insufficiency of either
the prior art or the content of the specification, in describ-
ing the starting material. There was no allegation that a
person of ordinary skill in this field would not understand
the description in the specification. The original specifi-
cation plainly, and without dispute, describes that the
starting material is an oxidized and stabilized fiber, cites
references showing this known material, and describes its
preparation. That a previously oxidized and stabilized
starting material was known to a person of ordinary skill
in the field was recognized by the reissue Examiner in his
statement that:
    Ex[amine]r agreed with applicant that partial ox-
    idation & heat stabilization temp. need not be re-
    cited in the claims since this temp. is within the
ZOLTEK CORP.   v. US                                      9



   prior art & claims do not have to recite what is
   well known in the prior art.
Examiner Interview Summary, Reissue Application No.
07/483,531 (May 5, 1992).
    The CFC had previously construed the reissue claims
as supported by the specification, finding that the reissue
claims were substantially the same as in the parent
patent and properly supported. The court stated:
   [I]t can hardly be said that the oxidizing and sta-
   bilizing step was removed from Reissue ’162. On
   the contrary, when the step was removed the ex-
   aminer rejected the application until Zoltek added
   “previously” in the claims to refer back to this de-
   scription of the method which requires it unless a
   previously oxidized and stabilized material is pur-
   chased.
Opinion on Defendant’s Motion for Partial Summary
Judgment on Matters Relating to Reissue filed on Janu-
ary 15, 1999, No. 96-166 C (Fed. Cl. Sept. 13, 1999) (un-
published).
    The government argues that the asserted claims are
not supported in the specification because the specifica-
tion does not state that these steps need not be performed
by the same entity. The question of who performs steps of
a fully described invention, including preparation of a
known starting material, is not a matter of the written
description requirement.
    The purpose of the written description requirement is
to assure that the public receives sufficient knowledge of
the patented technology, and to demonstrate that the
patentee is in possession of the invention claimed. See In
re Skvorecz, 580 F.3d 1262, 1269 (Fed. Cir. 2009). The
requirement is applied in the context of the state of
knowledge at the time of the invention. Capon v. Eshhar,
418 F.3d 1349, 1358 (Fed. Cir. 2005). The written de-
10                                          ZOLTEK CORP.   v. US



scription “need not include information that is already
known and available to the experienced public.” Space
Sys./Loral, Inc. v. Lockheed Martin Corp., 405 F.3d 985,
987 (Fed. Cir. 2005); see Enzo Biochem, Inc. v. Gen-Probe
Inc., 323 F.3d 956, 970 (Fed. Cir. 2002) (“[The written]
description is the quid pro quo of the patent system; the
public must receive meaningful disclosure in exchange for
being excluded from practicing the invention for a limited
period of time.”).
    Here, the ’162 specification describes the preparation
of the starting material, and states that it is commercially
available. ’162 patent, col.4 ll.45-55 (“[T]he carbonizable
tow is supplied to an oxidation operation 14 where it is
stabilized by being heated in atmospheric oxygen to a
temperature of about 220 degrees Centigrade . . . . The
resulting oxidized tow is sold under the trademark
‘PYRON.’”). The government does not argue that a person
of ordinary skill would not be able to make or acquire the
starting material based on the description in the specifi-
cation.
    The written description requirement relates to
whether the patentee possessed the invention that is
claimed. There was no suggestion that a person of ordi-
nary skill would not have understood that Boyd was in
possession of the invention that he claimed. See Centocor
Ortho Biotech, Inc. v. Abbott Labs., 636 F.3d 1341, 1348
(Fed. Cir. 2011) (“To satisfy the written description re-
quirement, the applicant must convey with reasonable
clarity to those skilled in the art that, as of the filing date
sought, he or she was in possession of the invention, and
demonstrate that by disclosure in the specification of the
patent.”) (internal quotation marks omitted); see also
Alcon Research Ltd. v. Barr Labs., Inc., 745 F.3d 1180,
1191–92 (Fed. Cir. 2014) (“Critically, Barr adduced no
evidence, let alone clear and convincing evidence, that
was probative of whether an ordinarily skilled artisan
would not have understood from the disclosures of Al-
ZOLTEK CORP.   v. US                                      11



