OPINION

Edward Furnace is a prisoner at Salinas Valley State Prison. Furnace alleges the Appellees wrongfully classified him as a gang member in retaliation for filing a § 1983 suit against the defendants’ colleagues. After Furnace filed a habeas petition, California courts rejected his claims on the ground that there was sufficient evidence to support the gang validation. Furnace then filed the present action under 42 U.S.C. § 1983 for violation of his Fourteenth Amendment rights, based on violation of the First Amendment and the Equal Protection Clause. The district court dismissed his suit on claim preclusion grounds. We affirm.

I. FACTS AND PROCEEDINGS .BELOW

In 2006 Furnace filed a § 1983 suit against eleven Salinas Valley Prison officials (none of whom is involved in this suit) for allegedly denying him visitation rights and other privileges. These defendants filed a motion to dismiss in '2008, which was denied. Furnace alleges that shortly after that, R.L. Martinez and M. Valdez, gang investigators at Salinas Valley, were “ordered to validate [Furnace] as a prison gang member to intimidate and retaliate against him” for filing the earlier suit. The decision to classify Furnace as a member of the Black Guerilla Family (BGF) was based on prison officials finding in Furnace’s cell the contact information of a validated BGF gang member as well as books, a CD, and a newspaper article relating to BGF.

Furnace filed an internal administrative appeal, claiming that the classification lacked evidence, was retaliatory, and was racially motivated. While the appeal was pending, K. Berkler, R.S. Marquez, and E.W. Fischer, also gang experts at Salinas Valley, again classified Furnace as a gang member. His internal administrative appeals were denied, and he was placed in the prison’s secured housing unit (SHU).

Furnace then filed a pro se habeas petition in California Superior Court. He named D. Adams (the prison warden), R.L. Martinez, Valdez, Berkler, R.S. Marquez, and Fischer as respondents (and others not involved in this appeal). He alleged that his gang classification and placement in secured housing lacked sufficient evidence, that it was done to “intimidate and retaliate against” Furnace for filing the earlier suit, and that it violated his federal constitutional rights to free speech, equal protection of the law, and due process. Furnace sought to be removed from secured housing and to have his record cleared of any allegation that he was gang affiliated.

The Superior Court denied Furnace’s petition on the ground that there was sufficient evidence to’ support the gang validation, without directly addressing whether the classification was retaliatory or racially discriminatory. Furnace filed another habeas petition in the California Court of Appeal, making the same allegations. The court denied his petition, holding, first, that there was sufficient evidence to support the validation and, second, that the validation did not violate his First Amendment rights. The court denied rehearing, and the California Supreme Court summarily denied review.

In February 2012, Furnace filed this § 1983 suit in federal district court. Furnace named as defendants Berkler, Marquez, Fischer, R.L.- Martinez, and Valdez, plus G. Giurbino (collectively, “Appellees”), who allegedly supervised the other Appel-lees. Furnace’s complaint alleged that.his classification was illegal and retaliatory in violation of his First Amendment rights, and a. violation, of his right to equal protection and due process under the Fourteenth Amendment. Furnace asked for declaratory relief, money damages, as well as in-junctive relief “to release him from the security housing unit” and to “expunge his prison file” of any allegation that he is associated with BGF.

The district court granted the Ap-pellees’ motion to dismiss on the ground that Furnace’s suit was barred by claim preclusion. The court concluded that “both the state action and the instant one arise out of the same incident and involve the same actors allegedly performing the same act of initiating gang validation procedures and ultimately validating [Furnace] as an active gang member without proper procer dural protections.” Because Furnace sought “to vindicate the same primary right in federal court as he [had] previously in state court,” his claim was precluded. Furnace timely appealed. On appeal, Ap-pellees ask us to assess a strike against Furnace under the Prison Litigation Reform Act for having filed a duplicative suit.

■ ■ II. ANALYSIS

This appeal raises two main issues. First, Furnace contends that the district court erred in dismissing his First Amendment and equal protection claims under California claim preclusion principles. Second, the Appellees ask .us to assess a “strike” against Furnace under the Prison Litigation Reform Act, We affirm the district court and decline to assess a strike against Furnace.

