JUSTICE BUSBY delivered the opinion of the Court. This interlocutory appeal concerns whether a subsequent purchaser of a home is required to arbitrate her claims against the builder for alleged construction defects. The trial court granted the builder’s motion to compel arbitration, and the builder joined two subcontractors in the arbitration, asserting that they owed it defense and indemnity obligations. After the arbitrator issued an award in favor of the builder, the builder and purchaser filed cross-motions to confirm and to vacate the award, disputing whether the subsequent purchaser was bound by arbitration clauses in the builder’s purchase-and-sale agreement with the original purchaser and in its deed to that purchaser. The trial court vacated the award against the subsequent purchaser, and it made no ruling regarding whether to vacate the award against the subcontractors, who were not yet before the court. The court of appeals affirmed. With respect to the subsequent purchaser, we hold that she was bound by the arbitration clause in the purchase-and-sale agreement under the doctrine of direct-benefits estoppel. As to the subcontractors, we agree with the court of appeals that the trial court did not vacate the award against them. They later intervened in the trial court, and our record contains no ruling on any motion to confirm or vacate the arbitration award with respect to the subcontractors. Accordingly, we reverse in part, render judgment confirming the award against the purchaser, and remand to the trial court for further proceedings. BACKGROUND In May 2014, Cody Isaacson signed an agreement with petitioner Lennar[1] to purchase a house it was building in the Enclave at Bay Colony subdivision in Galveston, Texas, as well as the underlying property. Among other matters, the Purchase and Sale Agreement (PSA) addressed how title to the property would be conveyed, the recording of the deed and what additional terms or documents were required therein, and Lennar’s right to notice and approval of any transfer or assignment of Isaacson’s rights under the PSA. The PSA also incorporated by reference the terms of Lennar’s warranty booklet (the Limited Warranty), stated that Lennar was making only those express limited warranties set forth in the Limited Warranty, and disavowed any other warranties or representations, including any warranties of workmanship, merchantability, habitability, or suitability and fitness. In addition, the PSA contained multiple disclosures regarding the home, including an Indoor Environmental Quality Disclosure concerning the likelihood of mold growth in the home. The PSA included two arbitration clauses. First, Isaacson and Lennar generally agreed to arbitrate any disputes in accordance with the American Arbitration Association’s Home Construction Mediation Procedures (the AAA rules), and the PSA defined disputes as follows: “Disputes” (whether contract, warranty, tort, statutory, or otherwise), shall include, but are not limited to, any and all controversies, disputes or claims (1) arising under, or related to, this Agreement, the Property, the Community or any dealings between Buyer and Seller; (2) arising by virtue of any representations, promises or warranties alleged to have been made by Seller or Seller’s representative; (3) relating to the personal injury or property damage alleged to have been sustained by Buyer, Buyer’s children or other occupants of the Property, or in the Community; or (4) issues of formation, validity or enforceability of this section. The general arbitration clause further provided that Isaacson had executed the agreement on behalf of his children and other occupants of the home with the intent that all such parties would likewise be bound. Second, the PSA included a clause specific to warranty disputes, which provided that “[a]ny disputes, claims or controversies relating to any items, problems, defects or difficulties covered by the Limited Warranty shall be resolved pursuant to the dispute settlement provisions covered by the Limited Warranty.” In its Limited Warranty booklet,[2] Lennar agreed to provide three types of express warranties for specific components of the home. First, Lennar provided a workmanship protection warranty that components of the home listed in the Workmanship Standards section of the booklet would perform in accordance with those standards for one year from the property’s closing date. Second, Lennar provided a systems protection warranty