  United States Court of Appeals
      for the Federal Circuit
                 ______________________

         THE DOW CHEMICAL COMPANY,
              Plaintiff-Cross-Appellant

                            v.

  NOVA CHEMICALS CORPORATION (CANADA),
     NOVA CHEMICALS INC. (DELAWARE),
             Defendants-Appellants
            ______________________

                  2014-1431, 2014-1462
                 ______________________

    Appeals from the United States District Court for the
District of Delaware in No. 1:05-cv-00737-LPS, Chief
Judge Leonard P. Stark.
                ______________________

                Decided: August 28, 2015
                ______________________

    HARRY J. ROPER, Jenner & Block LLP, Chicago, IL,
argued for plaintiff-cross-appellant. Also represented by,
AARON A. BARLOW, PAUL DAVID MARGOLIS; RAYMOND N.
NIMROD, GREGORY D. BONIFIELD, WILLIAM ADAMS,
CLELAND B. WELTON, II, Quinn Emanuel Urquhart &
Sullivan, LLP, New York, NY.

   DONALD ROBERT DUNNER, Finnegan, Henderson,
Farabow, Garrett & Dunner, LLP, Washington, DC,
argued for defendants-appellants. Also represented by
2           THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS
                                             CORPORATION


MARK J. FELDSTEIN, RONALD BLEEKER,                DARREL
CHRISTOPHER KARL.
              ______________________

     Before PROST, Chief Judge, DYK and WALLACH, Cir-
                      cuit Judges.
DYK, Circuit Judge.
    The Dow Chemical Company (“Dow”) filed suit
against NOVA Chemicals Corporation (Canada) and
NOVA Chemicals Inc. (Delaware) (collectively, “NOVA”),
alleging infringement of claims of U.S. Patent No.
5,847,053 (the “’053 patent”) and U.S. Patent No.
6,111,023 (the “’023 patent”). A jury found the asserted
claims to be infringed and not invalid. NOVA appealed,
and we affirmed, holding, inter alia, that the asserted
claims were not indefinite. Our mandate issued, and
NOVA’s petition for certiorari was denied by the Supreme
Court, NOVA Chems. Corp. v. Dow Chem. Co., 133 S. Ct.
544 (2012). The district court subsequently conducted a
bench trial for the supplemental damages period through
the expiration date of both patents. The district court
granted supplemental damages in the form of lost profits
and reasonable royalties and denied Dow’s request for
enhanced damages. NOVA appealed, and Dow cross-
appealed.
    Subsequently, the Supreme Court decided Nautilus,
Inc. v. Biosig Instruments, Inc., 134 S. Ct. 2120 (2014),
altering the standard for indefiniteness. We consider here
only whether, under Nautilus, the supplemental damages
award must be reversed because the claims are indefinite.
THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS             3
CORPORATION


NOVA does not request that we reopen our previous
judgment as to the infringement trial. 1
    We hold that the intervening change in the law of in-
definiteness resulting from Nautilus provides an excep-
tion to the doctrine of law of the case or issue preclusion.
In our review of the supplemental damages award, we
therefore evaluate the indefiniteness of the claims under
the Nautilus standard. In reviewing the supplemental
damages award under the Nautilus standard, we hold
that the claims are indefinite and reverse the award of
supplemental damages.
                       BACKGROUND
    On October 21, 2005, Dow filed suit against NOVA,
alleging infringement of claims of the ’053 patent and the
’023 patent. The asserted claims of both patents cover
ethylene polymer compositions (a type of plastic) with,
inter alia, improved modulus, yield strength, impact
strength, and tear strength. These polymers can be made
into films that can be down-gauged (made thinner) with-
out losing strength. The claims at issue are independent
claim 6 2 and dependent claims 7, 10, and 12 of the ’053


   1    NOVA did attack that judgment in a separate
case, alleging fraud and fraud on the court. We affirmed
the district court’s dismissal of NOVA’s complaint. See
NOVA Chems. Corp. v. Dow Chem. Co., No. 2015-1257,
2015 WL 3555764 (Fed. Cir. June 9, 2015); Transcript of
Hearing on Motion to Dismiss at 56, NOVA Chems. Corp.
v. Dow Chem. Co., No. 13-1601-LPS (D. Del. July 29,
2014).
    2   Claim 6 is representative and provides:
   6. An ethylene polymer composition comprising
   (A) from about 10 percent (by weight of the total
   composition) to about 95 percent (by weight of the
4             THE DOW CHEMICAL COMPANY   v. NOVA CHEMICALS
                                               CORPORATION


patent; and independent claim 1 3 and dependent claims 2,
5, and 8 of the ’023 patent. Both patents expired on Octo-
ber 15, 2011.




    total composition) of at least one homogeneously
    branched linear ethylene/α-olefin interpolymer
    having:
        (i) a density from about 0.89 grams/cubic
        centimeter (g/cm3) to about 0.935 g/cm3,
        (ii) a molecular weight distribution
        (Mw /Mn) from about 1.8 to about 2.8,
        (iii) a melt index (I2) from about 0.001
        grams/10 minutes (g/10 min) to about 10
        g/10 min,
        (iv) no high density fraction,
        (v) a single melting peak as measured us-
        ing differential scanning calorimetry, and
        (vi) a slope of strain hardening coefficient
        greater than or equal to 1.3; and
    (B) from about 5 percent (by weight of the total
    composition) to about 90 percent (by weight of the
    total composition) of at least one heterogeneously
    branched linear ethylene polymer having a densi-
    ty from about 0.93 g/cm3 to about 0.965 g/cm3.
’053 patent col. 16 ll. 4–25.
    3   Claim 1 is representative and provides:
    1. An ethylene polymer composition comprising
        (A) from about 10 percent (by weight of
        the total composition) to about 95 percent
THE DOW CHEMICAL COMPANY      v. NOVA CHEMICALS              5
CORPORATION