A. Claim Preclusion

Under'the Full Faith and Credit Statute, 28 UiS.C. § 1738, federal courts must give the same preclusive effect to state court judgments, including “reasoned” habeas judgments, as the rendering state court would. Gonzales v. Cal. Dep’t of Corr., 739 F.3d 1226, 1230-31 (9th Cir. 2014) (citing Migra v. Warren City Sch. Dist. Bd. of Educ., 465 U.S. 75, 81 , 104 S.Ct. 892 , 79 L.Ed.2d 56 (1984)). Accordingly, California claim preclusion law governs whether, in light of his earlier state habeas petition, Furnace’s § 1983 claims may be brought in federal court.

In California, “[c]laim preclusion arises if a second suit involves: (1) the same cause of action .(2). between the same parties [or parties in privity with them] (3) after a final judgment on the merits in the first suit.” DKN Holdings LLC v. Faerber, 61 Cal.4th 813 , 189 Cal.Rptr.3d 809 , 352 P.3d 378, 386 (2015) (citing Mycogen Corp. v. Monsanto Co., 28 Cal.4th 888 , 123 Cal.Rptr.2d 432 , 51 P.3d 297, 301 (2002)). Fur nace makes two arguments in response to the Defendants’ claim preclusion defense. First, he argues that the “primary rights” that were violated here are distinct from the primary right he sought to vindicate in his habeas action in California state courts. Second, he argues that the identity of the parties is different between the two suits. We address each argument in turn.

1. Primary Rights

California courts, unlike federal courts, do not determine whether two' suits involve the same cause of action by applying the “same transaction or occurrence” or “common nucleus of operative facts” test. Instead, California courts will hold that two suits involve the same cause of action when they involve the same “primary right.” Brodheim v. Cry, 584 F.3d 1262, 1268 (9th Cir. 2009). Under this theory “a ‘cause of action’ is comprised of a ‘primary right’ of the plaintiff, a corresponding ‘primary duty of the defendant, and a wrongful act by the defendant constituting a breach of that duty.” Mycogen, 123 Cal.Rptr.2d 432 , 51 P.3d at 306 . “The most salient characteristic of a primary right is that it is indivisible:.the violation of a. single primary right gives rise to but a single cause of action.” Id. Thus, in California, “if two actions involve the same injury to the plaintiff and the same wrong by the defendant then the same primary right is at stake even if in the second suit the plaintiff pleads different theories of recovery, seeks different forms of relief and/or "adds new facts supporting recovery.” San Diego Police Officers’ Ass’n v. San Diego City Emps. Ret. Sys., 568 F.3d 725, 734 (9th Cir. 2009) (quoting Éichman v. Fotomat Corp., 147 Cal.App.3d 1170 , 197 Cal.Rptr. 612, 614 (1983)). “The critical focus of primary rights analysis is the harm. suffered.” Brodheim, 584 F.3d at 1268 (citations and internal quotation marks omitted). California’s primary rights theory can be complicated, and we have cautioned against wielding the “primary right brush ... too carelessly” and noted the possibility that “different primary rights may be violated by the same wrongful conduct” under certain circumstances. San Diego Police Officers’ Ass’n, 568 F.3d at 734 (internal quotation marks omitted). But in this case, we have circuit precedent on point that, requires us to affirm.

The facts of Gonzales v. California Department of Corrections will sound familiar. There, Gonzales was validated as a gang member and placed in the SHU. 739 F.3d at 1229 . After exhausting his administrative remedies, and a series of state ha-beas- proceedings, he fíled a § 1983 suit alleging that “(1) the gang validation violated his rights to free speech and association under the First Amendment; (2) the validation regulations were applied in a racially discriminatory manner; (3) he was classified as a gang member as retaliation ...; [and] (4) his validation ,.. violated his due process rights.” Id. The district court dismissed the suit on claim preclusion grounds. Id. at 1230.