con’s . . . patents that the patentees invented, or pos-
sessed, the methods of the asserted claims. Without that
evidence, there was no basis on which to find a lack of
adequate written description.”).
    The CFC stated its concern that the reissue patent
claims could be infringed by an entity that did not itself
make the starting material, but purchased the known
starting material from a commercial source. However,
the reissue statute provides that reissue is available “by
reason of the patentee claiming more or less than he had
a right to claim . . . for the invention disclosed in the
original patent.” 35 U.S.C. § 251(a). A validly obtained
reissue does not violate the written description require-
ment if the patentee can reach an enlarged scope of
possible infringement.
    It is not an improper broadening amendment when a
reissue applicant, with the considered agreement of the
reissue Examiner, substitutes a preparatory step known
to those skilled in the art at the time of the invention with
a requirement to start with the product of that known
preparatory step. The CFC’s emphasis on who might
infringe the broadened reissue claims is an issue of in-
fringement, not written description.
    We conclude that the CFC erred in holding reissue
claims 1–22 and 33–38 invalid for failure to meet the
written description requirement of section 112. That
ruling is reversed.
                             II
                       Obviousness
    The science of carbonized fiber materials had been the
subject of study well before the Boyd patent application
was filed, as exemplified in the references cited during
patent prosecution and in these proceedings.
12                                        ZOLTEK CORP.   v. US



    The CFC relied on the government’s expert Dr. Sulli-
van, who cited references concerning carbon fiber prod-
ucts and developed a mathematical formula from which
he generated a graph duplicating that in Figure 4 of the
’162 patent. To produce this graph, Dr. Sullivan used
data from the ’162 patent record, from a Zoltek publica-
tion issued in 2000, and various references and articles.
He cited:
    [1] Akio Shindo, Studies on Graphite Fiber, Govern-
ment Industrial Research Institute of Osaka (1961), is a
research report discusses the manufacture and use of
carbon fibers of polyacrylonitrile. Shindo states that
increasing heat-treatment temperature of the fiber results
in increased conductivity of the fiber. Shindo does not
show or suggest the non-linear relationship between
temperature and resistivity that was discovered by Boyd,
or the use of such relationship to control surface resistivi-
ty.
    [2] Kitago, U.S. Patent No. 3,998,689 (Dec. 21, 1976),
describes the production of carbon fiber sheets by a pro-
cess that combines chopped carbon fibers with other
ingredients to form a slurry, which is shaped into a sheet,
saturated with a resin, and then carbonized, to form a
conductive sheet product. Kitago provides data for sheets
carbonized at 1000°C and 2000°C, showing significantly
lower resistivity at the higher temperature. Kitago does
not show or suggest the non-linear relationship discovered
by Boyd, or the use of such relationship to control surface
resistivity.
    [3] Layden, U.S. Patent No. 4,080,413 (Mar. 21, 1978),
shows carbonization of chopped polyacrylonitrile fiber
sheets over the range of 1000°C to 1260°C, to produce
hard, inflexible products with extremely low surface
resistivities, suitable for use as fuel cell electrodes. Ley-
den does not show or suggest the non-linear relationship
ZOLTEK CORP.   v. US                                    13



discovered by Boyd, or the use of such relationship to
control surface resistivity.
    [4] Topchjiev, U.K. Patent No. 979,122 (Jan. 1, 1965),
entitled “Method of Producing Semiconductive Polymer
Materials,” uses oxidized and stabilized carbon fibers that
are heat treated to produce materials with semiconductor
properties electrical conductivity. Topchjiev does not
show or suggest the non-linear relationship discovered by
Boyd, or the use of such relationship to control surface
resistivity.
    [5] D.B. Fischbach & Kunio Komaki, Electrical Re-
sistance of Carbon Fibers, University of Washington
(1979), is an article that explains that increasing the
treatment temperature results in decreased volume
resistivity. This article does not show or suggest the non-
linear relationship discovered by Boyd, or the use of such
relationship to control surface resistivity.
    These references variously show the heat treatment of
carbonized fibers and their resistivities or conductivities
at various treatment temperatures.             On cross-
examination, Dr. Sullivan agreed that these references
alone do not establish obviousness. The following ex-
change took place:
   Q. And the Fischbach and Komaki article . . . the
   Topchjiev patent . . . the Layden patent . . . all
   disclose nothing more than what was disclosed in
   the Otani reference before the Patent Office, cor-
   rect?
   A. I believe that is correct, yes.
   Q. And I believe it’s also your testimony — prior
   testimony that the Topchjiev patent and the Lay-
   den patent, by themselves, would not be sufficient
   to render the Zoltek patent obvious, correct?
   A. Yes, I think that is correct.
14                                         ZOLTEK CORP.   v. US



