The opinion
EMILIO M. GARZA, Circuit Judge,
dissenting:
I
Because royalty suspension is a term or condition of royalty payment under the lease and the “calculate and pay” clauses of the assignment contracts make the overriding royalty interests subject to the same terms and conditions as the landowner’s royalty under the lease, I respectfully dissent from the majority’s conclusion that the assignment contracts are ambiguous.
Royalty suspension is unambiguously a term or condition of the landowner’s royalty under the lease. The first footnote of the lease states, “This lease may be eligible for royalty suspension pursuant to PL *496 104-58.” PL 104-58 refers to Public Law No. 104-58, which includes the Outer Continental Shelf Deep Water Royalty Relief Act (hereinafter “DWRRA”). According to the DWRRA, “suspension of royalties shall be set at a volume of not less than ... 87.5 million barrels of oil equivalent for leases in water depths greater than 800 meters.” Pub.L. No. 104-58. It is undisputed that because this lease covered a block of property located in water depths greater than 800 meters, the landowner’s royalty is suspended on the first 87.5 million barrels of oil produced under the lease. The footnote next states, “If eligible, Sections 5 and 6 [providing for payment of royalty to Lessor] of this lease instrument will be suspended by 30 C.F.R. Part 26.... ” 30 CFR Part 260 1 refers to Outer Continental Shelf Oil and Leasing, 43 U.S.C. § 1331 et seq., where the provisions of the DWRRA are codified. The footnote thus clearly requires that if the lease is eligible for royalty suspension under the DWRRA, Sections 5 and 6 of the lease will be suspended. As Sections 5 and 6 of the lease provide instructions for calculating and paying the landowner’s royalty under the lease, the footnote unambiguously makes royalty suspension a term or condition of payment of the landowner’s royalty under the lease.
The majority, however, finds it ambiguous whether the footnote is a term or condition of the lease because the footnote states the lease “may be eligible” rather than “shall be eligible.” The majority might be correct if the footnote did not also state, “If eligible, Sections 5 and 6 of this lease instrument will be superseded by 30 CFR Part 26 .... ” (emphasis added). Black’s Law Dictionary defines a “term” as a “contractual stipulation,” Blaok’s Law DICTIONARY 1608 (9th ed. 2009), and a “condition” as “a future and uncertain event on which the existence or extent of an obligation or liability depends; an uncertain act or event that triggers or negates a duty to render a promised performance.” Id. at 333 . The footnote clearly stipulates that the lease’s provisions for payment of royalties are superseded by the DWRRA if the lease is eligible for royalty suspension, thus qualifying the lessee’s contractual duty to make royalty payments to the United States. Where the lease is eligible for royalty suspension, the footnote negates the lessee’s duty to make royalty payments. As such, royalty suspension is a term or condition of the landowner’s royalty under the lease.
The “calculate and pay” clauses in the assignment contracts unambiguously make the overriding royalty interests subject to the same terms and conditions as the landowner’s royalty under the lease. The “calculate and pay” clauses of the Westport Assignment to the Belcher Group state, “The overriding royalty interest assigned herein shall be calculated and paid in the same manner and subject to the same terms and conditions as the landowner’s royalty under the Lease.” The “calculate and pay” clause in the Westport to Chevron Assignment contains nearly identical language. The majority holds “the ‘calculate and pay’ clauses in the ORRI assignment contracts do not clearly and explicitly express the intent that overriding royalty payments shall be suspended whenever the U.S. landowner royalties are suspended under the DWRRA.” Ante, at 482. The majority thus finds it ambiguous whether the assignment contracts apply royalty suspension to overriding royalty interests. The plain language of the “calculate and pay” clauses state, however, that payment *497 of the overriding royalties must be subject to the same terms and conditions as the landowner’s royalty under the lease. The Oxford English dictionary defines “subject to” as “dependent or conditional upon.” OxfoRd English Dictionary 1427 (10th ed. 1999); see also Webster’s Third New International DiCtionary 2275 (1993) (defining “subject to” as “to be conditioned, affected, or modified in some indicated way: having a contingent relation to something and usually dependent on such relation for final form, validity, or significance”). Thus, the “calculate and pay” clauses clearly and explicitly import terms and conditions from the lease as limitations on the scope of the overriding royalty rights.
