
553 F.3d 1150 (2009)
UNITED STATES of America FOR the USE OF LIGHTING AND POWER SERVICES, INC., Plaintiff-Appellee,
v.
INTERFACE CONSTRUCTION CORPORATION, Defendant-Appellant.
No. 07-3678.
United States Court of Appeals, Eighth Circuit.
Submitted: June 12, 2008.
Filed: January 29, 2009.
*1152 Joshua Michael Avigad, Michael P. Stephens, St. Louis, MO, for appellant.
Joseph C. Blanner, St. Louis, MO, for appellee.
Before LOKEN, Chief Judge, COLLOTON, Circuit Judge, and PIERSOL,[*] District Judge.
LOKEN, Chief Judge.
When the government awarded Interface Construction Corp. ("Interface") a substantial contract to renovate portions of a federal building in St. Louis, the Miller Act required that Interface obtain a payment bond "for the protection of all persons supplying labor and material in carrying out the work provided for in the contract." 40 U.S.C. § 3131(b)(2). Interface subcontracted electrical work to Henderson Electrical Systems, LLC ("Henderson"), which in turn contracted with Lighting and Power Services, Inc. ("LPS"), to perform that work. When Interface and Henderson ignored LPS's repeated demands for unpaid progress payments, LPS stopped work and commenced this action against Interface, Henderson, and Western Surety Company, which had issued the payment bond to Interface, to recover the amount allegedly due LPS for unpaid labor and materials furnished for the Interface contract. Interface moved to compel arbitration and now appeals the district court's[1] denial of that motion, an interlocutory appeal expressly authorized by the Federal Arbitration Act. See 9 U.S.C. § 16(a)(1)(B). We affirm.

I. Background
Interface presented its motion to compel arbitration as a Rule 12(b)(1) motion to dismiss on a limited record. Thus, our cupboard of facts is relatively bare. We know that, on April 12, 2006, Henderson submitted a proposal to Interface to provide *1153 electrical work for $237,760. The proposal stated, "This Proposal is to be made an Attachment to the Sub-contract." On April 17, LPS submitted to Henderson a proposal identical in all material respects to Henderson's proposal to Interface, including the contract amount and the statement, "This Proposal is to be made an Attachment to the Sub-contract." On April 21, Interface entered into the Prime Contract with the United States. That same day, Western Surety issued the Payment Bond required by the Miller Act in favor of "all persons having a direct relationship with [Interface] or a subcontractor of [Interface] for furnishing labor, material or both in the prosecution of the work provided for in the [Prime Contract]."
On April 27, Henderson gave LPS written notice "to proceed with providing labor for electrical work" on the project. On May 5, Interface and Henderson signed a Standard Form of Agreement Between Contractor and Subcontractor (AIA Document A401-1997) (the "Subcontract"), presumably for the work and on the terms set forth in Henderson's April 12 proposal (that portion of the Subcontract was not included in the record on appeal). So far as we know, the Subcontract did not refer to LPS or to its April 27 contract with Henderson to perform the electrical work, nor was LPS's April 17 proposal attached to the Subcontract.
LPS stopped work on the project after its demands for the unpaid balance of $98,516.04 in progress payments went unheeded. LPS then commenced this action, asserting a claim under the Miller Act to recover that amount under the Western Surety bond. The Miller Act creates a federal cause of action "separate and distinct from state law breach of contract actions." United States ex rel. Consol. Elec. & Mechs., Inc. v. Biggs Gen. Contracting, Inc., 167 F.3d 432, 435 (8th Cir. 1999); see Lighting & Power Servs., Inc. v. Roberts, 354 F.3d 817, 822 (8th Cir.2004).[2] "[T]he substance of the rights created thereby is a matter of federal not state law." F.D. Rich Co. v. United States ex rel. Indus. Lumber Co., 417 U.S. 116, 127, 94 S.Ct. 2157, 40 L.Ed.2d 703 (1974); see 40 U.S.C. § 3133(b).
This appeal concerns only whether LPS must arbitrate its Miller Act claim. As arbitration is a matter of contract, "a party cannot be required to submit to arbitration any dispute which he has not agreed so to submit." AT & T Techs., Inc. v. Communications Workers of Am., 475 U.S. 643, 648, 106 S.Ct. 1415, 89 L.Ed.2d 648 (1986) (quotation omitted). Here, Western Surety's bond contains no agreement to arbitrate, and there is no written agreement between LPS and Henderson containing an agreement to arbitrate. But the Subcontract between Interface and Henderson does contain an agreement to arbitrate claims in accordance with the Construction Industry Arbitration Rules of the American Arbitration Association. This section of the Subcontract further provides: "Except by written consent of the person or entity sought to be joined, no arbitration arising out of or relating to the Subcontract shall include ... any person or entity not a party to the Subcontract."
