HOWARD, Circuit Judge.

The Section 8 program is a vast effort on the part of federal, state, and local authorities to provide decent, safe, and sanitary housing to low-income families, the elderly, and the disabled. The program is administered by the U.S. Department of Housing and Urban Development ("HUD") in conjunction with state and local public housing agencies across the country. Under the part of the program at issue here,1 state and local agencies enter into housing assistance payments ("HAP") contracts with private landlords, and the landlords agree to make units available to Section 8-assisted households. The assisted households, in turn, pay 30 percent of their monthly adjusted income to their landlords in rent; the landlords receive the remainder of the rent from the relevant public housing agency; and the public housing agencies are fully reimbursed by HUD.2 The payments from the state and local agencies to the Section 8 landlords are adjusted periodically according to guidelines promulgated by HUD.

Plaintiffs-appellants are five limited partnerships that own multifamily housing rental projects in southern and central Maine. All of the partnerships have entered into HAP contracts with the Maine State Housing Authority ("Maine-Housing") in order to participate in the Section 8 program. In December 2009, the partnerships sued MaineHousing in federal district court for breach of contract, alleging that MaineHousing had wrongfully refused to grant them certain annual increases in their Section 8 payments (although MaineHousing has allowed some upward adjustments). MaineHousing, while denying the plaintiffs' allegations, impleaded HUD as a third-party defendant, arguing that if MaineHousing had breached its contracts with the partnerships, then it had done so only at HUD's direction. All parties sought summary judgment; a magistrate judge recommended judgment for Maine-Housing and HUD on the grounds that no material breach of contract had occurred; and the district court adopted the magistrate's recommended decision. The partnerships appeal, and we affirm.

I.

Although this case ultimately turns on a narrow question of contract law, it arises in the context of a complex web of statutes and regulations governing federal housing aid. In 1974, Congress amended the New Deal-era Housing Act to add the provision commonly known as "Section 8"; this provision authorized the HUD Secretary "to enter into annual contributions contracts with public housing agencies pursuant to which such agencies may enter into contracts to make assistance payments to owners of existing dwelling units." Housing and Community Development Act of 1974, Pub.L. No. 93-383, § 201(a), 88 Stat. 633, 662 (codified as amended at 42 U.S.C. § 1437f(b)(1)) (amending United States Housing Act of 1937, Pub. L. No. 75-412, 50 Stat. 888). While these "annual contributions contracts" make reference to particular projects, the only parties to the annual contributions contracts are HUD and the public housing agencies administering the Section 8 program. Between 1975 and 1978, HUD and MaineHousing entered into annual contributions contracts covering each of the five sites at issue in the present litigation.

The original Section 8 statute provided that rents paid to landlords at program sites would be adjusted on at least an annual basis "to reflect changes in the fair market rentals established in the housing area for similar types and sizes of dwelling units or, if the Secretary determines, on the basis of a reasonable formula." 88 Stat. at 663 (codified at 42 U.S.C. § 1437f(c)(2)(A)). To guard against these rent adjustments producing a windfall for Section 8 landlords, the statute added the caveat that automatic adjustments "shall not result in material differences between the rents charged for assisted and comparable unassisted units, as determined by the Secretary." Id. (codified at 42 U.S.C. § 1437f(c)(2)(C)). These statutory provisions remain in force today.

Pursuant to Section 8, HUD publishes "automatic annual adjustment factors" for specific Census regions and metropolitan areas that reflect changes in the Consumer Price Index for rent and utilities over the previous year. See 24 C.F.R. §§ 888.201.204 (2012); 77 Fed. Reg. 22,340, 22,340-43 (Apr. 13, 2012). HUD regulations state that Section 8 rents should be calculated by multiplying the applicable annual adjustment factor for the appropriate Census region or metropolitan area by the rent stipulated by contract for each unit. 24 C.F.R. § 888.203.