Trial Tr. 269:5–15.
    Instead, Dr. Sullivan relied on a mathematical formu-
la he derived from the Rule of Mixtures, 2 citing several
articles, viz., “Theory of Reinforced Materials” by Z.
Hashin (1972), “Analysis of Composite Materials—A
Survey” by Z. Hashin (1981), “An Analysis Model for
Spatially Oriented Fiber Composites” by B.W. Rosen et al.
(1977), and “Mechanics of Composite Materials” by R.
Christensen (1979). The position of Dr. Sullivan was
summarized at trial as follows:
     Q.: So, to sum up your testimony, Dr. Sullivan,
     you’re asserting that it would be obvious to a per-
     son of ordinary skill in the art, as of October 1984,
     to rely upon four publications which do not men-
     tion surface resistivity, partially carbonized or
     semi-conductive carbon fibers, or the method to
     control the surface resistivity of carbon fiber sheet
     products made from the — made from the partial-
     ly carbonized fibers and controlling the volume re-
     sistivity of the partially carbonized fiber, the 1972
     Hashin and the 1977 Rosen articles referring to
     structural fibers, that it would have been obvious
     to a person of ordinary skill in the art, as of Octo-
     ber of 1984, to construct the mathematical meth-
     odology you described on your direct examination




     2  The Rule of Mixtures is a rule of materials science
in which a weighted mean is used to predict properties,
including electrical conductivity, of a composite material
made up of continuous and unidirectional fibers. It is a
mathematical equation by which properties of the indi-
vidual components of a mixture are weighted by their
volume fractions.
ZOLTEK CORP.   v. US                                     15



   to obtain carbon fiber sheet products having a
   controlled surface resistivity?
   [Objection]
   THE COURT: . . . . do you want the question bro-
   ken out or —
   THE WITNESS: No, because that is my testimo-
   ny.
Trial Tr. 245:12–246:8.
    No reference mentions “surface resistivity” or “the re-
quired limitation to pre-select individual fiber volume
resistivities to produce sheet products with desired sur-
face resistivities.” Zoltek Br. 4–5 (citing record). Dr.
Sullivan testified that he was not aware of anyone, includ-
ing himself, who had previously used the mathematical
formula he created to determine carbonization tempera-
ture-resistivity relationships.
    The ’162 patent teaches carbonized sheets that “re-
quire no insulating elements such as glass fiber in order
to adjust the surface resistances of the sheet product to a
desired surface resistance volume.” ’162 patent, col.2 ll.7–
11. The novelty of such sheets was not disputed. The
patent prosecution and trial records contain a letter from
George Rodgers, a materials engineer at Northrup
Grumman (the general contractor for the B-2 Bomber),
who stated:
   In December 1983, the Material & Processes De-
   partment of Northrop Advanced Systems Division
   ordered four rolls of carbon fiber paper from
   Stackpole Fibers Co. The product was unique in
   that the carbon fibers were not fully carbonized,
   increasing the volume resistivity of the fiber
   which in turn increases the surface resistivity of
   the paper. . . . At the time the order was placed,
   Northrop Materials & Processes had never seen a
16                                       ZOLTEK CORP.   v. US



     material of this type before and was not aware of
     any other company that could supply material in
     this form with varying electrical properties.
Letter from George Rodgers dated August 6, 1987, Prose-
cution File Wrapper 187. By deposition on August 18,
2009, Mr. Rodgers testified that, with regard to the accu-
racy of the contents of that letter, viewed in hindsight, “I
wouldn’t change anything.” Rogers Dep. 34:6.
    Dr. Sullivan also testified that he had no basis to dis-
agree with the Rodgers letter. Specifically, he testified:
     Q. Okay. And the last sentence reads, “At the time
     the order was placed, Northrop Materials & Pro-
     cesses had never seen a material of this type and
     were not aware of any other company that could
     supply material in this form with varying electri-
     cal properties.” Do you see that?
     A. I do.
     Q. Okay. And you have no basis to disagree with
     that statement, do you?
     A. No, I don’t.
Trial Tr. 274:16–25.
    There is no teaching or suggestion in the prior art to
select the data that Sullivan selected, and to plug the
selected data into the mathematical equation that Sulli-
van devised. As summarized by Zoltek, “Sullivan used
the variable fiber volume resistivities shown [in] the file
history of the ’395 parent patent at various temperatures
and constant volume resistivities for each remaining
component of the sheet products in making his calcula-
tions.” Zoltek Br. 23 (citing record). This is not evidence
of obviousness. See EWP Corp. v. Reliance Universal,
Inc., 755 F.2d 898, 907 (Fed. Cir. 1985) (“Patentability
under the statute, § 103, is a decision made on the basis of
a hypothesis: Would the invention have been obvious ‘to a
ZOLTEK CORP.   v. US                                    17



