OPINION

KETHLEDGE, Circuit Judge.

Ask 100 Americans whether a 74 year-old man's "family" includes his wife who lives with him, and every one of those Americans will likely answer yes. But here the Ohio Department of Medicaid answered no, with the result that it denied Joe Turner's application for benefits under the Medicaid Act. That Act requires States who receive Medicaid funding to provide certain low-income Medicare beneficiaries with financial assistance to help pay their out-of-pocket Medicare costs. Under federal law, to determine whether a beneficiary is eligible for such assistance, the State must compare the beneficiary's income to the federal poverty line "for a family of the size involved." The larger the size of the "family involved," the greater the income a beneficiary can earn and still be eligible for assistance. In making this comparison, however, Ohio generally does not count a Medicare beneficiary's spouse as a member of his "family." The question presented is whether Ohio's interpretation of the word "family," as applied here, is a permissible one. We hold it is not, and reverse the district court's judgment to the contrary.

I.

Most Medicare recipients must pay monthly premiums in addition to various co-payments and deductibles. See, e.g., 42 U.S.C. §§ 1395e, 1395j. Some Medicare recipients have difficulty making those payments. Consequently, as noted above, States that receive federal Medicaid funds must assist certain low-income Medicare beneficiaries with payment of their out-of-pocket expenses related to the Medicare program. See id. §§ 1396a(a)(10)(E), 1396d(p). To be eligible for such assistance (which we call "Assistance Payments" or "Payments"), a Medicare beneficiary must have income less than or equal to certain percentages of the federal poverty line "for a family of the size involved[.]" Id. §§ 1396d(p)(2)(A), 1396a(a)(10)(E)(iii), (iv). Of course, the federal poverty line rises as a family gets larger. See Annual Update of the HHS Poverty Guidelines, 80 Fed.Reg. 3236, 3237 (Jan. 22, 2015). All else being equal, therefore, it is easier for beneficiaries with larger families to qualify for Assistance Payments than it is for beneficiaries with smaller families.

The State of Ohio receives federal Medicaid funds and hence must provide Assistance Payments to beneficiaries who qualify for them. In determining whether a beneficiary qualifies for these Payments, however, the Ohio Department of Medicaid (the "Department") generally excludes the beneficiary's spouse in determining the size of the beneficiary's family. Thus, when determining whether Medicare beneficiaries are eligible for these Payments, the Department generally treats married beneficiaries as unmarried.

The plaintiffs here — Leslie Wheaton, George Hart, and Joe Turner — are Medicare beneficiaries who are each married to a resident spouse. Each plaintiff's monthly income, according to their amended complaint, is about $1,300. That amount, the plaintiffs allege, would make each plaintiff eligible for Assistance Payments if his wife were included as part of his "family" for purposes of determining his eligibility for those payments. Per the Department's regulations, however, the Department treated each plaintiff as belonging to a family of one. The Department therefore denied each of their applications for Assistance Payments.

The plaintiffs responded with this lawsuit, alleging that the Department's denial of their applications violated the Medicaid Act. As relief, the plaintiffs sought declaratory and injunctive relief on behalf of themselves and a putative statewide class. The Director later filed a motion to dismiss the suit, which the district court granted. The court dismissed each plaintiff's claim for a different reason. The court held that Wheaton's claim was barred by res judicata because of a prior state-court judgment. The court held that Hart's claim was barred because the amended complaint recited his monthly income for 2011 rather than 2012, which was the year the amended complaint was filed. The court rejected Turner's claim on the merits, holding that, because the Medicaid Act did not specify a definition of "family," the Department was free to define that term to exclude Turner's resident spouse.

This appeal followed.

II.

We review de novo the district court's dismissal of plaintiffs' claims. Mich. Spine & Brain Surgeons, PLLC v. State Farm Mut. Auto. Ins. Co., 758 F.3d 787, 789 (6th Cir.2014).

A.