The majority, emphasizing the longstanding distinction between overriding royalty interests and royalties reserved by the landowner, holds it is ambiguous whether the “calculate and pay” clauses require application of royalty suspension to the overriding royalty interests. Ante at 491. The majority holds the assignment contracts lack “any clear indication” that royalty suspension was intended to apply to the overriding royalty interests. Id. The majority is correct that overriding royalty interests are generally paid in addition to the usual landowner’s royalty reserved to the lessor. 38 Am.Jur.2d Gas and Oil § 201. As such, the parties to overriding royalty interest assignment contracts are free to set terms for the calculation and payment of such interests that are distinct from the terms of payment of the landowner’s royalty. See id. Here, however, the assignment contracts contain a clear directive that the overriding royalty interests “shall be calculated and paid in the same manner and subject to the same terms and conditions as the landowner’s royalty under the Lease.” If the parties did not intend the clear import of the contracts’ language, they may seek to reform the contract. Agurs v. Holt, 232 La.1026, 95 So.2d 644, 645 (1957). Where, however, the language of a contract is clear and unambiguous, we lack the authority to look beyond the four corners of the document in search of the parties’ intent. La. Civ.Code Ann. art.2046; Taita Chem. Co., v. Westlake Styrene Corp., 246 F.3d 377, 386 (5th Cir.2001).
The majority relies on the fact that it was not certain the lease would qualify for suspension of the United States’ landowner royalty under the DWRRA at the time the lease at issue in this case was signed as a core source of ambiguity in the “calculate and pay” clauses. The majority correctly notes that prior to our decisions in Santa Fe Snyder Corp. v. Norton, 385 F.3d 884 (5th Cir.2004), and Kerr-McGee Oil & Gas Corp. v. U.S. Dep’t of Interior, 554 F.3d 1082 (5th Cir.2009), there was some uncertainty surrounding whether a particular lease would qualify for royalty suspension. 2 Nonetheless, this uncertainty does not translate into ambiguity as to whether the assignment contracts require the overriding royalty payments to be subject to the same terms and conditions as the landowner’s royalty under the lease. The majority assumes that because it was debatable whether royalty suspension would apply, the parties to the assignment contracts did not intend royalty suspension to be one of the terms and conditions of payment that the overriding royalties are subject to. Ante, at 492-93.
*498 This assumption is unwarranted. The parties to the assignment contract may have intended exactly what the plain language of the “calculate and pay” clauses state: to make the calculation and payment of the overriding royalties subject to the same terms and conditions as the landowner’s royalty under the lease. A lack of clarity surrounding when the royalty suspension period would apply does not evince a lack of clarity regarding whether the royalty suspension period was a term of the lease that the overriding royalties became subject to through the “calculate and pay” clauses.
The majority also concludes the “granting” clauses of the assignment contracts make the meaning of the “calculate and pay” clauses ambiguous. The granting clause in the Westport Assignment to the Belcher Group states, “The undersigned ... does hereby CONVEY, TRANSFER, ASSIGN, AND SET OVER unto the following parties ... the interest set out opposite their names, as an overriding royalty interest payable out of all oil, gas, casinghead gas and associated substances produced, saved and marketed from the lease.” (emphasis added). The granting clause in the Westport to Chevron Assignment states, “The interest assigned herein is subject to ... an overriding royalty interest totaling one percent (1%) of 8/8ths ... of oil and gas production saved, removed, or sold from the Lease.” (emphasis added). The majority implies that if the parties intended to require the overriding royalty owners to wait until the lease produced 87.5 million barrels of oil before receiving royalty payments, the phrasing of the granting clauses would not have explicitly granted the overriding royalty owners an interest in all or 8/8ths of production. This is unconvincing. Even within the four corners of the assignment contract to the Belcher group, the “granting” clause was clearly never meant to be unqualified. In the ORRI assignment to the Belcher group, exceptions to royalty due on production are listed explicitly in the assignment contract. For example, the assignment contract states,
The overriding royalty interest conveyed shall not, in any event, be paid or accrued upon any oil, gas, casinghead gas and other hydrocarbon substances used for operation, development or production purposes or unavoidably lost; and no overriding royalty shall be paid upon gas used in repressuring or recycling operations or pressure maintenance operations.
Moreover, the clear language of the “calculate and pay” clauses in both of the assignment contracts qualify the granting clauses by stating that the overriding royalty interests are to be calculated and paid “subject to the same terms and conditions as the landowner’s royalty under the lease.” (emphasis added).