On appeal, Gonzales argued “that his retaliation, First Amendment, and Equal Protection claims [were] not precluded,” because those claims arose under “a distinct primary right,” from his earlier due process claim. Id. at 1233 (internal quotation marks omitted). Specifically, he argued that his earlier inadequate evidence/due process claim was “procedural” while his First Amendment and Equal Protection Clause arguments were “inherently substantive,” and he pointed to our decision in Brodheim as having recognized a procedural/substantive divide. Id. We noted that in Brodheim , the two harms— one substantive, one procedural—were distinct because “[t]hey were caused at different times, by different acts, and by different actors.” Id. (quoting Brodheim, 584 F.3d at 1268-69). By contrast, Gonzales was “challenging the same actions by the same group of officials at the same time that resulted in the same harm.” Id. at 1234. Accordingly, the procedural/substantive distinction for identifying a distinct primary right was of- no use, because whether a party alleges “a different remedy or asserts a different legal theory .., is irrelevant under California claim preclusion doctrine.” Id. Since Gonzales’s claims would be barred in California’s courts under California’s .claim preclusion doctrine, they were barred in federal courts under the Full Faith and Credit statute. Id. at 1230,

Gonzales requires that we affirm. Furnace challenges “the same actions by the same group of officials at the same time that resulted in the same harm.” Id. at 1234 . In his state court action, Furnace raised a due process claim, challenging the evidentiary basis of his gang validation and SHU placement. He also claimed that the validation and SHU placement were retaliatory, racially motivated, and violated his First Amendment rights. And, like the plaintiff in Gonzales , Furnace attempts to argue that the primary right he sought to vindicate in the state proceedings is somehow distinct from the rights he now seeks to vindicate. But, as .the California Supreme Court has made clear, a plaintiffs primary right is the “right to be free from the particular injury suffered” and “must therefore be distinguished from the legal theory on which liability for that injury is premised.” Mycogen, 123 Cal.Rptr.2d 432 , 61 P.3d at 306-07. At heart, Furnace has always complained about the same alleged injury: his gang validation and SHU placement. He has come up with numerous legal theories as to why it was unlawful—lack of evidence, retaliation, and racial discrimination—but it does not change the primary right he seeks to vindicate,1 and Gonzales makes that point clear. See Gonzales, 739 F.3d at 1233 (the plaintiffs “primary right was his protected liberty interest in remaining free from SHU placement” and the “harm suffered” was his “gang validation and indeterminate SHU detention”).

Furnace raises two principal arguments in an effort to get around our holding in Gonzales , First, he argues that a claim challenging the sufficiency of the gang evidence is qualitatively different from a claim that the gang classification was the result of retaliation for the exercise of First Amendment rights or was racially motivated in violation of the Equal Protection Clause. Second,- he argues that he may maintain this suit for damages because he could not have obtained damages in his prior habeas action. Furnace’s points are technically correct; but, in the context of California’s primary rights ‘doctrine, both are irrelevant.

First, we recognize that Furnace’s sufficiency-of-the-evidence claim, which he raised in his state habeas proceedings, and his retaliation and racial discrimination claims, which he raises here, are distinct claims. But they are both part and parcel of the same primary right—Furnace’s right not to be wrongfully placed in the SHU. They are alternative arguments for accomplishing the same result—his release from the SHU. The primary rights doctrine under California claim preclusion forecloses Furnace’s ability to.file separate suits challenging the same wrong.