HUD has also drafted a standard form contract for state and local agencies to use when entering into agreements with Section 8 landlords. Once HUD and Maine-Housing had entered into annual contributions contracts covering the five sites in question, MaineHousing entered into housing assistance payments contracts with owners of the five properties. The HAP contracts varied in duration, with the longest providing for renewals over the course of 40 years, until 2018. All of the HAP contracts contained a provision, section 1.9(b)(2), stating that each year, "the Contract Rents shall be adjusted by applying the applicable Automatic Annual Adjustment Factor most recently published by the Government." All of the contracts also included an "overall limitation clause" (section 1.9(d)), which states that:

At the outset of the Section 8 program's existence, public housing agencies applied the automatic annual adjustment factors published by HUD and granted regular rent increases to Section 8 landlords; HUD, for its part, funded these rent increases through its annual contributions to the public housing agencies. In the early 1980s, however, officials at HUD became concerned that the automatic annual adjustments were pushing rents at some Section 8 sites well above the market rates for comparable unsubsidized units. In 1983, when HUD and a local housing authority sought to prevent an automatic annual adjustment from taking effect at a Section 8 site in Bremerton, Washington, the affected landlord filed a federal suit. The Ninth Circuit held that — despite the overall limitation clause in the HAP contract between the Section 8 landlord and the local housing agency — the landlord was still entitled to automatic annual adjustments in rental payments. Rainier View Assocs. v. United States, 848 F.2d 988, 990-91 (9th Cir. 1988), cert. denied, 490 U.S. 1066, 109 S.Ct. 2065, 104 L.Ed.2d 630 (1989). HUD refused to apply the Rainier View decision outside of the Ninth Circuit, and other courts disapproved of Rainier View's holding. See, e.g., Carmichaels Arbors Assocs. v. United States, 789 F.Supp. 683, 685, 688-89 (W.D.Pa.1992); Sheridan Square P'ship v. United States, 761 F.Supp. 738, 743-44 (D.Colo.1991); Nat'l Leased Hous. Ass'n v. United States, 22 Cl.Ct. 649, 652, 659-60 (Cl.Ct.1991).

With litigation over the HAP contracts pending in various federal courts, Congress passed a series of amendments addressing HUD's efforts to rein in rent increases. The first two of these amendments, enacted in 1988 and 1989, clarified the process by which the HUD Secretary could deny automatic annual adjustments at Section 8 sites. Under the amendments, HUD or a public housing agency could deny an automatic annual adjustment at a Section 8 site by submitting a "comparability study" to the project owner at least sixty days before the annual adjustment was set to take effect. See Housing and Community Development Act of 1987, Pub. L. 100-242, § 142(c)(2), 101 Stat. 1815, 1850 (1988) (codified at 42 U.S.C. § 1437f(c)(2)(C)); Department of Housing and Urban Development Reform Act of 1989, Pub. L. No. 101-235, § 801(c), 103 Stat. 1987, 2058 (same).

After the 1988 and 1989 amendments, Section 8 landlords in Washington and California brought suit again, claiming that their HAP contracts entitled them to automatic annual adjustments without regard to the results of comparability studies conducted by HUD. The Ninth Circuit reiterated its holding in Rainier View and "rejected HUD's argument that an `Overall Limitation' provision in the contracts permitted HUD to use market rates to cap rent adjustments." Alpine Ridge Grp. v. Kemp, 955 F.2d 1382, 1383-84 (9th Cir. 1992) (citing Rainier View, 848 F.2d at 990-91). The Supreme Court granted certiorari and reversed the Ninth Circuit's decision. As Justice White wrote for a unanimous Court, "the contract language is plain that no project owner may claim entitlement to formula-based rent adjustments that materially exceed market rents for comparable units." Cisneros v. Alpine Ridge Grp., 508 U.S. 10, 21, 113 S.Ct. 1898, 123 L.Ed.2d 572 (1993). The Alpine Ridge Court concluded that the overall limitation clause affords HUD "sufficient discretion" to design and implement a method for ensuring that contract rents do not rise above market rates. Id.