that components of the home listed in the Systems Standards section of the booklet would perform in accordance with those standards for two years. Third, Lennar provided a warranty that structural components of the home listed in the booklet’s Structural Standards section would perform in accordance with that section’s standards for ten years. Like the PSA, the Limited Warranty provided for arbitration of disputes—defined using substantially similar language to the PSA— in accordance with the AAA rules. On May 16, 2014, Lennar executed and recorded a Special Warranty Deed conveying title to the home and underlying property to Isaacson. The deed provided that the conveyance was made subject to “[a]ny and all restrictions, encumbrances, easements, covenants, conditions, outstanding mineral interests held by third parties, and reservations” for the property that had been recorded in the County Clerk’s office. The deed also provided that it was subject to an arbitration provision attached to the deed as Exhibit A. The attached arbitration provision contained language substantially similar to the provisions in the PSA and the Limited Warranty. That provision defines disputes as follows: “Disputes” (whether contract, warranty, tort, statutory or otherwise) shall include, but are not limited to, any and all controversies, disputes or claims (1) arising under, or related to, this Deed, the underlying purchase agreement for the sale and conveyance of the Property, the Property, the community in which the Property is located, or any dealings between Grantee and Grantor; (2) arising by virtue of any representations, promises or warranties alleged to have been made by Grantor or Grantor’s representative; and (3) relating to personal injury or property damage alleged to have been sustained by Grantee, Grantee’s children or other occupants of the Property, or in the community in which the Property is located. The attachment further provides that Exhibit A “shall run with the land and be binding upon the successors and assigns of” Isaacson. On July 31, 2015, Isaacson sold the property to respondent Kara Whiteley, conveying title via a General Warranty Deed that Isaacson executed and recorded in the county records. Shortly after purchasing the home, Whiteley “noticed a serious mold problem” and ultimately sued Lennar on March 1, 2017, after providing notice and participating in settlement negotiations pursuant to the Residential Construction Liability Act.[3] Asserting claims for negligent construction and breach of the implied warranties of habitability and good workmanship, Whiteley alleged that the home’s heating, ventilation, and cooling (HVAC) system had deficiencies that were contributing to the mold problem by creating excessive, long term, and unacceptable moisture levels. With respect to her claims for negligent construction and breach of the implied warranty of good workmanship, Whiteley alleged that Lennar had breached its duty to exercise ordinary care in its construction of the home and failed to construct the home in the same manner as would a generally proficient builder engaged in similar work and performing under similar circumstances. With respect to her habitability claim, Whiteley alleged that “[t]he mold itself, as well as the construction defects which caused the mold, are latent defects that rendered the Home unsafe, unsanitary, or otherwise unfit for living therein.” Whiteley sought actual damages, including (1) repair costs for the construction defects, (2) replacement or repair costs for goods damaged inside the home, (3) engineering and consulting fees, (4) temporary housing expenses for the duration of any repairs, and (5) attorney’s fees. Lennar filed an application to stay proceedings pending arbitration, relying on the arbitration agreements in the PSA and Limited Warranty. Whiteley opposed Lennar’s request for arbitration, arguing that she was not a party to and did not sign any of the relied-upon arbitration agreements and therefore was not bound to arbitrate under them. In reply, Lennar argued that (1) Whiteley was bound to arbitrate either as a successor in interest to Isaacson, under the doctrine of direct-benefits estoppel, or because she assumed Isaacson’s obligations under the PSA; and (2) the trial court should refer such questions of arbitrability to the arbitrator because each of the relevant arbitration clauses incorporates the AAA rules, which empower the arbitrators to determine their own