Second, it is also true, but again irrelevant, that Furnace' could not have obtained damages through habeas. Habeas, by its very nature, is an action to challenge “the fact or length of custody” for which the remedy is release from custody, Wolff v. McDonnell, 418 U.S. 539, 554 , 94 S.Ct. 2963 , 41 L.Ed.2d 935 (1974); it is not an action in damages, Preiser v. Rodriguez, 411 U.S. 475 ,. 494, 93 S.Ct. 1827 , 36 L.Ed.2d 439 (1973). We know of no reason, however, that Furnace could not have brought his § 1983 action instead of his state habeas action, see Shoemaker v. Harris, 214 Cal.App.4th 1210 , 155 Cal.Rptr.3d 76, 84 (2013), or, even better, joined his habeas and § 1983 actions to seek alternative forms of relief, Cal. Penal Code § 1473 (d) (“[The state habeas statute] shall not be construed ... as precluding the use of any other remedies.”). And therein lies the problem. Having lost his habeas case, Furnace has made a new run at the officials through § 1983. The U.S. Supreme Court has held, and the California courts have agreed, that § 1983 suits cannot be used to collaterally attack the validity of a conviction. Thus, “the ... principle that civil tort actions are not appropriate vehicles for challenging the validity of outstanding criminal judgments applies to § 1983 damages actions that necessarily require the plaintiff to prove the unlawfulness of his conviction or confinement.” Heck v. Humphrey, 512 U.S. 477, 486 , 114 S.Ct. 2364 , 129 L.Ed.2d 383 (1994); see also Susag v. City of Lake Forest, 94 Cal.App.4th 1401 , 115 Cal. Rptr.2d 269, 273 (2002) (“[The] requirement [that a plaintiff can pursue relief under § 1983 only after obtaining habeas relief] avoids a collateral attack on the conviction and relitigation of issues of probable cause and guilt, and protects the strong judicial policy against inconsistent resolutions.”). The Heck principle means that “a § 1983 plaintiff must prove that the conviction or sentence has been reversed on direct appeal, expunged by executive order, declared invalid by a state tribunal authorized to make such determination, or called into question by a federal court’s issuance of a writ of habeas corpus.” Heck, 512 U.S. at 486-87 , 114 S.Ct. 2364 .

Heck is not directly on point here, but the principle will help us focus in this case. Heck prohibits the use of § 1983 to attack the validity of a conviction, because a recovery in the damages action would necessarily imply that the conviction was wrongfully obtained. The judgment of conviction and the judgment for damages would be inconsistent, and there would be no means to reconcile the two. Like the Heck principle, one reason for California’s primary right doctrine is to avoid piecemeal litigation and the possibility of inconsistent judgments. See, e.g., People v. Bar-ragan, 32 Cal.4th 236 , 9 Cal.Rptr.3d 76 , 83 P.3d 480, 494 (2004) (“[T]he purposes of the res judicata doctrine include prevent ing inconsistent judgments which undermine the integrity of the judicial system .... ” (internal quotation marks and alterations omitted)). Furnace has already challenged his placement in the SHU in habeas and lost; he cannot now challenge his placement through § 1983 without collaterally attacking—and thereby rendering inconsistent—the judgment denying him habeas relief. If he were successful on his § 1983 claim against the officials who put him in the SHU, it would necessarily be inconsistent with the' judgment that he was not entitled to habeas relief.

For example, were he to prevail here, Furnace would be entitled to damages for the time he has been wrongfully placed in the SHU and, in fact, he might be entitled to damages on a continuing basis if he were left in the SHU. The Appellees would be in the untenable position that California courts have said he is lawfully housed in the SHU, while the federal courts would have concluded that he is unlawfully housed in the SHU. Following the California.judgment, the warden might have a duty by virtue of his office to keep him in the SHU, while after the federal judgment, the warden (and others) would be personally liable for damages if they keep him there. The two judgments would be irreconcilable. It is of no consequence that § 1983 is a different remedy from habeas; both are means of challenging the lawfulness of his plaeement. The primary rights doctrine prevents such inconsistent judgments by requiring a party to bring all of his claims— as many causes of action, or theories of recovery, or remedies as he has—in a single suit. See Mycogen, 123 Cal.Rptr.2d 432 , 51 P.3d at 302 (“Res judicata precludes piecemeal litigation by splitting a single cause of action or relitigation of the same cause of action on a different legal theory or for different relief.” (emphasis added) (internal quotation marks omitted)); id., 123 Cal.Rptr.2d 432 , 51 P.3d at 307 (“The primary right must also be distinguished from the remedy sought: The violation of one primary right constitutes a single cause of action, though it may entitle the injured party to many forms of relief, and the relief is not to be confounded with the cause of action, one not being determinative of the other.” (second emphasis added) (internal quotation marks omitted)); Eich-man, 197 CaLRptr. at 614 (“[I]f two actions involve the same injury to the plaintiff and the same wrong by the defendant then the same primary right is at stake even if in the second suit the plaintiff ... seeks different forms of relief....” (emphasis added)). The district court correctly held that in these circumstances, Furnace’s “retaliation, First Amendment, and Equal Protection claims” involved the same “primary right” at issue in the Furnace’s earlier state habeas proceeding. Gonzales, 739 F.3d at 1233-34 .