The majority also finds the assignment contracts ambiguous because there is no reference to royalty suspension in the assignment contracts. The lack of the explicit reference to royalty suspension in the assignment contracts proves nothing. The “calculate and pay” clauses incorporate the terms and conditions of the landowner’s royalty under the lease. Even under the proposed interpretation of the “calculate and pay” clauses that the majority urges, the terms and conditions the “calculate and pay” clauses allegedly refer to, the so-called “mechanics” of payment, are not explicitly stated in the assignment contracts. The fact that the assignment contracts do not both incorporate the royalty suspension provision by reference to the terms and conditions of the landowner’s royalty under the lease and mention the royalty suspension provision by name does not an ambiguity make. Where a term is incorporated by reference to an extrinsic agreement, the contract need not *499 also mention the incorporated term within the four corners of the contract. See Petrohawk Props., L.P. v. Chesapeake La., L.P., 689 F.3d 380, 394 (5th Cir.2012) (holding provisions incorporated by reference have identical force and effect to provisions within the contract itself). 3
The majority also finds support for concluding the “calculate and pay” clauses are ambiguous in the fact that the overriding royalty interest owners were not a party to the lease. This is puzzling. It is well-established that when a contract incorporates terms of an extrinsic agreement by reference, the parties to the contract may not rely on the fact that they are not parties to the extrinsic agreement as a source of ambiguity. See JS & H Constr. Co. v. Richmond Cnty. Hosp. Auth., 473 F.2d 212, 216 (5th Cir.1973) (holding sub-contractor bound by arbitration provision incorporated by reference from the general conditions of contract between primary contractor and principal). 4 Despite the *500 majority’s assertions to the contrary, the assignment contracts make a clear and unambiguous statement that payments of the overriding royalties will be limited by the terms and conditions of the landowner’s royalty under the lease.
Finally, Judge Higginson’s concurring opinion contends the grammatical structure of the “calculate and pay” clauses support a finding of ambiguity. Although I agree with Judge Higginson that grammatically the clauses are susceptible to two different interpretations, under either reading the “calculate and pay” clauses unambiguously require application of royalty suspension to the overriding royalty interests. Admittedly, the prepositional phrase and subordinated clause “in the same manner and subject to the same terms and conditions” may modify the “calculate and pay” verb phrase, as Appellants imply, or may modify the subject of the sentence, “The overriding royalty interest,” as Total and Statoil urge. Judge Higginson thus asserts it is ambiguous whether the “calculate and pay” clauses answer the question of whether the overriding royalty owners are entitled to a royalty payment, or merely provide instructions for the how to calculate and pay the royalty payments that are due under the assignment contract. Regardless of whether the lease is eligible for royalty suspension and the payment due is zero or the lease is ineligible for royalty suspension and a monetary payment is due, however, royalty suspension is inextricably linked to the calculation of the amount of payment due to the landowner under the lease. Thus, even if “terms and conditions” modifies “calculated and paid,” “terms and conditions” modifies entitlement to the royalties vel non.
II
Appellants also claim that in the event we reject their interpretation of the “calculate and pay” clauses as unreasonable, the original parties to the assignment contracts made a mutual mistake in drafting the “calculate and pay” clauses. The district court cited two reasons for denying Appellants’ claim for reformation. First, the district court held Appellants were attempting “to make an end-run around the parole-evidence rule by framing [their] argument as a request for reformation.” The district court held that because the assignment contracts were unambiguous, parole evidence is not admissible to create ambiguity. Second, the district court held that because Total and Statoil, as non-parties to the original contracts, were entitled to rely on the integrity of the assignment contracts, reformation would imper-missibly prejudice Total and Statoil. The district court misconstrued Louisiana’s reformation law on both points.
The district court erred by failing to admit Appellants’ extrinsic evidence of mutual mistake. When making a claim for reformation the claimant may offer parole evidence, not to vary the terms of the written instrument, but to show the “writing does not express the true intent or agreement of the parties.” First State Bank & Trust Co. of E. Baton Rouge Parish v. Seven Gables, Inc., 501 So.2d 280, 289 (La.Ct.App.1986) (citing Valhi, Inc. v. Zapata Corp., 365 So.2d 867, 870 (La.Ct.App.1978)). “Even if the language utilized is clear and unambiguous, parol evidence is admissible to establish that the language does not embody the essence of the agreement to which there was mutual assent.” Valhi, Inc., 365 So.2d at 870 . The district court thus erred by refusing to admit extrinsic evidence of mutual mistake simply because the contract is unambiguous.
The district court also erred by denying Appellants’ reformation claim on the grounds that Total and Statoil, as third parties, were entitled to rely on the integ *501 rity of the assignment contracts. Under Louisiana law, reformation of a contract is impermissible once third parties have relied on the integrity of the written instrument. Lewis, 653 So.2d at 1260. Where, however, the rights of third parties would not be prejudiced by reformation, reformation is permissible. See Samuels v. State Farm Mut. Auto. Ins. Co., 939 So.2d 1235, 1241 (La.2006); M.R. Bldg. Corp. v. Bayou Utils., Inc., 637 So.2d 614, 617 (La.Ct.App.1994) (permitting reformation where rights of third party successor in chain of title would not be prejudiced by reformation). While Louisiana law is clear that third parties are entitled to rely on the integrity of the contracts, third parties must have actually relied on the erroneous contract language to be prejudiced. See Samuels, 939 So.2d at 1241 (“There are simply no rules of contractual interpretation that would lead us to ignore the clear intent of the parties to the fortuitous benefit of a third party insurance company who did not even rely on this error in issuing its own policy.”); cf. Am. Elec. Power Co. v. Affiliated FM Ins. Co., 556 F.3d 282, 288 (5th Cir.2009) (denying claim for reformation where third party assumed and relied on contract and there was no indication third party would have known of error). The district court thus erred in denying Appellants’ claim for reformation on the basis that Total and Statoil were entitled to rely on the unambiguous contract language.