One year after the Alpine Ridge decision, Congress amended the Section 8 statute to place further limits on automatic annual adjustments. The 1994 law provided, in pertinent part, that:

Pub. L. No. 103-327, 108 Stat. 2298, 2315 (codified at 42 U.S.C. § 1437f(c)(2)(A)).3

Whereas the 1988 and 1989 amendments saddled HUD with the burden of producing a "comparability study" whenever it sought to withhold an automatic adjustment, the 1994 amendment seemed to shift the onus onto landlords to demonstrate that adjusted rents would not exceed the market rent for comparable units. See Greenleaf Ltd. P'ship v. Ill. Hous. Dev. Auth., No. 08 C 2480, 2009 WL 5166225, at *4-5, 2009 U.S. Dist. LEXIS 119375, at *11-14 (N.D.Ill. Dec. 23, 2009). HUD addressed this apparent tension in 1995 with the promulgation of Notice H 95-12, which provided state and local housing authorities with detailed guidelines for implementing the previous year's statutory changes. Notice H 95-12 directed housing authorities to consult a document published annually by HUD that lists "fair market rents" for different unit types on a regional basis.4 Where the rent for a Section 8 unit that would result from the automatic adjustment is higher than the corresponding fair market rent listed in the HUD-published tables, Notice H 95-12 instructs the public housing authority to presume that the contract rent is above-market. See U.S. Dep't of Hous. & Urban Dev., Notice H 95-12 (Mar. 7, 1995); see also U.S. Dep't of Hous. & Urban Dev., Notice H 2002-10 (May 17, 2002) (carrying forward Notice H 95-12 method); 77 Fed. Reg. 22,340, 22,341 (Apr. 13, 2012) (carrying forward Notice H 2002-10).

In promulgating Notice H 95-12, HUD was aware that most Section 8 sites were subject to the same standard form HAP contracts, and HUD was likewise aware that under the overall limitation clause in those contracts, Section 8 landlords were entitled to receive above-market rents to the extent that such differences existed at the outset of their contracts. See Notice H 95-12, at 3 ("need to assure that the initial difference which existed in the initial contract rents is protected, as required by the [HAP] contract"). Accordingly, Notice H 95-12 prescribed a formula for calculating this "initial difference": 0.1 times the initial Section 8 contract rent. Put differently, HUD adopted an assumption that, from the outset, public housing agencies were paying Section 8 landlords 10 percent more than the fair market rents for comparable units.

As long as the difference between the adjusted rent and the fair market rent is less than this "initial difference," Notice H 95-12 allows state and local housing agencies to continue to grant rent increases based on the automatic annual adjustment factors. However, if the difference between the adjusted rent and the HUD-published fair market rate rises to more than 10 percent of the initial contract rent, Notice H 95-12 instructs housing authorities to deny further upward adjustments to Section 8 landlords. A Section 8 landlord can only escape from under this ceiling by submitting its own rent comparability study showing that, despite the discrepancy with HUD's published fair market rents, the Section 8 unit is actually underpriced relative to comparable unsubsidized units in the area.

Up until the publication of Notice H 95-12, MaineHousing made rent adjustments at all five properties every year in accordance with the automatic annual adjustment factors published by HUD. For the first decade after Notice H 95-12 was promulgated, MaineHousing denied the landlords' requests for further upward adjustments, citing the limitations imposed by the HUD notice. In 2005, all five landlords submitted rent comparability studies to MaineHousing in an effort to show that the 10 percent formula underestimated the "initial difference" at their sites. Based on these studies, and at the urging of Maine-Housing, HUD agreed to let the five landlords use an alternative method for calculating the initial differences at their sites. Rents rose at all five sites in 2005, with increases of up to $1,092 per unit per year (although the amount of the increase varied from unit to unit and site to site). Rents at three of the five sites have remained at 2005 levels, while HUD has allowed further upward adjustments at the two other sites in subsequent years.

II.

Despite the 2005 rent adjustments for all five sites and additional increases at two of the five sites in subsequent years, owners of the five sites filed a complaint against MaineHousing in federal district court in December 2009 alleging three counts of breach of contract. Before addressing the merits of the landlords' complaint, we pause to consider whether the suit belongs in federal court at all. Although none of the parties raise the issue on appeal, we have an obligation to inquire into our subject matter jurisdiction sua sponte. Liu v. Amerco, 677 F.3d 489, 492-93 (1st Cir.2012).