As an initial matter, the State argues that §§ 1396a(a)(10)(E) and 1396d(p) do not give rise to a cause of action under 42 U.S.C. § 1983. Section 1983 provides "a cause of action against any person who under color of state law, deprives `any citizen of the United States... of any rights, privileges, or immunities secured by the Constitution and laws.'" Harris v. Olszewski, 442 F.3d 456, 460 (6th Cir.2006) (quoting § 1983). In order for a statutory provision to give rise to an action under § 1983, however, the provision must (1) "unambiguously confer" an "individual entitlement" on particular persons, (2) describe the entitlement in "mandatory, rather than precatory, terms[,]" and (3) make its command definite enough that courts can enforce it. Id. at 461 (emphasis omitted).

The State argues that §§ 1396a(a)(10)(E) and 1396d(p) do none of these things. But even the State concedes that binding precedent bars its argument on this point. Specifically, in Harris, we held that a related provision of the Medicaid Act gave rise to a cause of action under § 1983. See 442 F.3d at 461-62. There, the provision stated that a "State plan for medical assistance ... must ... provide that [] any individual eligible for medical assistance (including drugs) may obtain such assistance from any" medical provider. 42 U.S.C. § 1396a(a)(23). Here, the relevant provisions state that a "State plan for medical assistance ... must ... provide [] for making medical assistance available for medical cost sharing ... for qualified medicare beneficiaries" — i.e., "individual[s]" whose incomes are below the federal poverty line for their "family" size. Id. §§ 1396a(a)(10)(E)(i), 1396d(p). Suffice it to say that we have no reason to distinguish the provision in Harris from the provisions here, which means they presumptively create a right enforceable under § 1983.

The State says that presumption is rebutted here because the Medicaid Act contemplates a comprehensive enforcement scheme that is incompatible with individual suits under § 1983. But again we rejected that argument in Harris. See 442 F.3d at 463. The plaintiffs therefore can proceed with their action under § 1983.

B.

On the merits we begin with Turner's claim, since he undisputedly faces no procedural bar to bringing it. As noted above, the Medicaid Act requires States that receive federal Medicaid funds to make Assistance Payments to certain low-income Medicare beneficiaries. Specifically, 42 U.S.C. § 1396a(a)(10)(E)(i) provides:

The upshot of this provision is that States receiving Medicaid funds must make Assistance Payments available to "qualified medicare beneficiaries."

Section 1396d(p) in turn defines "qualified medicare beneficiary" as an "individual" whose income does not exceed 100 percent "of the official poverty line (as defined by the Office of Management and Budget, and revised annually in accordance with section 9902(2) of this title) applicable to a family of the size involved." Finally, §§ 1396a(a)(10)(E)(iii) and (iv) require States receiving Medicaid funds to make a smaller range of Assistance Payments available to Medicare beneficiaries whose income falls between 100 and 135 percent of the federal poverty line "for a family of the size involved[.]"

Meanwhile, subject to two exceptions, the Ohio Department of Medicaid interprets "family," for purposes of these provisions, not to include a Medicare beneficiary's resident spouse. Ohio Admin.Code § 5160:1-3-03.5(C). The exceptions are that a spouse who is herself eligible for Medicare, or a spouse who earns more than a certain amount of income (currently about $4400 a year), does count as part of the beneficiary's family. See id. §§ 5160:1-303.5(C)(2), 1-3-03.9(E). The parties agree that neither of these exceptions applies here.

Thus, on the facts as alleged here, the question presented is whether Ohio complies with federal law — which requires the State to compare a Medicare beneficiary's income with the federal poverty line "for a family of the size involved" — when the State excludes a beneficiary's resident spouse from his "family" for purposes of that comparison. One might think that, for a State to adopt a definition of "family" so unusual as to exclude a person's resident spouse from it, the Medicaid Act itself must expressly include that definition. But the Medicaid Act does not define the term "family" as used in the provisions at issue here. That means we look to the term's ordinary meaning. See Engine Mfrs. Ass'n v. S. Coast Air Quality Mgmt. Dist., 541 U.S. 246, 252, 124 S.Ct. 1756, 158 L.Ed.2d 529 (2004); United States v. Zabawa, 719 F.3d 555, 559 (6th Cir.2013).