person having ordinary skill in the art to which the sub-
ject matter pertains’ in the light of all knowledge con-
veyed by ‘prior art’ as defined by statute and case law.”).
    Zoltek also points to several errors made by Dr. Sulli-
van, to which Sullivan admitted on cross-examination.
Zoltek mentions “Sullivan’s erroneous fiber volume frac-
tion (0.3), fiber density (1.81 g/cm3), and resin volume
fraction (0.54).” Zoltek Br. 24 n.5. With respect to Dr.
Sullivan’s testimony that he used a volume fraction of 0.3
in his Rule of Mixtures calculation purportedly reflective
of the Zoltek patented product, Zoltek’s expert Mr. Rumy
testified:
   In the paper process, you can’t even make that
   kind of conduct — that kind of concentration of
   carbon fibers, only possibly by taking a regular
   paper product that is made probably no more than
   10 to 15 percent carbon content, and then you
   compress it. But we — that’s — that would be de-
   stroying our entire invention.
Trial Tr. 326:22–327:2.
    As another error, while the Rule of Mixtures requires
the use of volume fractions of each component of a compo-
site mixture, Dr. Sullivan used a weight percent for each
component in order to place data points on the Figure 4
template. See Zoltek Br. 28.
    These errors taint Dr. Sullivan’s reproduction of Fig-
ure 4. Indeed, Dr. Sullivan made several confessions of
error in his selection or calculation of data points to
produce the graph he created to track Figure 4. As an-
other example:
   Q. . . . So, you’ve inserted a uniform density of
   1.81 grams per cubic centimeter, which is the den-
   sity of fully carbonized fibers, when there should
   have been a gradually increasing density from
18                                         ZOLTEK CORP.   v. US



     1.36 through the temperature range shown on
     [your spreadsheet], correct?
     [Objection for lack of foundation; overruled]
     A. It is true that the carbon fiber density will
     change with heat treatment temperature and that
     it probably is true that a different value, other
     than a uniform 1.81, would have been more ap-
     propriate
     Q. Okay.
     A. I will concede that.
Trial Tr. 257:2–19.
     Zoltek also points to Dr. Sullivan’s admission that his
critical fiber volume fraction, 0.3%/30%, fundamental to
his calculations based on the Rule of Mixtures, was wrong
and that Dr. Sullivan used data from a 2000 Zoltek User’s
Guide directed to fully carbonized composites at a tem-
perature of 1400°C, a reference published fourteen years
after the ’162 patent’s filing date.
     Dr. Sullivan conceded that there were errors in his
calculations, stating that the reason was that he did not
have complete information. That is not surprising, for
there was not complete information in the prior art—
weighing against the government’s argument that it
would have been obvious to a person of ordinary skill to
recreate the Boyd graph from known information. Dr.
Sullivan’s plaint that he could not accurately duplicate
Boyd’s discovery because of lack of information is power-
ful evidence of non-obviousness—not the contrary.
    Dr. Sullivan stated that he obtained some of the val-
ues he used in his calculations from the ’162 patent itself.
However, for the volume fraction of carbon fiber, de-
scribed by Dr. Sullivan as by far the most important
element in the equation, he ignored the figure in the
patent (0.83) and used a value of 0.3, which he testified
ZOLTEK CORP.   v. US                                      19