jurisdiction. The trial court granted Lennar’s application for a stay and the parties proceeded to arbitration. In arbitration, Whiteley pursued her claims for negligent construction and implied warranties against Lennar. In addition to its general denial, Lennar asserted a number of affirmative defenses, including that (1) Whiteley’s claims are barred by the economic loss rule, waiver, and release; (2) Whiteley’s negligence claim is barred because she purchased the home “as is”; (3) Whiteley may not assert a claim for breach of the implied warranty of good workmanship because it was disclaimed by the original purchaser; (4) the alleged defects were not hidden or latent; (5) Whiteley misused the HVAC system and failed to mitigate her damages; and (6) the alleged defects are not attributable to Lennar. Lennar also filed counterclaims against Whiteley in the arbitration, including claims that Whiteley breached her contractual obligations under the PSA and Limited Warranty. Additionally, Lennar filed a third-party complaint against its subcontractors Big Tex Air Conditioning, Inc. f/k/a Big Tex Air Conditioning L.P. and Xalt Holding, LLC f/k/a DPIS Engineering LLP. Big Tex designed and installed the home’s HVAC system, and Xalt was responsible for various inspections of the home during construction. Lennar’s third-party complaint sought contribution and indemnity based on the subcontractors’ separate agreements with Lennar. The proceedings were conducted in accordance with the Federal Arbitration Act (FAA), see 9 U.S.C. §§ 1-16, and the arbitrator issued his award in December 2018. The arbitrator denied Whiteley all the relief she sought against Lennar and awarded Lennar attorney’s fees and costs from Whiteley, Big Tex, and Xalt. Lennar then returned to the trial court, filing a Motion to Confirm Arbitration Award and Motion to Join Additional Parties. Asserting that there was no basis for contesting the award under the FAA, see id. §§ 10-11, and that the deadline for doing so had passed, Lennar argued that the arbitrator’s Final Award must be confirmed and judgment rendered in conformance with the award. Recognizing that Big Tex and Xalt were not yet parties in the trial court, Lennar also asked that they be joined as necessary parties. Whiteley opposed Lennar’s request and filed a combined motion that included her response to Lennar’s motion to confirm, as well as a motion to vacate the arbitration award. Whiteley argued that her claims against Lennar never should have been arbitrated because (1) no valid agreement to arbitrate existed between her and Lennar, and (2) even if the PSA applies to her, her claims fall outside the scope of the agreement’s arbitration provision. Lennar filed a combined reply and response to Whiteley’s motion to vacate. In addition to arguing that Whiteley’s conduct following the trial court’s initial stay waived any objection to arbitration,[4] Lennar again argued that Whiteley was estopped from denying that she is subject to the PSA’s arbitration provisions. Lennar also argued that the recording of Exhibit A along with the Special Warranty Deed rendered that arbitration agreement a covenant that runs with the land and binds successive owners like Whiteley. The trial court denied Lennar’s motion and granted Whiteley’s, vacating the arbitration award against Whiteley. Lennar then filed this interlocutory appeal. The court of appeals affirmed. 625 S.W.3d 569 (Tex. App.— Houston [14th Dist.] 2021). Rejecting each of Lennar’s theories, the court of appeals held that (1) Exhibit A is not a covenant running with the land because an arbitration agreement does not “touch and concern” the land, id. at 577-78; (2) Whiteley did not assume the Special Warranty Deed’s arbitration agreement when she purchased the home, id. at 578-79; (3) Whiteley was not bound to arbitrate as a third-party beneficiary of the Limited Warranty, id. at 580-81; (4) direct-benefits estoppel does not apply to claims for breach of the implied warranty of good workmanship or habitability, id. at 581-82; and (5) Whiteley did not waive her objection to arbitration, id. at 582-83. The court of appeals also affirmed the trial court’s denial of the portions of Lennar’s motion specific to Big Tex and Xalt. Id. at 574-75. We granted Lennar’s petition for review. ANALYSIS Lennar challenges the court of appeals’ affirmance of the trial court’s order and raises the following issues. First, Lennar contends the trial court erred in denying its