    Relevant here, claim 6 of the ’053 patent and claim 1
of the ’023 patent, the independent claims, require “a
slope of strain hardening coefficient greater than or equal
to 1.3.” ’053 patent col. 16 ll. 19–20; ’023 patent col. 16 ll.
29–30. NOVA argues that the patents are indefinite
because they fail to teach a person having ordinary skill
in the art how to measure the “slope of strain hardening,”


        (by weight of the total composition) of at
        least one ethylene interpolymer having:
            (i) a density from about 0.89
            grams/cubic centimeter (g/cm3) to
            about 0.935 g/cm3,
            (ii) a melt index (I2) from about
            0.001 grams/10 minutes (g/10
            min.) to about 10 g/10 min.,
            (iii) a slope of strain hardening co-
            efficient greater than or equal to
            1.3, and
            (iv) a Composition Distribution
            Branch Index (CDBI) greater than
            50 percent; and
        (B) from about 5 percent (by weight of the
        total composition) to about 90 percent (by
        weight of the total composition) of at least
        one ethylene polymer characterized as
        having a density from about 0.93 g/cm3 to
        about 0.965 g/cm3 and comprising a linear
        polymer fraction, as determined using a
        temperature rising elution fractionation
        (TREF) technique.
’023 patent col. 15 l. 59–col. 16 l. 39.
6            THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS
                                               CORPORATION


which is required to calculate the strain hardening coeffi-
cient.
    On June 15, 2010, a jury found that NOVA infringed
the claims of the asserted patents and that the patents
were not invalid for indefiniteness. The jury had been
instructed that “[i]f the meaning of the claims is discerni-
ble, it is definite, even though the task may be formidable
and even if the conclusion may be one over which reason-
able persons will disagree.” J.A. 12702. NOVA appealed,
arguing, inter alia, that the patents were invalid for
indefiniteness. Dow Chem. Co. v. Nova Chems. Corp., 458
F. App’x 910, 911, 917–18 (Fed. Cir. 2012). In that previ-
ous appeal, on January 24, 2012, we held that the patents
were not indefinite. Id. at 911, 920. In so holding, we
applied the law as then established by our pre-Nautilus
precedent, including Exxon Research & Engineering Co. v.
United States, 265 F.3d 1371 (Fed. Cir. 2001). See Dow,
458 F. App’x at 917–20.
     On remand, the district court, inter alia, held a bench
trial on supplemental damages for the period between
January 1, 2010, through October 15, 2011, the date on
which the patents expired. On March 28, 2014, the dis-
trict court granted supplemental damages to Dow in the
form of lost profits and reasonable royalties and denied
Dow’s request for enhanced damages. Final judgment was
entered on April 14, 2014. NOVA appealed on April 23,
2014. Dow cross-appealed on May 1, 2014.
    While the appeals were pending, on June 2, 2014, the
Supreme Court decided Nautilus. In Nautilus, the Su-
preme Court held that our standard for indefiniteness
was contrary to 35 U.S.C § 112, and it announced a new
standard described in detail below. See 134 S. Ct. at 2124.
The Court abrogated our previous inquiry into whether
the claims were “amenable to construction” or “insolubly
ambiguous,” id., which we applied in cases such as Exxon,
and relied on in the earlier appeal in this case, Dow, 458
THE DOW CHEMICAL COMPANY   v. NOVA CHEMICALS             7
CORPORATION


F. App’x at 917, 919–20. Under the new standard, “a
patent is invalid for indefiniteness if its claims, read in
light of the specification delineating the patent, and the
prosecution history, fail to inform, with reasonable cer-
tainty, those skilled in the art about the scope of the
invention.” Nautilus, 134 S. Ct. at 2124.
     On appeal, NOVA argues that (1) the supplemental
damages award should be vacated because the patents-in-
suit are invalid for indefiniteness after the Supreme
Court’s decision in Nautilus or (2) in the alternative, the
supplemental damages award was not supported by the
evidence. In its cross-appeal, Dow contends that the
district court erred by not awarding enhanced damages
for the supplemental damages period.
     We have jurisdiction pursuant to 28 U.S.C.
§ 1295(a)(1). 35 U.S.C. § 112 ¶ 2 provides that “[t]he
specification shall conclude with one or more claims
particularly pointing out and distinctly claiming the
subject matter which the applicant regards as his inven-
tion.” 35 U.S.C. § 112 (2006). Indefiniteness is a question
of law that this court reviews de novo. Teva Pharm. USA,
Inc. v. Sandoz, Inc., 789 F.3d 1335, 1341 (Fed. Cir. 2015).
    We conclude that our prior decision is not binding on
the issue of indefiniteness because Nautilus changed the
applicable law, our prior decision rested on the earlier
law, and the patents-in-suit are invalid for indefiniteness
under the new Nautilus standard. We do not address the
other issues. We reverse the district court’s award of
supplemental damages and dismiss the cross-appeal as
moot.
                       DISCUSSION
                             I
    Dow argues that we are bound by our decision in the
previous appeal—an appeal from a final judgment under
Federal Rule of Civil Procedure 54(b)—that the claims
8            THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS
                                               CORPORATION