To ask whether the ordinary meaning of "family" includes a person's resident spouse, one might say, is like asking whether our solar system includes the planet Venus; but we proceed with the analysis nonetheless. "In determining [a term's ordinary] meaning, dictionaries are a good place to start." Zabawa, 719 F.3d at 559. A "family" can refer to a "group of individuals living under one roof and usually under one head[,]" or "the basic unit in society traditionally consisting of two parents rearing their children[,]" or "a group of persons of common ancestry[,]" or "a group of people united by certain convictions or a common affiliation[.]" Merriam-Webster Dictionary (online ed.). The latter two definitions are inapposite here: nobody contends that, in determining the "size of the family involved" for purposes of determining eligibility for Assistance Payments, the State should count persons who are joined to the beneficiary only by, say, a common great-grandparent or shared political beliefs.

The former two definitions — in short, persons living under one roof, or "the basic unit in society" — are admittedly unclear at the margins. Reasonable people might disagree, as a matter of ordinary usage, as to whether the term "family" should include adult children who live with their parents, or a 17 year-old child who does not, or nieces and nephews who live with their aunts and uncles. Thus, as a practical matter, it is likely up to the State whether to count those persons as part of the beneficiary's family under §§ 1396d(p)(2) and 1396a(a)(E)(10). But that does not mean the term family is ambiguous as applied here. Sometimes, of course, a statutory term is ambiguous in toto; the so-called "residual clause" of the Armed Career Criminal Act, 18 U.S.C. § 924(e)(2)(B), is an example. See Johnson v. United States, ___ U.S. ___, 135 S.Ct. 2551, 2557, 192 L.Ed.2d 569 (2015). Terms that are ambiguous in that sense do not clearly encompass anything. But some terms are ambiguous only at the margins, while clearly encompassing a certain core. The phrase "uses a firearm during and in relation to a drug crime" — to paraphrase 18 U.S.C. § 924(c)(1)(A) — might be ambiguous as applied to a defendant who barters his pistol for cocaine, see Smith v. United States, 508 U.S. 223, 113 S.Ct. 2050, 124 L.Ed.2d 138 (1993); but there is no doubt that it covers a defendant who demands payment for drugs at gunpoint. The term "planet" might be ambiguous as applied to Pluto, but is clear as applied to Jupiter. And though there might be some ambiguity in 2015 as to whether Ukraine's borders encompass the Crimean Peninsula, there is no doubt that Kiev lies within them. So too here: whatever ambiguity the "persons living under one roof" or "basic unit of society" definitions might have at the margins, there is no doubt that, under either definition, a person's family includes her resident spouse. Even the State does not argue the contrary.

But the State does make some other arguments. One is that, if Congress seeks to impose a condition on a State's receipt of federal funds, "it must do so unambiguously[.]" Haight v. Thompson, 763 F.3d 554, 569 (6th Cir.2014) (internal quotation marks omitted). That is a rule we take seriously, and thus Ohio has considerable latitude as to how it defines family for purposes of §§ 1396d(p)(2) and 1396a(a)(E)(10). But Ohio does not have so much latitude as to exclude a beneficiary's resident spouse from his family for purposes of those provisions. For the reasons stated above, it should have been clear to Ohio that the word "family," as used in the provisions here, does not mean whatever the State's officials want it to mean, but instead includes at least a beneficiary's resident spouse.