LPS argues that it never agreed, and may not be compelled, to arbitrate its Miller Act claim. Interface argues that LPS is subject to the agreement to arbitrate in the Subcontract because the statement in its proposal to Henderson, "This Proposal is to be made an Attachment to *1154 the Sub-contract," incorporated the terms of Henderson's Subcontract with Interface by reference. Moreover, Interface argues, LPS is equitably estopped to claim benefits under the Subcontract and yet refuse to arbitrate in accordance with its terms. We review these issues de novo. See Nitro Distrib., Inc. v. Alticor, Inc., 453 F.3d 995, 998 (8th Cir.2006).

II. Who Decides Arbitrability?
Interface argues that the issue of arbitrability must be determined by an arbitrator, not by the court. We disagree. "A dispute ... over whether the parties agreed to arbitrate [ ] will be resolved by the district court `[u]nless the parties clearly and unmistakably provide otherwise.'" Express Scripts, Inc. v. Aegon Direct Mktg. Servs., Inc., 516 F.3d 695, 701 (8th Cir.2008) (citation omitted). "Any other rule would `too often force unwilling parties to arbitrate a matter they reasonably would have thought a judge, not an arbitrator, would decide.'" McLaughlin Gormley King Co. v. Terminix Int'l Co., 105 F.3d 1192, 1194 (8th Cir.1997), quoting First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 945, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995). Here, the Subcontractthe only document containing an agreement to arbitratewas silent on this question. Accordingly, the question whether non-party LPS is bound by the Subcontract's agreement to arbitrate is for the court, not for an arbitrator, to decide. See Liberty Mut. Ins. Co. v. Mandaree Pub. Sch. Dist. # 36, 503 F.3d 709, 713 (8th Cir.2007). Interface's reliance on Buckeye Check Cashing, Inc. v. Cardegna, 546 U.S. 440, 126 S.Ct. 1204, 163 L.Ed.2d 1038 (2006), is misplaced. Buckeye expressly distinguished between the issue whether a contract is validwhich is for the arbitratorand the issue whether a valid contract contains an enforceable agreement to arbitrate a particular disputewhich is for the court. Id. at 444 & n. 1, 126 S.Ct. 1204. Here, no party challenges the validity of the Subcontract, only the scope of its agreement to arbitrate.

III. Arbitrability of the Miller Act Claim
Interface's principal argument turns on two premisesthat LPS's Complaint asserted a breach of contract claim against Interface, and that the only possible basis for this contract claim is the Subcontract. Therefore, Interface argues, LPS is bound by the arbitration provision in the Subcontract, either because LPS stated that its proposal was to be "made an Attachment to the Sub-contract," or by reason of equitable estoppel. We conclude that the first premise is faulty because LPS's Complaint asserted only a Miller Act claim to recover under the Western Surety bond. Interface asserts that "hidden within the Complaint [is] a breach of contract claim" against Interface. In support, it cites an allegation in paragraph 11: "Defendants Interface and Henderson breached their contract with [LPS]." But the Complaint did not allege a breach of contract cause of action. Rather, the paragraph alleging breach of a contractual obligation to LPS was an integral part of LPS's Miller Act claim for unpaid labor and material "provided for in a contract for which a payment bond is furnished." 40 U.S.C. § 3133(b)(1). Whether the alleged payment default was committed by Henderson or by Interface may become an issue, but it seems unlikely to affect whether LPS may recover under the Miller Act.
LPS as bond obligee could have asserted its Miller Act claim against only the bond issuer, Western Surety, without joining Interface and Henderson, as the obligee did in AgGrow Oils, L.L.C. v. Nat'l Union Fire Ins. Co. of Pittsburgh, 242 F.3d 777 *1155 (8th Cir.2001).[3] However, it is not uncommon for an obligee to join the bond obligor and the bond issuer as defendants in a Miller Act claim. See generally United States ex rel. Morris Constr., Inc. v. Aetna Cas. Ins. Co., 908 F.2d 375 (8th Cir.1990) (applying predecessor statute). That decision is understandable here, because LPS as Miller Act plaintiff may be required to prove its claim under 40 U.S.C. § 3133(b)(2) if the facts show that it had "a direct contractual relationship with a subcontractor [Henderson] but no contractual relationship, express or implied, with the contractor furnishing the payment bond [Interface]."