were not indefinite. While a judgment entered under Rule
54(b) is a final judgment, that final judgment cannot have
any greater effect than any other final judgment. The
earlier appeal was from the entry of judgment in the jury
verdict (for the period March 2002–December 31, 2009)
while the current appeal is from the supplemental dam-
ages judgment (for the period January 1, 2010–October
15, 2011). An award of supplemental damages is designed
to compensate the patentee “for periods of infringement
not considered by the jury,” Whitserve, LLC v. Comput.
Packages, Inc., 694 F.3d 10, 38 (Fed. Cir. 2012) (emphasis
added), and necessarily implicates patent validity. In
order to prevail on a claim for supplemental damages, a
patentee must establish infringement for the supple-
mental damages period. If “an act that would have been
an infringement or an inducement to infringe pertains to
a patent that is shown to be invalid, there is no patent to
be infringed.” Commil USA, LLC v. Cisco Sys., Inc., 135 S.
Ct. 1920, 1929 (2015).
    The doctrine of claim preclusion does not apply as be-
tween the claims for the first and second damages peri-
ods. It is well-established that, as to claims for continuing
conduct after the complaint is filed, each period consti-
tutes a separate claim. 4 See 18 Charles Alan Wright,



    4   Likewise, claims that have accrued at the time of
the complaint generally must be brought together, and
the plaintiff need not supplement the complaint to cover
continuing conduct. 18 Charles Alan Wright, Arthur R.
Miller & Edward H. Cooper, Federal Practice and Proce-
dure § 4409 (2d ed. 2002) (“Most cases rule that an action
need include only the portions of the claim due at the time
of commencing that action, frequently observing that the
opportunity to file a supplemental complaint is not an
obligation.”); see also, e.g., Gillig v. Nike, Inc., 602 F.3d
THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS             9
CORPORATION


Arthur R. Miller & Edward H. Cooper, Federal Practice
and Procedure § 4409 (2d ed. 2002) (“A substantially
single course of activity may continue through the life of a
first suit and beyond. The basic claim-preclusion result is
clear: a new claim or cause of action is created as the
conduct continues.”); Crowe v. Leeke, 550 F.2d 184, 187
(4th Cir. 1977) (“We glean from the[] cases that res judi-
cata [claim preclusion] has very little applicability to a
fact situation involving a continuing series of acts, for
generally each act gives rise to a new cause of action.”);
Exhibitors Poster Exchange, Inc. v. Nat’l Screen Serv.
Corp, 421 F.2d 1313, 1316, 1318–19 (5th Cir. 1970) (res
judicata [claim preclusion] does not apply where plaintiff
alleges “same facts—[a] 1961 refusal to deal [as an anti-
trust violation]”—but sought in a second and third suit to
recover damages suffered since losing on summary judg-
ment in the first suit since the damages arose from “non
actions” subsequently occurring).
    This rule applies to patent infringement claims. As we
explained just last year,
   traditional notions of claim preclusion do not ap-
   ply when a patentee accuses new acts of infringe-
   ment, i.e., post-final judgment, in a second suit—


1354, 1363 (Fed. Cir. 2010) (res judicata [claim preclu-
sion] does not apply where claims accrue during action
and are not the subject of the first judgment because “the
doctrine of res judicata does not punish a plaintiff for
exercising the option not to supplement the pleadings
with an after-acquired claim” (citations omitted)); Spiegel
v. Cont’l Ill. Nat’l Bank, 790 F.2d 638, 646 (7th Cir. 1986)
(claim preclusion barred suit except for claims related to
two new acts which “occurred after the filing” of the
earlier suit).
10            THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS
                                                 CORPORATION


     even where the products are the same in both
     suits. Such claims are barred under general pre-
     clusion principles only to the extent they can be
     barred by issue preclusion, with its attendant lim-
     itations.
Brain Life, LLC v Elekta Inc., 746 F.3d 1045, 1056 (Fed.
Cir. 2014); see Aspex Eyewear, Inc. v. Marchon Eyewear,
Inc., 672 F.3d 1335, 1342–44 (Fed. Cir. 2012); see also,
e.g., SynQor, Inc. v. Artesyn Techs., Inc., 709 F.3d 1365,
1385–86 (considering whether intent element of induced
infringement had been shown in the supplemental dam-
ages period).
    Here, the bulk of the supplemental damages accrued
after the Rule 54(b) judgment, and it is clear that claim
preclusion also does not apply to damages accruing after
the filing of the complaint and not the subject of the first
judgment. See note 4, supra. All supplemental damages
here accrued after the filing of the complaint.
    While claim preclusion does not apply, ordinarily is-
sue preclusion (or law of the case) would bar relitigation
in the supplemental damages period of issues (such as
validity) that were resolved as to the earlier time periods.
18 Charles Alan Wright, Arthur R. Miller & Edward H.
Cooper, Federal Practice and Procedure § 4409 (2d ed.
2002 (“[Although] claim preclusion often cannot apply in
settings of continuing . . . conduct, . . . it may be proper to
conclude that the issues precluded by the first litigation
embrace [issues in the second] . . . .”). That would be the
case whether the supplemental damages proceeding were
viewed as a continuation of the ongoing case or as a new
proceeding. 5 In the former event, the doctrine of law of