The State also argues that the relevant term here is not simply "family," but "family of the size involved"; and in the State's view that phrase does not have any ordinary meaning, which means the State can define it in whatever way makes good policy sense. The word "involved," especially, the State seems to regard as an interpretive wormhole, whose supposed ambiguity leads to a galaxy of unfettered agency discretion. But the meaning of that word and this phrase as a whole is not nearly so abstruse as the State suggests. The word "involved" simply — and we think clearly — directs the State to consider the federal poverty line for the beneficiary's family, rather than someone else's. And the meaning of "size" is disputed by no one. Thus, as applied here, the meaning of this phrase is just as clear as the meaning of "family" — which as applied here is clear enough to enforce its core meaning rather than a conflicting State one.

The State's next argument is based upon the Medicaid Act's definition of "qualified medicare beneficiary," which provides in relevant part:

42 U.S.C. § 1396d(p) (emphasis added).

The State points out, correctly, that this definition allows the State to determine a beneficiary's income in the same manner that the State would determine a person's income "for purposes of the supplemental security income [SSI] program[.]" Id. § 1396d(p)(1)(B). The State thus infers — we think incorrectly — that it may then compare the beneficiary's income not to the need standard specified in paragraph (2)(A) (i.e., "the official poverty line ... applicable to a family of the size involved"), but to the so-called "individual-need" standard used under the SSI program. See generally id. § 1382; 20 C.F.R. Ch. III., Pt. 416, Subpts. D and K. That is precisely the standard the State used to deny the plaintiff's applications here. But § 1396d(p)(2)(A) conspicuously omits any cross-reference to the SSI program's individual-need standard. Instead, paragraph (2)(A) expressly adopts a "family" need standard. The Medicaid Act's definition of "qualified medicare beneficiary" therefore refutes the State's position rather than supports it.

Relatedly, the State argues that we should defer to a 2010 "guidance letter" in which the Centers for Medicare and Medicaid Services — a federal agency — said that States are free to use the SSI program's individual-needs standard in determining a Medicare beneficiary's eligibility for Assistance Payments. But that letter is entitled to "respect" only to the extent its interpretation of §§ 1396d(p)(2) and 1396a(a)(E)(10) has "the power to persuade." Christensen v. Harris County, 529 U.S. 576, 587, 120 S.Ct. 1655, 146 L.Ed.2d 621 (2000) (internal quotation marks omitted). And here the letter is conclusory: it offers no analysis of those provisions at all. Thus, "we find unpersuasive the agency's interpretation" — if one may even call it that — "of the statute at issue in this case." Id.

Finally, the State argues that its use of an individual-need standard furthers the purposes of the Medicaid Act. "But disembodied notions of statutory purpose cannot override what the statute actually says." Zabawa, 719 F.3d at 560. Here, §§ 1396d(p)(2) and 1396a(a)(E)(10) require the State to use a family-need standard, not an individual-need standard, when considering the plaintiffs' applications for Assistance Payments.

In sum, that a statute is complicated does not mean an agency can interpret it any way the agency wants. And the operative term as applied here — "family" — is simple. For the reasons stated above, the Department's use of an individual-need standard to deny the plaintiffs' applications, and specifically the State's exclusion of each plaintiff's spouse in determining the size of his family, was contrary to federal law.

C.

That still leaves the separate grounds — res judicata as to Wheaton, a putative pleading defect as to Hart — on which the district court dismissed those plaintiffs' claims. The dismissal of Hart's claim, especially, seems questionable on its face, particularly given that he will presumably have a chance to amend his complaint on remand. But we think it prudent not to address either ground of dismissal in this appeal. The declaratory and injunctive relief that Wheaton and Hart seek is identical to the relief that Turner seeks. And given our holding as to Turner's claim, we think it at least questionable that the grounds on which the district court dismissed Wheaton and Hart's claims will affect the relief ultimately granted on remand. An opinion as to the validity of those grounds might therefore be merely advisory, and so we choose not to address them in this appeal.

* * *

The district court's judgment is reversed, and the case remanded for proceedings consistent with this opinion.