In their complaint, the plaintiffs invoke federal subject matter jurisdiction pursuant to 28 U.S.C. § 1331, which grants district courts "original jurisdiction of all civil actions arising under the Constitution, laws, or treaties of the United States." Yet their only claims are for breach of contract, and they appear to acknowledge that their breach-of-contract claims arise under the laws of the State of Maine. As a general rule, federal courts lack subject matter jurisdiction over state law breach-of-contract actions where, as here, the plaintiffs and the defendant hail from the same state. See Mass. Universalist Convention v. Hildreth & Rogers Co., 183 F.2d 497, 499 (1st Cir.1950) (per curiam). Federal courts allow an exception to this rule only in the rare instance where the contract is governed by state law but a "federal issue is decisive" to the dispute and "the federal ingredient ... is sufficiently substantial to confer the arising under jurisdiction." E.g., W. 14th St. Commercial Corp. v. 5 W. 14th Owners Corp., 815 F.2d 188, 196 (2d Cir.1987).

The federal ingredient doctrine applies in a "special and small category of cases" where a "state-law claim necessarily raise[s] a stated federal issue, actually disputed and substantial, which a federal forum may entertain without disturbing any congressionally approved balance of federal and state judicial responsibilities." Gunn v. Minton, ___ U.S. ___, 133 S.Ct. 1059, 1065, 185 L.Ed.2d 72 (2013) (internal quotation marks omitted); see also Rosselló-González v. Calderón-Serra, 398 F.3d 1, 12-13 (1st Cir.2004). The Supreme Court recently reaffirmed the doctrine's vitality in Grable & Sons Metal Products, Inc. v. Darue Engineering & Manufacturing, 545 U.S. 308, 125 S.Ct. 2363, 162 L.Ed.2d 257 (2005). And although we have emphasized that federal ingredient jurisdiction "should be applied with caution," Metheny v. Becker, 352 F.3d 458, 460 (1st Cir.2003) (internal quotation marks omitted), this is one of the few cases that fits squarely within the federal ingredient exception.

The dispute in this case involves a federal contractor's implementation of a federal program; the contracts at issue were drafted and approved by a federal agency and signed by a federal official; and the plaintiffs allege that the contractor (here, MaineHousing) was in breach of the agreement by following a guideline promulgated by a federal agency pursuant to a federal statute. Singly, none of these "federal ingredients" — a claim against a federal contractor; an agreement drafted and approved by a federal agency; a defense based on a federal statute or guideline — would be sufficient to establish "arising under" jurisdiction. See, e.g., Empire Healthchoice Assur., Inc. v. McVeigh, 547 U.S. 677, 699-701, 126 S.Ct. 2121, 165 L.Ed.2d 131 (2006); Louisville & Nashville R.R. Co. v. Mottley, 211 U.S. 149, 152-153, 29 S.Ct. 42, 53 L.Ed. 126 (1908); Lindy v. Lynn, 501 F.2d 1367, 1369 (3d Cir.1974); Ippolito-Lutz, Inc. v. Harris, 473 F.Supp. 255, 259 (S.D.N.Y.1979). Yet the scope of federal ingredient jurisdiction is determined by the totality of the circumstances, not by a single-factor test. See Grable, 545 U.S. at 313-14, 125 S.Ct. 2363. Based on the totality of the circumstances, we find that the federal ingredients of the case predominate.

It is of particular significance here that "[f]ederal jurisdiction is favored in cases that present `a nearly pure issue of law that could be settled once and for all and thereafter would govern numerous cases.'" Bender v. Jordan, 623 F.3d 1128, 1130 (D.C.Cir.2010) (quoting Empire Healthchoice, 547 U.S. at 700, 126 S.Ct. 2121) (alterations and some internal quotation marks omitted). We note that other Section 8 landlords have brought almost identical actions elsewhere.5 The outcomes of the legal questions in these cases will dictate whether HUD and/or the public housing agencies that administer Section 8 must pay millions of dollars in additional rents to landlords, which — in turn — could require the agencies to scale back the scope of the Section 8 program. "The issue is potentially so important to the success of the [Section 8] program — since on its resolution may turn the amount of lower-income housing actually provided — that we believe that Congress, had it thought about the matter, would have wanted the question to be decided by federal courts applying a uniform principle." Price v. Pierce, 823 F.2d 1114, 1119-20 (7th Cir.1987) (Posner, J.); see also Almond v. Cap. Props., Inc., 212 F.3d 20, 24 (1st Cir.2000) (First Circuit is "content to follow Price pending further enlightenment from the Supreme Court"). Moreover, "there is no discernable state interest in a state forum" that would outweigh the federal interest in uniformity. See Bender, 623 F.3d at 1131; see also R.I. Fishermen's Alliance, Inc. v. R.I. Dep't of Envtl. Mgmt., 585 F.3d 42, 51-52 (1st Cir.2009).