motion to confirm the arbitration award against Whiteley because (1) direct-benefits estoppel applied to estop Whiteley from avoiding the PSA’s arbitration clause; (2) the arbitration agreement attached to Isaacson’s Special Warranty Deed was a covenant running with the land; or (3) Whiteley could be compelled to arbitrate as a third-party beneficiary of Lennar’s “1-2-10 Single-Family Warranty.” Alternatively, Lennar asserts the trial court should have confirmed the arbitration award because Whiteley waived her objection to arbitration during the parties’ arbitration proceedings. Finally, Lennar argues the trial court erroneously refused to confirm the arbitration award against Big Tex and Xalt. We address each issue in turn. I. The trial court erred in granting Whiteley’s motion to vacate the final arbitration award. Under the FAA, “a party seeking to compel arbitration must establish the existence of a valid arbitration agreement and the existence of a dispute within the scope of the agreement.” Baby Dolls Topless Saloons, Inc. v. Sotero, 642 S.W.3d 583, 585-86 (Tex. 2022) (footnote omitted).[5] “[A]bsent unmistakable evidence that the parties intended the contrary, it is the courts rather than arbitrators that must decide ‘gateway matters’ such as whether a valid arbitration agreement exists” and “[w]hether an arbitration agreement is binding on a nonparty.” In re Weekley Homes, L.P., 180 S.W.3d 127, 130 (Tex. 2005).[6] These gateway matters are questions of law that we review de novo. J.M. Davidson, Inc. v. Webster, 128 S.W.3d 223, 227 (Tex. 2003). “Who is bound by an arbitration agreement is normally a function of the parties’ intent, as expressed in the agreement’s terms.” Jody James Farms, JV v. Altman Grp., 547 S.W.3d 624, 633 (Tex. 2018). “But sometimes a person who is not a party to the agreement can compel arbitration with one who is, and vice versa.” Meyer v. WMCO-GP, LLC, 211 S.W.3d 302, 305 (Tex. 2006) (footnotes omitted). Courts “have recognized six theories, arising out of common principles of contract and agency law, that may bind non-signatories to arbitration agreements: (1) incorporation by reference; (2) assumption; (3) agency; (4) alter ego; (5) equitable estoppel; and (6) third-party beneficiary.” In re Kellogg Brown & Root, Inc., 166 S.W.3d 732, 739 (Tex. 2005). We first consider whether Lennar has met its burden of showing that Whiteley is bound by the PSA’s arbitration provision under the equitable doctrine of direct-benefits estoppel. “Consistent with the federal doctrine of ‘direct benefits estoppel,’ this Court has held that a non-signatory plaintiff may be compelled to arbitrate if its claims are ‘based on a contract’ containing an agreement to arbitrate.” Id.; see also In re FirstMerit Bank, N.A., 52 S.W.3d 749, 755 (Tex. 2001) (“[A] litigant who sues based on a contract subjects him or herself to the contract’s terms.”).[7] But because direct-benefits estoppel is limited to cases where the non-signatory “seeks, through the claim, to derive a direct benefit from the contract,” although “a non-signatory’s claim may relate to a contract containing an arbitration provision, that relationship does not, in itself, bind the non-signatory to the arbitration provision.” Kellogg Brown & Root, 166 S.W.3d at 741. “While the boundaries of direct-benefits estoppel are not always clear, nonparties generally must arbitrate claims if liability arises from a contract with an arbitration clause, but not if liability arises from general obligations imposed by law.” In re Vesta Ins. Grp., Inc., 192 S.W.3d 759, 761 (Tex. 2006). “[T]he claim must depend on the existence of the contract . . . and be unable to stand independently without the contract.” G.T. Leach Builders, LLC v. Sapphire V.P., LP, 458 S.W.3d 502, 527-28 (Tex. 2015) (quotation marks omitted). When “the alleged liability arises from the contract or must be determined by reference to it . . . [,] equity prevents [the non-signatory plaintiff] from avoiding [an] arbitration clause that was part of that [contract].” Jody James Farms, 547 S.W.3d at 637. “[W]hether a claim seeks a direct benefit from a contract containing an arbitration clause turns on the substance of the claim, not artful pleading.” Weekley Homes, 180 S.W.3d at 131-32. But where the relied-upon arbitration clause is broad enough to cover both tort and contract claims, if the plaintiff pursues one “claim ‘on the contract,’ then [the plaintiff] must pursue all claims—tort and contract—in arbitration.” Id. at 132; see also Taylor Morrison of Tex., Inc. v. Skufca, 660 S.W.3d 525, 527-28 (Tex. 2023) (“If any one of the children’s claims is based on the parents’ purchase agreement, then the children must arbitrate all claims that fall under the scope of the purchase agreement’s arbitration clause.”).