We hold that the same primary right— Furnace’s right to be free from unlawful gang validation and placement in the SHU—was at issue in both suits.

2. Identity of Parties

As we suggested above, Furnace’s suit involves “challenging the same actions by the same group of officials at the same time that resulted in the same harm.” Id. at 1234 (emphasis added). Furnace asserts that the defendants in this suit are-different from the defendants in his state habeas suit. And Appellees counter that California claim preclusion only requires identity of the party against whom preclusion is sought. Neither party is entirely correct on these points, though we ultimately conclude that the requisite identity of parties is met.

Appellees rely solely on California issue preclusion case law to sustain the proposition that only the party against whom preclusion is sought need be the same in both suits. See, e.g., Lucido v. Superior Court, 51 Cal.3d 335 , 272 Cal. Rptr. 767 , 795 P.2d 1223, 1225 (1990). California’s claim preclusion case law—which has distinct requirements—prevents reliti-gation “between the same parties or parties in privity with them.” DKN Holdings, 189 Cal.Rptr.3d 809 , 352 P.3d at 386 (emphasis added) (internal quotation marks omitted). That said, we cannot agree with Furnace that “the defendants in this action were not defendants in Furnace’s state habeas proceeding.” At the time of his state habeas petition, he named the then-warden, D. Adams, “et al.” as respondents. He made numerous references to “prison officials” throughout the petition, and most importantly, he specifically named “R.L. Martinez,” “M. Valdez,” “Keri Berkler,” “R.S. Marquez,” and “Everett W. Fischer” as respondents.

Accordingly, because Furnace’s suit involves “(1) the same cause of action (2) between the same parties [or parties in privity with them] (3) after a final judgment on the merits in the first suit,” we affirm. DKN Holdings, 189 Cal.Rptr.3d 809 , 352 P.3d at 386 .

B. PLRA Strike

The Appellees ask us to assess a strike against Furnace under the Prison Litigation Reform Act (PLRA), 28 U.S.C. § 1915 (g). Under § 1915(g), a prisoner can lose the ability to file suits in forma pau-peris (IFP) if he “has, on 3 or more prior occasions, while incarcerated or detained in any facility, brought an action or appeal in a court of the United States that was dismissed on the grounds that it is frivolous, malicious, or fails to state a claim upon which-relief may be granted.” Appel-lees assert that since this suit “duplicates claims brought in an earlier action” it is “malicious” within the meaning of the PLRA. See Pittman v. Moore, 980 F.2d 994 (5th Cir. 1993). The Appellees therefore want us to deem the district court’s dismissal as Furnace’s first “strike.”

The question of whether Furnace’s dismissal in this case was frivolous, malicious, or dismissed for failure to state a claim is not germane at this point. Generally, “district courts do not issue these strikes one by one, in their orders of judgment,” because nothing in the PLRA requires them to do so. Andrews v. King, 398 F.3d 1113 , 1119 n.8 (9th Cir. 2005) (internal quotation marks omitted). And by extension, nothing in the PLRA requires us to do so at this time. Typically it is not until a defendant “challenge^] a prisoner-plaintiffs IFF status,” id. at 1120 , that a backwards-looking inquiry is done to assess whether “on 3 or more occasions,” the prisoner-plaintiffs suit was “dismissed on the grounds that it [wa]s frivolous, malicious, or fail[ed] to state a claim upon which relief may be granted,” 28 U.S.C. § 1915 (g). Accordingly, we decline the Ap-pellees’ request to assess a strike.

III. CONCLUSION

The judgment is AFFIRMED.