The decision to apply the federal ingredient doctrine in a particular case is necessarily fact-bound. See Gully v. First Nat'l Bank in Meridian, 299 U.S. 109, 117, 57 S.Ct. 96, 81 L.Ed. 70 (1936) (Cardozo, J.) (federal ingredient doctrine requires "common-sense accommodation of judgment to kaleidoscopic situations"). In the circumstances of this case, we conclude that federal question jurisdiction exists, as (1) "[t]he imposition of liability on Government contractors will directly affect the terms of Government contracts," Boyle v. United Techs Corp., 487 U.S. 500, 507, 108 S.Ct. 2510, 101 L.Ed.2d 442 (1988); (2) the "dispute ... turn[s] on the interpretation of a contract provision approved by a federal agency pursuant to a federal statutory scheme," Almond, 212 F.3d at 25; (3) the alleged breach occurred only because the contractor was following the federal agency's explicit instructions, see Corr. Servs. Corp. v. Malesko, 534 U.S. 61, 74 n.6, 122 S.Ct. 515 (2001); (4) the case presents a pure question of law that will govern numerous cases nationwide, see Bender, 623 F.3d at 1130; (5) the federal government has an overwhelming interest in seeing the issue decided according to a uniform principle, see Price, 823 F.2d at 1119-20; and (6) there is no countervailing state interest in having the dispute adjudicated in a state forum, see Bender, 623 F.3d at 1131; R.I. Fishermen's Alliance, Inc., 585 F.3d at 51-52. Having satisfied ourselves that we have jurisdiction over the claims that remain live in this case, we move on to the merits.6

III.

The merits issues that we must decide are (1) whether the HAP contracts allow MaineHousing to invoke the overall limitation clause to limit payments to the plaintiffs and (2) if so, whether Maine-Housing properly invoked the overall limitation by employing the Notice H 95-12 method to calculate the difference between the plaintiffs' contract rents and those of comparable unassisted units.7 We are the first federal appellate court to reach this question.8 Although some federal trial courts in other circuits have answered this question in the negative,9 we ultimately take our guidance from the Supreme Court's Alpine Ridge decision. There, a unanimous Court concluded that the terms of the overall limitation clause — which apply "notwithstanding any other provisions" of the HAP contract — "override conflicting provisions of any other section." Alpine Ridge, 508 U.S. at 18, 113 S.Ct. 1898. That conclusion survives the 1994 amendment to the Section 8 statute and controls our analysis here.

As we have noted, the overall limitation clause allows MaineHousing to withhold the otherwise-automatic annual adjustments in rental payments so long as MaineHousing has "determined" that the adjustments would "result in material differences between the rents charged for assisted and comparable unassisted units." The one caveat is that the overall limitation clause preserves the landlord's right to receive above-market rental payments to the extent of the initial difference between the contract rent and the market rate. MaineHousing argues that it has used the method set forth in Notice H 95-12 to "determine" that further automatic adjustments would result in "material differences" between contract rents and market rates. That method relies on the tables of fair market rents published annually by HUD: If the contract rent is higher than the corresponding fair market rent for comparable units in the region (and if the difference is more than 10 percent of the initial contract rent), then a Section 8 landlord cannot receive a further rent increase unless the landlord can show — based on "at least three examples of unassisted housing in the same market area of similar age, type and quality" — that the resulting rent level after application of the automatic annual adjustment will still be below the market rate. Notice H 95-12, at 3.