[8] In arguing that direct-benefits estoppel is inapplicable to her claims, Whiteley relies primarily upon (1) this Court’s prior statements that the right to pursue an implied warranty claim derives from the common law, and (2) the fact that her purchase of the home was not through the PSA with Lennar, but rather through a separate contract with Isaacson. For the reasons discussed below, we conclude that Whiteley was required to arbitrate her claims under the doctrine of direct-benefits estoppel. First, we reject Whiteley’s suggestion that any implied warranties, because they derive from the common law, would not have “become a part of or derive from the home Purchase Agreement.” To the contrary, as we have previously noted, “a warranty which the law implies from the existence of a written contract is as much a part of the writing as the express terms of the contract.” Certain-Teed Prods. Corp. v. Bell, 422 S.W.2d 719, 721 (Tex. 1968). Although such warranties are “imposed by operation of law, the obligation still arises from the contract and becomes part of the contract. Absent a contract, the warranty would not arise.” Nghiem v. Sajib, 567 S.W.3d 718, 725 (Tex. 2019).[9] Indeed, in extending the warranties of good workmanship and habitability to benefit subsequent purchasers in Gupta v. Ritter Homes, Inc., we held that such implied warranties are “implicit in the contract between the builder/vendor and original purchaser and [are] automatically assigned to the subsequent purchaser.” 646 S.W.2d 168, 169 (Tex. 1983) (emphases added).[10] Second, although Whiteley is correct that “the mere fact that the claims would not have arisen but for the [PSA] is not enough to establish equitable estoppel,” G.T. Leach Builders, 458 S.W.3d at 530, Whiteley’s implied warranty claims share more than a but-for relationship with the PSA. Because “different implied warranties behave differently,” Nghiem, 567 S.W.3d at 724, we discuss each claim in turn.[11] “The implied warranty of good workmanship serves as a ‘gap-filler’ or ‘default warranty’; it applies unless and until the parties express a contrary intention.” Centex Homes v. Buecher, 95 S.W.3d 266, 273 (Tex. 2002). Although parties may not “disclaim this warranty outright, an express warranty in their contract can fill the gaps covered by the implied warranty and supersede it if the express warranty specifically describes the manner, performance, or quality of the services.” Gonzales v. Sw. Olshan Found. Repair Co., 400 S.W.3d 52, 59 (Tex. 2013). “Thus, the implied warranty of good workmanship attaches to a new home sale if the parties’ agreement does not provide how the builder or the structure is to perform.” Centex Homes, 95 S.W.3d at 273 (emphasis added). Moreover, because “implied warranties . . . move with the used [home] by operation of law, from purchaser to purchaser,” a downstream purchaser like Whiteley “cannot obtain a greater warranty than that given to the original purchaser.” Man Engines & Components, Inc. v. Shows, 434 S.W.3d 132, 140 (Tex. 2014). Because any implied warranty of good workmanship must survive supplantation by an express warranty in the original purchase contract, Lennar’s liability for breach is not “independent of [its] contractual undertaking.” Chapman Custom Homes, Inc. v. Dall. Plumbing Co., 445 S.W.3d 716, 718 (Tex. 2014). Indeed, although Whiteley’s response brief challenges whether the PSA sufficiently set out the manner in which Lennar was to construct the home, even that assertion is one that “must be determined by reference to” the PSA. Weekley Homes, 180 S.W.3d at 132. Similarly, Whiteley’s argument that section 23 of the PSA prohibited assignment is one that cannot be determined without reference to the PSA. In other words, although liability arises in part from the general law, nonliability arises from the terms of the express warranties described in Lennar’s “1-2-10 Single-Family Warranty,” which the PSA incorporated by reference. Cf. Vesta Ins. Grp., 192 S.W.3d at 761-62 (“Thus, while liability for tortious interference arises from the general law, nonliability arises from connections with the contract.”). We therefore conclude that