When LPS as bond obligee chose to join both obligor Interface and subcontractor Henderson as defendants in its Miller Act claim under the Western Surety bond, it could have joined state law breach of contract claims with its Miller Act claim. See United States ex rel. Consol. Elec. & Mechs., Inc. v. Biggs Gen. Contracting, Inc., 167 F.3d 432, 435 (8th Cir.1999); United States ex rel. Newton v. Neumann Caribbean Int'l, Ltd., 750 F.2d 1422, 1425-26 (9th Cir.1985). But the plain language of LPS's complaintwhich is all we may consider because Interface proceeded on a limited recordstates only a Miller Act claim.[4]
Stripped of its faulty premise concerning the nature of LPS's claim, Interface's incorporation by reference argument must fail. Interface relies on LPS's proposal, stating that it should be "made an Attachment to the Sub-contract." Under Missouri law, merely saying a contract is "attached" is insufficient to incorporate an arbitration clause in that contract by reference. See Dunn Indus. Group, Inc. v. City of Sugar Creek, 112 S.W.3d 421, 436 (Mo. banc 2003). Moreover, "an incorporation clause is effective only when the provision to which reference is made has a reasonably clear and ascertainable meaning." AgGrow Oils, 242 F.3d at 781 (quotation omitted). The first ambiguity is, to what "Sub-contract" was LPS's attachment statement referringa contemplated agreement that LPS and Henderson never entered into, or the subsequent Subcontract between Henderson and Interface which, as it appears in the record on appeal, contained no such attachment? The second, more serious ambiguity is, did the "attachment" proposal reflect LPS's agreement to arbitrate a future Miller Act claim on Interface's payment bond? That is exceedingly doubtful because, under Missouri law, a contract cannot incorporate by reference a second contract that is not yet in existence. See Metro Demolition & Excavating Co. v. H.B.D. Contracting, Inc., 37 S.W.3d 843, 846 (Mo.App.2001). In these circumstances, we agree with the district court that, like the bond incorporation provisions at issue in AgGrow Oils, 242 F.3d at 781, and Mandaree, 503 F.3d at 711, the ambiguous attachment statement in LPS's proposal to Henderson may not be construed as LPS's express agreement to arbitrate future Miller Act claims on the payment bond subsequently issued to Interface.
*1156 Interface's equitable estoppel argument fares no better. Interface argues that it would be inequitable to allow LPS to pursue a breach of contract claim without enforcing the arbitration provision because the Subcontract is the only basis for a contract claim against Interface. The principle is soundunder Missouri law, "A party will not be allowed to assume the inconsistent position of affirming a contract in part by accepting or claiming its benefits, and disaffirming it in part by repudiating or avoiding its obligations, or burdens." Dubail v. Med. West Bldg. Corp., 372 S.W.2d 128, 132 (1962) (quotation omitted); see Dominium Austin Partners, L.L.C. v. Emerson, 248 F.3d 720, 728-29 (8th Cir.2001) (enforcing arbitration clause). But as we have explained, LPS's Complaint asserted only a Miller Act claim which, under federal law, LPS may pursue against the bonding company without regard to Interface's fault. Interface cites no case invoking equitable estoppel to compel arbitration of a Miller Act claim. Cf. Nitro Distrib., 453 F.3d at 998-99 (refusing to compel arbitration when plaintiff did not allege violations of the contract containing the arbitration clause). Moreover, recent amendments strengthening the Act's protections cut strongly against using equitable estoppel to weaken the Act's cause of action. See 40 U.S.C. § 3133(c).
For these reasons, we conclude that the district court correctly denied Interface's motion to compel arbitration of LPS's Miller Act claim.[5] Accordingly, the order of the district court is affirmed.
NOTES
[*]  The HONORABLE LAWRENCE L. PIERSOL, United States District Judge for the District of South Dakota, sitting by designation.
[1]  The HONORABLE E. RICHARD WEBBER, United States District Judge for the Eastern District of Missouri, affirming the Report and Recommendation of the HONORABLE DAVID D. NOCE, United States Magistrate Judge for the Eastern District of Missouri.
[2]  As subcontractors may not place liens on government property, the Miller Act bond ensures full recovery of a subcontractor's out-of-pocket expenditures for labor and materials, regardless of the general contractor's fault.
[3]  In that case, bond obligor Interface might well have sought to intervene to pursue contract issues such as arbitration. See United States ex rel. MPA Constr., Inc. v. XL Specialty Ins. Co., 349 F.Supp.2d 934, 940-43 (D.Md. 2004).
[4]  Interface submitted by Supplemental Appendix an affidavit asserting that LPS during settlement negotiations confirmed that it is also seeking state law breach of contract relief. This affidavit was not part of the district court record and is not a proper part of the record on appeal. See F.R.A.P. 10(a). Accordingly, LPS's motion to strike the Supplemental Appendix is granted.
[5]  Even when a claim or issue is not subject to an agreement to arbitrate, "the district court has discretion to stay third party litigation that involves common questions of fact that are within the scope of the arbitration agreement." AgGrow Oils, 242 F.3d at 782 (quotation omitted). Stays are not uncommon in construction industry disputes involving Miller Act claims, see Consol. Elec., 167 F.3d at 435, and were explicitly contemplated by Congress when it added 40 U.S.C. § 3133(c):

This bill does not void subcontract provisions requiring arbitration or other alternative methods of resolving disputes. Such provisions would remain enforceable with a claimant's Miller Act rights preserved by a timely suit that can be stayed pending the outcome of the subcontract dispute resolution procedure. The bill respects the freedom of the parties to the subcontract to specify means to resolve their disputes and the exclusive jurisdiction of the district court to decide issues arising under the Miller Act.
H.R.Rep. No. 106-277(I), at 5 (1999). However, this issue was not raised in the district court.