Ill
Accordingly, I would affirm the district court’s holding that the assignment contracts unambiguously apply the royalty suspension provision of the DWRRA to the overriding royalty interest owners. I would reverse the district court’s grant of summary judgment on Appellants’ claim for reformation, but only on the grounds specifically stated by the district court.
Respectfully, I dissent.
. Because 30 CFR Part 260 refers to Outer Continental Shelf Oil and Leasing, 43 U.S.C. § 1331 et seq., and 30 CFR Part 26 does not exist, the footnote likely intended to refer to 30 CFR Part 260.
. See Santa Fe Snyder Corp., 385 F.3d at 892-93 (holding Department of Interior regulation restricting the DWRRA's royalty suspension provisions to fields that had not produced prior to enactment of Act was invalid); Kerr-McGee Oil & Gas Corp., 554 F.3d at 1083 (holding Department of Interior regulation requiring payment of royalties on volumes less than volume thresholds set by the DWRRA when gas prices reached certain levels was invalid).
. The majority’s attempt to distinguish Petro-hawk Properties is unavailing. Ante at 491 n. 13. In that case we held the parties adopted a provision of an earlier lease that was incorporated by reference in the new lease. Petrohawk Props., 689 F.3d at 394 . Importantly, the new lease did not explicitly mention the provision at issue, an exclusion of the warranty of title. Id. Rather, the new lease merely incorporated all provisions other than those explicitly designated. Id. The majority attempts to distinguish Petrohawk Properties on two grounds. First, the majority notes that in Petrohawk Properties the parties to the new lease were the same parties as the parties to the old lease. This is a distinction without a difference. Nowhere in Petrohawk Properties did we state or imply the fact the parties to the new lease and the old lease were identical was relevant to our holding that the exclusion of the warranty of title was incorporated by reference. Id. Moreover, the majority cites no authority for the proposition that incorporation by reference is more effective where the parties to both contracts are identical. Second, the majority states that, unlike here, the parties in Petrohawk Properties "expressly re-adopted the exclusion of warranty of title clause.” Ante at 491 n. 13. This assertion is false. In Petrohawk Properties the new lease stated, "In conjunction with this correction of the description of the leased premises, of the primary term and with the additional provisions, Lessor ratifies, adopts, and confirms the Lease, as corrected....” Record Excerpt of Appellant Petrohawk Properties, L.P. at 80, Petrohawk Props., (No. 11-30576). Nowhere did the new lease mention the exclusion of warranty of title provision of the old lease. Id. at 79-81. Moreover, the exclusion of the warranty of title "provision” in the old lease was hardly a model of clarity. The district court held the old lease had no implied warranty of title provision because it contained "a scratched through warranty of title provision.” Chesapeake La., L.P. v. Petrohawk Props., L.P., 5:09-cv-013 85-DEW-MLH, No. 09-1385, Ruling on Merits at 6 (E.D.La. May 27, 2011). Therefore, Petrohawk Properties supports the proposition I rely on it for: the fact the assignment contracts here did not mention royalty suspension by name is not a convincing reason for finding it ambiguous whether the contracts incorporated the royalty suspension provision of the lease.
. The majority emphasizes that in JS & H Constr. Co. the provision at issue was an agreement to arbitrate disputes arising under the contract. Ante at 491 n. 13. We thus based our holding that the sub-contractor was bound to arbitrate both on (1) the strong Congressional policy favoring arbitration and (2) "[t]he ... undisputed proposition ... that as a matter of contract law, incorporation by reference is generally effective to accomplish its intended purpose where, as here, the provision to which reference is made has a reasonably clear and ascertainable meaning.” JS & H Const. Co., 473 F.2d 212 at 215 . In JS & H Const. Co. we correctly recognized that under Louisiana law where a contract incorporates terms of an extrinsic agreement by reference, the fact the identity of the parties to the contract differ from the parties to the extrinsic agreement does not render the incorporation ineffective. See also Harper v. Home Indem. Co., 140 So.2d 653, 657 (La.Ct.App.1962) ("[W]e conclude that all the provisions of the initial contract have been incorporated into and form a part and portion of the subcontract just as effectively as if fully written and incorporated therein.”).