     5 Because Dow does not seek to reopen the in-
fringement trial judgment, Dow’s arguments that we lack
THE DOW CHEMICAL COMPANY   v. NOVA CHEMICALS            11
CORPORATION


the case would preclude relititgation. In the latter event
(treating the supplemental damages proceeding as a new
proceeding) issue preclusion would bar relitigation. “[T]he
doctrine [of law of the case] posits that when a court
decides upon a rule of law, that decision should continue
to govern the same issues in subsequent stages in the
same case.” Christianson v. Colt Indus. Operating Corp.,
486 U.S. 800, 815–16 (1988) (quoting Arizona v. Califor-
nia, 460 U.S. 605, 618 (1983)) (emphasis added) (altera-
tions in original). Issue preclusion “bars ‘successive
litigation of an issue of fact or law already litigated and
resolved in a valid court determination essential to the
prior judgment.’” Taylor v. Sturgell, 553 U.S. 880, 892
(2008) (quoting New Hampshire v. Maine, 532 U.S. 742,
748–49 (2001)) (emphasis added). 6 But both doctrines are


jurisdiction on the indefiniteness issue are without merit.
The cases that Dow cites relate to situations where a
party sought to reopen a previous judgment. See Brown v.
Eli Lilly & Co., 654 F.3d 347, 354–55 (2d Cir. 2011)
(holding that court was without jurisdiction to consider
appeal as to two parties because the judgment against one
party was appealed but the appeal was dismissed as
untimely and the judgment against the other party was
not appealed); In re Martin, 400 F.3d 836, 841 & n.1 (10th
Cir. 2005) (appeal limited to later order because earlier
order was a final judgment and that judgment was not
appealed); Crowder v. Telemedia, Inc., 659 F.2d 787, 787–
88 (7th Cir. 1981) (per curiam) (holding that court lacked
jurisdiction over previous judgment that had become final
and had not been timely appealed).
    6   While we apply the law of the regional circuit to
general procedural questions, we apply this court’s prece-
dent to questions implicating substantive issues of patent
law or issues implicating the scope of our own previous
decisions. See Soverain Software LLC v. Victoria’s Secret
12           THE DOW CHEMICAL COMPANY   v. NOVA CHEMICALS
                                              CORPORATION


subject to an exception—when governing law is changed
by a later authoritative decision. See 18B Charles Alan
Wright, Arthur R. Miller & Edward H. Cooper, Federal
Practice and Procedure § 4478 (2d ed. 2002) (law of the
case); 18 Charles Alan Wright, Arthur R. Miller & Ed-
ward H. Cooper, Federal Practice and Procedure § 4425
(2d ed. 2002) (issue preclusion).
    With respect to law of the case, “[p]erhaps the most
obvious justifications for departing . . . arise when there
has been an intervening change of law outside the con-
fines of the particular case.” 18B Charles Alan Wright,
Arthur R. Miller & Edward H. Cooper, Federal Practice
and Procedure § 4478; see Rose Acre Farms, Inc. v. United
States, 559 F.3d 1260, 1277–78 (Fed. Cir. 2009) (holding
that intervening Supreme Court decision issued after
prior appeal rendered prior decision “obsolete,” “[g]iven
the significant change in the law”); Wopsock v. Natchees,
454 F.3d 1327, 1333 (Fed. Cir. 2006) (finding that law of
the case did not apply because “this is a case in which
there has been a change in the law”). The exception
applies even if the issue was resolved on appeal in an
earlier stage of the proceeding. Indeed, the premise of the
exception in the appellate context is that there was such
an earlier resolution. See Litton Sys., Inc. v. Honeywell
Inc., 238 F.3d 1376, 1379–81 (Fed. Cir. 2001) (revisiting
prior holding on prosecution history estoppel because
intervening en banc authority adopted a contrary ap-
proach, noting “[w]e are aware of no decision of this court
that has applied the law of the case in the face of a rele-
vant change in controlling legal authority”); Mendenhall
v. Barber-Greene Co., 26 F.3d 1573, 1576, 1580, 1583



Direct Brand Mgmt., LLC, 778 F.3d 1311, 1314 (Fed. Cir.
2015). We therefore apply our own law where, as here, we
are interpreting our own prior decision.
THE DOW CHEMICAL COMPANY   v. NOVA CHEMICALS            13
CORPORATION