The landlords maintain that MaineHousing never "determined" that automatic adjustments would result in material differences between contract rents and market rates because the verb "determine" means "to reach a decision after thought and investigation," Webster's New World Dictionary (2d ed. 1986) (emphasis added), whereas MaineHousing rotely applied the Notice H 95-12 formula without any independent inquiry. But to "determine" also means to "ascertain definitely by ... calculation." Oxford English Dictionary (Online ed. 2013); see also The American Heritage Dictionary (2d College ed. 1982) ("ascertain definitely, as after ... calculation"). MaineHousing certainly calculated that the adjusted rents at assisted units would rise above the fair market rents for comparable units, and it based this calculation on a HUD-prescribed formula and HUD-published data. The landlords' cherry-picked dictionary definitions do not convince us that MaineHousing's act of calculation was anything but a "determination."10

The landlords also argue that the fair market rents published by HUD cannot be used as a measure of "the rents charged for ... comparable unassisted units." The landlords suggest that unassisted units are only "comparable" to Section 8 units if they are in a similar neighborhood and share other common characteristics such as size, age, physical configuration, amenities, and utilities. HUD's fair market rent figures, by contrast, are calculated on a county-wide or metropolitan-area-wide basis. HUD reports 40th-percentile rents for zero-, one-, two-, three-, and four-bedroom units in each area, but the fair market rent figures do not include a more fine-grained breakdown by unit type.

MaineHousing and HUD counter that the fair market rent figures are designed to reflect "the rent, including the cost of utilities (except telephone) ..., that must be paid in the market area to rent privately owned, existing, decent, safe and sanitary rental housing of modest (non-luxury) nature with suitable amenities." 24 C.F.R. § 888.111(b). The figures are adjusted to "exclude public housing units, newly built units and substandard units." Id. § 888.113(a). Thus, the fair market rent figures do provide a basis for comparing rents at privately owned Section 8 sites to rents for other units in the general vicinity, taking account of unit quality, amenities, utilities, and (to some extent) age. Since HUD reports rents at the 40th percentile in each county or metropolitan area, this means that contract rents will only be deemed above-market for purposes of Notice H 95-12 if rents at the Section 8 site are more expensive than rents for four out of ten existing decent, safe, and sanitary units in the area with the same number of bedrooms, same ownership status, and roughly the same amenities. Moreover, HUD has established a procedural mechanism by which landlords can challenge the results of the Notice H 95-12 calculation: by submitting an appraiser's market rent estimates — based on at least three comparable units — showing that adjusted rents would be consistent with prevailing market rates. See Notice H 95-12, at 5-6; see also U.S. Dep't of Hous. & Urban Dev., Estimates of Market Rent by Comparison (Form HUD-92273) (July 2003). Indeed, the plaintiffs all took advantage of this mechanism when they submitted their own comparability studies to MaineHousing and HUD in the mid-2000s, and HUD responded by approving upward adjustments at all five sites.

Ultimately, we need not decide whether the Notice H 95-12 method is the best way to calculate rents for "comparable unassisted units" under the HAP contracts. The contracts construed by the Supreme Court in Alpine Ridge are in all relevant respects identical to the contracts at issue here, and consistent with Alpine Ridge, we read the overall limitation clause as "expressly assign[ing] to [the agency] the determination of whether there exist material differences between the rents charged for assisted and comparable unassisted units." See Alpine Ridge, 508 U.S. at 21, 113 S.Ct. 1898. Thus, our role is not to determine de novo whether this calculation was correct. Rather, our role is to determine whether the Notice H 95-12 method represents a "reasonable means" of making the comparison. Id.; accord Carmichaels Arbors Assocs., 789 F.Supp. at 689 n. 6 ("Under our interpretation of the HAP contract, ... any reasonable means of ascertaining whether material differences in rents exist is authorized under the terms of the contract."); Nat'l Leased Hous. Ass'n, 22 Cl.Ct. at 659 ("the HAP contracts do not contain any provision limiting HUD to any particular methodology for making its comparability determination").11 We have already explained that MaineHousing's reliance on the Notice H 95-12 method — while not the same as the site-specific studies that the landlords seek — still does incorporate important considerations of comparability. This method, combined with the procedural safeguards which we described above (and which were actually utilized in this case), certainly qualifies as "reasonable." We do not read the contracts of the Alpine Ridge decision to demand more than that.

IV.

In sum, we hold that the overall limitation clauses in each of the housing assistance payments contracts allow Maine-Housing to withhold otherwise — automatic annual adjustments in contract rents where MaineHousing determines — based on the formula prescribed by HUD in Notice H 95-12 and the fair market rent data published by HUD — that further adjustments would result in material differences between contract rents and market rates. The district court's decision granting MaineHousing's motion for summary judgment with respect to the plaintiffs' complaint is affirmed.