came from a Zoltek 2000 User’s Guide. Zoltek points out
that this Guide was directed to an entirely different
product, and also that the Guide was written fourteen
years after the ’162 patent application was filed. There
was no showing that the information on which Dr. Sulli-
van relied was available to persons of skill at the time of
the Boyd invention. Zoltek states, and Dr. Sullivan did
not contradict, that Dr. Sullivan selected values from
various sources in order to fit the template of Boyd’s
results.
    Neither the government’s attorney argument, nor Dr.
Sullivan’s testimony, nor the opinion of the Court of
Federal Claims, points to any suggestion in the prior art
to select the data selected by Dr. Sullivan and create the
mathematical formula to construct a graph to track
Figure 4. See KSR Int’l Co. v. Teleflex, Inc., 550 U.S. 398,
418–19 (2007) (“Although common sense directs one to
look with care at a patent application that claims as
innovation the combination of two known devices accord-
ing to their established functions, it can be important to
identify a reason that would have prompted a person of
ordinary skill in the relevant field to combine the ele-
ments in the way the claimed new invention does. This is
so because inventions in most, if not all, instances rely
upon building blocks long since uncovered, and claimed
discoveries almost of necessity will be combinations of
what, in some sense, is already known.”).
    Even Dr. Sullivan called his reconstruction of Figure
4 “somewhat arbitrary.” Trial Tr. 259:18. Hindsight
reconstruction for litigation ends is not of probative value.
See Outside the Box Innovations, LLC v. Travel Caddy,
Inc., 695 F.3d 1285, 1298 (Fed. Cir. 2012) (“Precedent
recognizes the pitfalls of judicial hindsight exercised at
the time of litigation . . . .”).
   The Court has recognized “the distortion caused by
hindsight bias” and “arguments reliant upon ex post
20                                        ZOLTEK CORP.   v. US



reasoning” in determining obviousness. KSR, 550 U.S. at
421; see InTouch Technologies, Inc. v. VGO Commc’ns,
Inc., 751 F.3d 1327, 1351 (Fed. Cir. 2014) (“It appears
that [the expert] relied on the . . . patent itself as her
roadmap for putting what she referred to as pieces of a
‘jigsaw puzzle’ together.”); W.L. Gore & Associates, Inc. v.
Garlock, Inc., 721 F.2d 1540, 1553 (Fed. Cir. 1983) (“To
imbue one of ordinary skill in the art with knowledge of
the invention in suit, when no prior art reference or
references of record convey or suggest that knowledge, is
to fall victim to the insidious effect of a hindsight syn-
drome wherein that which only the inventor taught is
used against its teacher.”).
     The government does not attempt to rehabilitate Dr.
Sullivan’s errors. Instead, the government’s argument
appears to be that since Dr. Sullivan is a renowned scien-
tist in this field, and since Dr. Sullivan was able to repro-
duce the Figure 4 graph, it was obvious to do so. This was
error, since, as we have repeatedly cautioned, “[t]hat
which may be made clear and thus ‘obvious’ to a court,
with the invention fully diagrammed and aided . . . by
experts in the field, may have been a break-through of
substantial dimension when first unveiled.” Uniroyal,
Inc. v. Rudkin-Wiley Corp., 837 F.2d 1044, 1051 (Fed. Cir.
1988) (internal quotation marks omitted); see also KSR,
550 U.S. at 421 (“A factfinder should be aware, of course,
of the distortion caused by hindsight bias and must be
cautious of arguments reliant upon ex post reasoning”)
(citing Graham v. John Deere Co., 383 U.S. 1, 36 (1966) as
“warning against a temptation to read into the prior art
the teachings of the invention in issue and instructing
courts to guard against slipping into use of hindsight”)
(internal quotation marks omitted); W.L. Gore, 721 F.2d
at 1553 (“It is difficult but necessary that the deci-
sionmaker forget what he or she has been taught at trial
about the claimed invention and cast the mind back to the
time the invention was made (often as here many years),
ZOLTEK CORP.   v. US                                    21



to occupy the mind of one skilled in the art who is pre-
sented only with the references, and who is normally
guided by the then-accepted wisdom in the art.”).
    There was not clear and convincing evidence of obvi-
ousness of the Boyd discovery and its use to produce
carbon fiber sheets of pre-selected homogeneous electrical
resistance. The CFC’s ruling of invalidity on the ground
of obviousness is reversed.
                       CONCLUSION
    The Court of Federal Claims erred in holding the as-
serted claims of the ’162 patent invalid under sections 103
and 112. The judgment of invalidity is reversed. We
remand for resolution of all remaining issues.
            REVERSED AND REMANDED