(Fed. Cir. 1994) (holding that an exception to law of the
case applied and the asserted claims were invalid, revisit-
ing a previous final decision that the claims were not
invalid); see also United States v. Plugh, 648 F.3d 118,
121–24 (2d Cir. 2011) (revisiting holding on first appeal
due to intervening Supreme Court precedent); Spiegla v.
Hull, 481 F.3d 961, 963–67 (7th Cir. 2007) (holding that
“because the judgment in this case is not yet final, we are
obliged to reevaluate” a previous appellate holding under
intervening Supreme Court precedent); United States v.
Windom, 82 F.3d 742, 746, 748–49 (7th Cir. 1996), vacat-
ed on other grounds, 103 F.3d 523 (7th Cir. 1996) (holding
that defendant was “not foreclosed from re-raising” merits
of conviction previously affirmed where an intervening
Supreme Court decision was issued after remand for
sentencing); United States v. Garcia, 77 F.3d 274, 276–77
(9th Cir. 1996) (reconsidering affirmance of conviction sua
sponte in light of intervening authority after an earlier
remand “for the limited purpose of reimposing the manda-
tory” sentence). But the exception of course does not apply
if the proceeding has reached the stage of final judgment.
See Mendenhall, 26 F.3d at 1582 (Fed. Cir. 1994). Here,
the supplemental damages proceeding had not been
concluded at the time of Nautilus.
    Similarly, issue preclusion does not apply where “a
new determination is warranted in order to take account
of an intervening change in the applicable legal context or
otherwise to avoid inequitable administration of the
laws.” Restatement (Second) of Judgments § 28(2) (1982).
Therefore, a court is not bound by a previous decision
where there is a change in the controlling precedent. 18
Charles Alan Wright, Arthur R. Miller & Edward H.
Cooper, Federal Practice and Procedure § 4425 (“Preclu-
sion is most readily defeated by specific Supreme Court
overruling of precedent relied upon in reaching the first
decision.”); see Bobby v. Bies, 556 U.S. 825, 836 (2009)
(“[E]ven if the core requirements for issue preclusion had
14           THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS
                                               CORPORATION


been met, an exception to the doctrine’s application would
be warranted due to this Court’s intervening deci-
sion . . . .”); Bingaman v. Dep’t of Treasury, 127 F.3d 1431,
1438 (Fed. Cir. 1997) (“In a number of cases, this court
and others have held that a significant change in the
‘legal atmosphere’—whether in the form of new legisla-
tion, a new court decision, or even a new administrative
ruling—can justify a later court’s refusal to give collateral
estoppel effect to an earlier decision.”); Wilson v. Turnage,
791 F.2d 151, 156–57 (Fed. Cir. 1986) (holding that issue
preclusion did not apply where Federal Circuit decision
was “such an intervening change in the legal atmosphere
that it renders the bar of collateral estoppel inapplicable
in this case”); see also Comm’r of Internal Revenue v.
Sunnen, 333 U.S. 591, 600 (1948) (“[A] supervening
decision cannot justly be ignored by blind reliance upon
the rule of collateral estoppel”).
     The change in law exception applies whether the
change in law occurs while the case is before the district
court or while the case is on appeal. See Spiegla, 481 F.3d
at 964 (7th Cir. 2007) (holding that defendants had not
waived challenge to holding in first appeal where issue
not raised on remand in district court or initial briefing
because intervening decision was issued after appellate
briefing); Mendenhall, 26 F.3d at 1583 (law of the case did
not apply where new decision issued while case on ap-
peal); Morris v. Am. Nat’l Can Corp., 988 F.2d 50, 51–53
(8th Cir. 1993) (law of the case did not apply where, after
first appeal and decision on remand by district court,
Supreme Court case changed prevailing law); Wilson, 791
F.2d at 154, 157 (exception to issue preclusion applied
where intervening decision issued while case pending
before this court).
    Three conditions must be satisfied to reopen a previ-
ous decision under the change of law exception for both
law of the case and issue preclusion. First, the governing
law must have been altered. See 18 Charles Alan Wright,
THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS             15
CORPORATION


Arthur R. Miller & Edward H. Cooper, Federal Practice
and Procedure § 4425 (2d ed. 2002) (exception to issue
preclusion only available as a result of “independent
changes” in the law and not “merely because the defeated
party wishes to reargue the law”); 18B Charles Alan
Wright, Arthur R. Miller & Edward H. Cooper, Federal
Practice and Procedure § 4478 (2d ed. 2002) (“The easiest
cases [for departing from law of the case] occur when the
law has been changed by a body with greater authority on
the issue . . . .”).
    Second, the decision sought to be reopened must have
applied the old law. See, e.g., Litton, 238 F.3d at 1380
(holding that intervening law exception to law of the case
applied where previous opinion had followed approach
expressly repudiated by intervening en banc decision);
Rose Acre Farms, 559 F.3d at 1278 (intervening law
exception applied where prior opinion had “clearly applied
the [old] test”).
      Third, the change in law must compel a different re-
sult under the facts of the particular case. See Hughes
Aircraft Co. v. United States, 140 F.3d 1470, 1475 (Fed.
Cir. 1998), overruled on other grounds by Festo Corp. v.
Shoketsu Kinzoku Kogyo Kabushiki Co., 234 F.3d 558
(Fed. Cir. 2000) (rejecting argument that issue should be
reopened because the “analysis performed in [the previous
appeal] satisfies the . . . rule as stated in [an intervening
Supreme Court decision]”); Hughes Aircraft Co. v. United
States, 86 F.3d 1566, 1576 (Fed. Cir. 1996), cert. granted,
judgment vacated on other grounds, 520 U.S. 1183 (1997)
(holding that intervening law exception to law of the case
did not apply where “analysis in the court’s prior decision
is . . . entirely consistent” with intervening en banc deci-
sions); Cal. Fed. Bank v. United States, 395 F.3d 1263,
1274–75 (Fed. Cir. 2005) (holding that intervening en
banc decision did not warrant reopening previous decision
because principles of en banc decision did not apply on the
facts of the case on appeal). Here, as the Supreme Court
16            THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS
                                               CORPORATION