Whiteley’s claim for breach of the implied warranty of good workmanship does not “stand independently” of the PSA. Kellogg Brown & Root, 166 S.W.3d at 740. As we have previously recognized, however, “[w]hile the parties are free to define for themselves the quality of workmanship, there is generally no substitute for habitability.” Centex Homes, 95 S.W.3d at 275. This common-law warranty requires that “at the [completion of the purchase] there are no latent defects in the facilities that are vital to the use of the premises for residential purposes and that these essential facilities will remain in a condition which makes the property livable.” Kamarath v. Bennett, 568 S.W.2d 658, 661 (Tex. 1978). The implied warranty “only extends to defects that render the property so defective that it is unsuitable for its intended use as a home.” Centex Homes, 95 S.W.3d at 274; see also Kamarath, 568 S.W.2d at 661 (“[T]he defect must be of a nature which will render the premises unsafe, or unsanitary, or otherwise unfit for living therein.”). Unlike the implied warranty of workmanlike construction, the warranty of habitability “focuses on the state of the completed structure” and “can be waived only to the extent that defects are adequately disclosed.” Centex Homes, 95 S.W.3d at 272-74. “Thus, only in unique circumstances, such as when a purchaser buys a problem house with express and full knowledge of the defects that affect its habitability, should a waiver of this warranty be recognized.” Id. at 274. On the other hand, the implied warranty “does not include defects, even substantial ones, that are known by or expressly disclosed to the buyer.” Id. at 275. Here, among other potentially relevant provisions, the PSA included (1) a general disclaimer of the warranty of habitability,[12] (2) a section of disclosures regarding the home, (3) an Indoor Environmental Quality Disclosure concerning the likelihood of mold growth in the home, and (4) Lennar’s “1-2-10 Single-Family Warranty.” Whether those portions of the PSA were sufficient to negate any implied warranty of habitability with respect to mold growth will depend on the particulars of Lennar’s express disclosures. In sum, although its liability for breach of the implied warranty of habitability does not “arise[] solely from” the PSA, Lennar’s liability still “must be determined by reference to it,” Weekley Homes, 180 S.W.3d at 132, and therefore Whiteley’s claims do not “stand independently” of the PSA. Kellogg Brown & Root, 166 S.W.3d at 740. Because we conclude that Whiteley was bound to arbitrate pursuant to the PSA under the doctrine of direct-benefits estoppel and Whiteley did not preserve any other grounds for vacating the arbitration award, we do not reach the parties’ remaining arguments. II. The trial court has not yet addressed the award against the subcontractors. Lennar next asserts that the trial court erroneously denied its motion to confirm the arbitration award as to subcontractors Big Tex and Xalt. But in the court of appeals, Lennar focused its challenge primarily on the trial court’s grant of Whiteley’s motion to vacate, arguing that it had erroneously vacated the award against the subcontractors as well. The court of appeals disagreed, holding that the trial court’s vacatur did not extend to the award against the subcontractors. 625 S.W.3d at 574. Lennar does not challenge that holding. In addition, Lennar does not challenge the denial of its motion to join the subcontractors as parties. As a result of that ruling, the subcontractors were not before the trial court when it denied Lennar’s motion to confirm the award, and there is no indication they received proper notice of the motion or had an opportunity to be heard on the issue. Thus, like the court of appeals, “we do not construe the order as adjudicating any issues with respect to those parties.” Id. at 575. After this interlocutory appeal was taken, the subcontractors intervened in the trial court proceeding, and Lennar then filed a separate motion to confirm the award against them. No ruling on that motion appears in the record, and we express no view on its proper disposition. CONCLUSION The trial court erred in granting Whiteley’s motion to vacate and denying Lennar’s motion to confirm. Accordingly, we reverse the court of appeals’ judgment, render judgment confirming the award against Whiteley, and remand to the trial court for further proceedings. J. Brett Busby Justice OPINION DELIVERED: May 12, 2023