recognized in Nautilus, the Supreme Court’s new stand-
ard does not always lead to a different result. 134 S. Ct. at
2130–31 (remanding for consideration of whether claims
were definite under the new standard).
     Each of these requirements was satisfied here.
    First, there can be no serious question that Nautilus
changed the law of indefiniteness. This was indeed the
very purpose of the Nautilus decision. Prior to Nautilus,
we applied the following test:
     [W]hat we have asked is that the claims be ame-
     nable to construction, however difficult that task
     may be. If a claim is insolubly ambiguous, and no
     narrowing construction can properly be adopted,
     we have held the claim indefinite. If the meaning
     of the claim is discernible, even though the task
     may be formidable and the conclusion may be one
     over which reasonable persons will disagree, we
     have held the claim sufficiently clear to avoid in-
     validity on indefiniteness grounds.
Exxon, 265 F.3d at 1375. In Nautilus, the Supreme Court
expressly rejected that “insolubly ambiguous” or “amena-
ble to construction” standard. Nautilus, 134 S. Ct. at
2124. Rather, the Court “h[e]ld that a patent is invalid for
indefiniteness if its claims, read in light of the specifica-
tion delineating the patent, and the prosecution history,
fail to inform, with reasonable certainty, those skilled in
the art about the scope of the invention.” Id. The Court
explained further: “[i]t cannot be sufficient that a court
can ascribe some meaning to a patent’s claim; the defi-
niteness inquiry trains on the understanding of a skilled
artisan at the time of the patent application, not that of a
court viewing matters post hoc.” Id. at 2130.
   Nautilus emphasizes “the definiteness requirement’s
public-notice function.” 134 S. Ct. at 2130; see also id. at
2129 (“[A] patent must be precise enough to afford clear
THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS               17
CORPORATION


notice of what is claimed, thereby ‘appris[ing] the public
of what is still open to them’” (quoting Markman v.
Westview Instruments, Inc., 517 U.S. 370, 373 (1996))
(alterations in original)). Although the Court recognized
that “[s]ome modicum of uncertainty” may be tolerated,
id. at 2128, the patent and prosecution history must
disclose a single known approach or establish that, where
multiple known approaches exist, a person having ordi-
nary skill in the art would know which approach to select.
See Teva, 789 F.3d at 1341, 1344–45 (holding claim indef-
inite where molecular weight could be measured three
different ways and would yield different results and the
patent and prosecution history did not provide guidance
as to which measure to use). Particularly this is so where
different approaches to measurement are involved. See id.
at 1341, 1344–45. Thus, contrary to our earlier approach,
under Nautilus, “[t]he claims, when read in light of the
specification and the prosecution history, must provide
objective boundaries for those of skill in the art.” Interval
Licensing LLC v. AOL, Inc., 766 F.3d 1364, 1371 (Fed.
Cir. 2014) (citing Nautilus, 134 S. Ct. at 2130 & n.8).
     Second, there is also no question that our original de-
cision applied pre-Nautilus law. Dow argues that our
opinion in the previous appeal was not inconsistent with
Nautilus and that we did not apply the “amenable to
construction” or “insolubly ambiguous standard.” But the
fact that we did not include that particular language does
not mean that we were not applying the prevailing legal
standard. We cited Exxon, see Dow, 458 F. App’x at 917,
which Nautilus specifically cited as exemplary of the
rejected Federal Circuit standard. See Nautilus, 134 S. Ct.
at 2130 n.9. Applying Exxon, we explained that a patent
is definite under § 112 ¶ 2 if:
    “one skilled in the art would understand the
    bounds of the claim when read in light of the spec-
    ification.” A claim is not indefinite merely because
    it is difficult to construe. To be indefinite, a claim
18            THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS
                                                  CORPORATION


     term must be such that “no narrowing construc-
     tion can properly be adopted” to interpret the
     claim.
Dow, 458 F. App’x at 917 (quoting Exxon, 265 F.3d at
1375). We also explained that “the test for indefiniteness
is not whether the scope of the patent claims is easy to
determine, but whether ‘the meaning of the claim is
discernible, even though the task may be formidable and
the conclusion may be one over which reasonable persons
will disagree.’” Id. at 920 (quoting Exxon, 265 F.3d at
1375). This language corresponds exactly to the “amena-
ble to construction” or “insolubly ambiguous” standard
rejected in Nautilus.
   Third, as we now discuss, our original decision would
have been different under the new Nautilus standard.
                              II
    The claim term at issue here provides for “a slope of
strain hardening coefficient greater than or equal to 1.3.”
’053 patent col. 16 ll. 19–20; ’023 patent col. 16 ll. 29–30.
The patents provide that the “slope of strain hardening
coefficient” (“SHC”) is calculated according to the follow-
ing equation:
     SHC = (slope of strain hardening)*(I2)0.25
where I2=melt index in grams/10 minutes. ’053 patent col.
6 ll. 45–50; ’023 patent col. 7 ll. 22–28. “The SHC coeffi-
cient is a new Dow construct, not previously known in the
art . . . .” Dow, 458 F. App’x at 918.
    Strain hardening is a property wherein a material be-
comes harder as it is stretched. The ’053 and ’023 patents
teach that tensile properties, including strain hardening,
may be tested using a device called the Instron Tensile
Tester. The Instron Tensile Tester subjects a sample to an
increasing load, stretching it until it breaks. The machine
THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS           19
CORPORATION


measures the force, or load, applied to the sample and the
length that the sample stretches.
     The measurements taken by the Instron Tensile Test-
er are then plotted on a graph. The resulting curve is
called the “tensile curve” or “stress/strain curve.” On the
stress/strain curve, the force (or load) applied to the
sample is plotted on the y-axis, and the resulting elonga-
tion (or displacement) of the sample is plotted on the x-
axis. The behavior of the material claimed by the patent
changes as it is stretched, and those changes are shown
on the stress/strain curve. A figure from the prior art
utilized in Dow’s brief illustrates a typical stress/strain
curve.




Appellee’s Br. 7; J.A. 10493.
    There are three main phases of behavior, correspond-
ing to regions I, III, and IV on the figure. At first, when
an increasing force is applied to a sample of the compound
claimed by the patent, the sample pulls its initial load
20           THE DOW CHEMICAL COMPANY      v. NOVA CHEMICALS
                                                 CORPORATION


and has little or no elongation. In other words, when an
increasing force is initially applied, the sample stretches
very little, if at all. This is shown in region I in the figure
above. Then, after the sample has been subjected to the
initial load, it stretches a relatively large amount in
response to little or no increase in force. The portion of the
stress/strain curve showing these latter effects is called
the “drawing region.” The drawing region has a lower, or
relatively flat, slope because the force increases little (or
not at all), while the elongation increases significantly.
The drawing stage is shown as region III in the figure
above. 7
     After the drawing stage, there is a third phase—the
strain hardening region—which corresponds to region IV
in the figure above. The strain hardening region is the
focus of the claim term at issue here. In the strain hard-
ening region, the material hardens, and it stretches much
less in response to an increased force than in the drawing
region. At first, in the strain hardening region, there is
still some drawing effect. As the material continues to
stretch, the strain hardening effect increases and the
drawing effect decreases. When plotted, the strain hard-
ening region is curved in most instances. Because the
strain hardening region is typically curved, it does not
have a single slope. Typically, the curve will get steeper
as more force is applied.
    NOVA argues that the term “slope of strain hardening
coefficient,” ’053 patent col. 16 l. 19, is indefinite because
the patent fails to teach with reasonable certainty where




     7 Region II in the figure corresponds to a region
where the force decreases and is not relevant here.
THE DOW CHEMICAL COMPANY    v. NOVA CHEMICALS             21
CORPORATION


and how the “slope of strain hardening” should be meas-
ured. 8
     Although the patents state that “FIG. 1 shows the
various stages of the stress/strain curve used to calculate
the slope of strain hardening,” ’053 patent col. 6 ll. 40–41;
’023 patent col. 7 ll. 18–19, the patents do not contain the
FIG. 1 referenced in those passages. Nor do the patents
include any other figure showing the stress/strain curve.
The specification of the ’053 and ’023 patents teach that
“[t]he slope of strain hardening is calculated from the
resulting tensile curve by drawing a line parallel to the
strain hardening region of the . . . stress/strain curve.”
’053 patent col. 6 ll. 27–29; ’023 patent col. 7 ll. 5–7.
    At trial, Dow’s expert Dr. Hsiao testified that “one of
ordinary skill in the art would know that the slope of the
hardening curve would have to be measured at its maxi-
mum value, which reflects the best tensile performance of
the material.” Dow, 458 F. App’x at 919. We may assume
that, as Dr. Hsiao testified and as Dow repeatedly argues,
it was known that the maximum slope should be meas-
ured.
    But three methods existed to determine the maximum
slope, each providing, as Dow admits, “simply a different
way of determining the maximum slope.” Appellee’s Br. 45
(emphasis added). Dow admitted that those three meth-
ods “all typically occur at the same place—at the end of
the curve where the maximum slope is located.” Id. We
refer to these methods as the “10% secant tangent meth-
od,” “final slope method,” and “most linear method.”



    8   NOVA also argues that the claim is indefinite be-
cause it failed to identify the units for the slope of strain
hardening. In light of our disposition we need not reach
this issue.
22           THE DOW CHEMICAL COMPANY      v. NOVA CHEMICALS
                                                CORPORATION


    The 10% secant tangent method is taught by a later
Dow patent, U.S. Patent No. 6,723,398 (the “’398 patent”).
Under the 10% secant tangent method, “[t]he slope of
strain hardening is conveniently taken as the line repre-
senting a 10 percent secant tangent which is calculated
from the failure point to the point at 10 percent extension
before the failure point (where 10 percent extension
before is equal to 90 percent of the total extension or
strain).” ’398 patent col. 11 ll. 6–11. In other words, a line
is drawn between two points, one at the failure point and
one at 10% before the failure point. The slope of that line
is then calculated. See id. FIG. 2. In the final slope meth-
od, the “slope of strain hardening [is] calculated from the
slope of [a] tensile curve just prior to break.” J.A. 6662. In
the most linear method, “[t]he slope of the strain harden-
ing region (SSH) was measured by manually selecting two
points in the most linear part of the [strain hardening]
region” and dividing the change in force by the change in
elongation. J.A. 6704. The constant slope region closely
precedes the breaking point.
    For purposes of this case, Dr. Hsiao developed yet an-
other method—of his own invention—to calculate the
slope of strain hardening. Dr. Hsiao’s testing produced
curves with 1,500 data points representing the force
applied to a sample and the sample’s elongation. He then
analyzed subsets of fifty data points. For each set of fifty
data points, Dr. Hsiao used a computer to apply a linear
regression routine to fit a line to the fifty points and
calculate a slope of the resulting line. He then selected the
highest of those resulting slopes in order to find the
maximum slope.
    There is no question that each of these four methods
may produce different results, i.e., a different slope. Dr.
Hsiao testified that the 10% secant tangent method, the
final slope method, the most linear method, and the
method he invented could produce different results. In
comparison to the three other methods, Dr. Hsiao’s meth-
THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS              23
CORPORATION


od would produce a higher value. Because the methods do
not always produce the same results, the method chosen
for calculating the slope of strain hardening could affect
whether or not a given product infringes the claims.
    Neither the patent claims nor the specification here
discusses the four methods or provides any guidance as to
which method should be used or even whether the possi-
ble universe of methods is limited to these four methods.
Nor does either party argue that the prosecution history
provides any guidance. Further, Dr. Hsiao did not testify
that one of ordinary skill in the art would choose his
method over the three known methods. Indeed, he was
not even aware of the other methods at the time he did
his analysis. He admitted that he applied only his judg-
ment of what a person of ordinary skill would believe and
did not interview anyone or cite any references discussing
how a person at the time of the patent application would
have calculated the slope of strain hardening.
    The question is whether the existence of multiple
methods leading to different results without guidance in
the patent or the prosecution history as to which method
should be used renders the claims indefinite. Before
Nautilus, a claim was not indefinite if someone skilled in
the art could arrive at a method and practice that method.
Exxon, 265 F.3d at 1379. In our previous opinion, relying
on this standard, we held that the claims were not indefi-
nite, holding that “the mere fact that the slope may be
measured in more than one way does not make the claims
of the patent invalid.” Dow, 458 F. App’x at 920. This was
so because Dow’s expert Dr. Hsiao, a person skilled in the
art, had developed a method for measuring maximum
slope. See id. at 919–20.
    Under Nautilus this is no longer sufficient. “[A] pa-
tent is invalid for indefiniteness if its claims, read in light
of the specification delineating the patent, and the prose-
cution history, fail to inform, with reasonable certainty,
24           THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS
                                               CORPORATION


those skilled in the art about the scope of the invention.”
134 S. Ct. at 2124; see also id. at 2129 (“[W]e read § 112,
¶ 2 to require that a patent’s claims, viewed in light of the
specification and prosecution history, inform those skilled
in the art about the scope of the invention with reasona-
ble certainty.”). Here the required guidance is not provid-
ed by the claims, specification, and prosecution history.
    In this respect this case is quite similar to our recent
decision in Teva, decided under the Nautilus standard. In
Teva, 9 the claim limitation at issue recited the term
“molecular weight.” 789 F.3d at 1338. But there were
three relevant measures for molecular weight—peak
average molecular weight (“Mp”), number average molecu-
lar weight (“Mn”), and weight average molecular weight
(“Mw”)—where each was calculated in a different manner
and each typically had a different value. Id. We looked to
“the patent record—the claims, specification, and prosecu-
tion history—to ascertain if they convey to one of skill in
the art with reasonable certainty the scope of the inven-
tion claimed.” Id. at 1341. Neither the claims nor the
specification contained an explicit definition of molecular
weight, id., and the prosecution history contained incon-
sistent statements, id. at 1342–1344. Therefore, the
claims were indefinite under Nautilus. Id. at 1344–45.
This was so even though the patentee’s expert—like Dr.
Hsiao here—testified that someone skilled in the art could
determine which method was the most appropriate. Id. at
1338, 1341.




     9  This case was on remand from the Supreme
Court, where the Court held that subsidiary factual
findings made by a district court in claim construction are
reviewed for clear error. Teva Pharm. USA, Inc. v.
Sandoz, Inc., 135 S. Ct. 831, 841 (2015).
THE DOW CHEMICAL COMPANY     v. NOVA CHEMICALS              25
CORPORATION


    The claims here are even more clearly indefinite than
those in Teva. Here, Dr. Hsiao’s chosen method was not
even an established method but rather one developed for
this particular case. As we held in Interval Licensing, a
claim term is indefinite if it “leave[s] the skilled artisan to
consult the ‘unpredictable vagaries of any one person’s
opinion.’” 766 F.3d at 1374 (quoting Datamize, LLC v.
Plumtree Software, Inc., 417 F.3d 1342, 1350 (Fed. Cir.
2005)). 10 The claims here are invalid as indefinite, and the
award of supplemental damages must be reversed. Under
these circumstances, we need not address the cross-
appeal as to enhanced damages.
          APPEAL NO. 2014-1431 REVERSED
   APPEAL NO. 2014-1462 DISMISSED AS MOOT
                            COSTS
    Costs to NOVA.




    10  This case is unlike Biosig Instruments, Inc. v.
Nautilus, Inc., 783 F.3d 1374, 1377 (Fed. Cir. 2015). In
Biosig, we held that the prosecution history, the language
of the claims, and the knowledge of one skilled in the art
demonstrated that “a skilled artisan would understand
the inherent parameters of the invention as provided in
the intrinsic evidence” and that the claim term at issue
“informs a skilled artisan with reasonable certainty of the
scope of the claim.” Id. at 1382–84.