. We review de novo a dismissal on res judi-cata grounds, Manufactured Home Communities Inc. v. City of San Jose, 420 F.3d 1022, 1025 (9th Cir. 2005), as well as the district court’s interpretation of the Prison Litigation Reform Act, Andrews v. King, 398 F.3d 1113, 1118 (9th Cir. 2005). . Furnace claims that in Gonzales we said that the patties’ "dispute [was] in defining the primary duty,” Gonzales, 739 F.3d at 1233 , and that he is disputing his primary right, not the Appellees’ duty. This argument is unavailing. Rights and duties are correlative—they do not exist independent of each other. The possession of a right necessarily implies the existence of a duty; conversely, to say that a party has a duty means that someone is possessed of a right. As California has explained, "a ‘cause of action’ is comprised of a ‘primary right’ of the plaintiff, a corresponding 'primary duty’ of the defendant, and a wrongful act by the defendant constituting a breach of that duty.” Myeogen, 123 Cal.Rptr.2d 432, 51 P.3d at 306 (emphasis added). Here, as in Gonzales , Furnace’s primary right is the right not to be unlawfully determined to be a gang member and placed in the SHU; and it "cor-respondes]” to the Appellees' duty not to unlawfully label an inmate a gang member and place-him in the SHU. ■ - . We offer no definitive opinion whether, under California law, Furnace could, in fact, have brought both an action in habeas and a § 1983 law in the same suit, nor do we offer any opinion whether Furnace could have decided to forego his habeas action and bring only a § 1983 suit. What we hold is that he cannot bring them seriatim. . We recognize that some California appellate cases lend support to Furnace's claim that the ability to be free from retaliation and/or discrimination might be a distinct primary right from the substantive outcome of an adverse administrative decision, see Agarwal v. Johnson, 25 Cal.3d 932 , 160 Cal.Rptr. 141 , 603 P.2d 58, 72 (1979) (holding that Title VII claim was distinct primary right from defamation and intentional infliction of emotional distress claims under state law); Henderson v. Newport-Mesa Unified Sch. Dist., 214 Cal. App.4th 478 , 154 Cal.Rptr.3d 222, 226, 237-40 (2013) (claim that teacher was not properly given "first priority” in hiring under state statute arose under distinct primary right from discrimination claim); George v. Cal. Unemployment Ins. Appeals Bd., 179 Cal.App.4th 1475 , 102 Cal.Rptr.3d 431, 438-41 (2009) (ALJ's retaliation claim arose under distinct primary right from wrongful suspension claim), and that some cases might suggest that the availability of differing remedies would counsel against the application of claim preclusion, see Shoemaker v. Harris, 214 Cal.App.4th 1210 , 155 Cal.Rptr.3d 76 , 84 & n.13; Branson v.- Sun-Diamond Growers of Cal, 24 CaI.App.4th 327, 29 Cal,Rptr.2d 314, 323 (1994); Roberts v. Redlich, 111 Cal.App.2d 566 , 244 P.2d 933, 935 (1952). These decisions all arose in very different contexts, predate our decision in Gonzales , and do not, in any event, shake our confidence that Gonzales ■ was rightly decided. . The only current defendant not named was Giurbino, a party who was nonetheless in privity with the other officials due to his supervisory relationship in the prison system. DKN Holdings, 189 Cal.Rptr.3d 809 , 352 P.3d at 389 (noting that privity is found where "separate defendants' interests” are "closely align[ed]” like "between a corporation and its employees, a general contractor and subcontractors, an association of securities dealers and member agents, and among alleged co-conspirators" (emphasis added) (citations omitted)). . Alternatively, the Appellees argue that Furnace failed to state a retaliation claim because his placement in the SHU was supported under the "some evidence” standard. See Superintendent v. Hill, 472 U.S. 445, 455 , 105 S.Ct. 2768 , 86 L.Ed.2d 356 (1985). Because we affirm the district court on claim preclusion grounds, we decline to address the Appellees' argument, as well as Furnace’s response, that a retaliation claim can survive a motion to dismiss in the face of "some evidence” supporting a SHU placement. See Bruce v. Ylst, 351 F.3d 1283, 1289 (9th Cir. 2003); Hines v. Gomez, 108 F.3d 265, 269 (9th Cir. 1997). . We do note our skepticism, however, of labeling Furnace's suit “malicious” merely because of its repetitiveness. The fact that Furnace had a good faith argument that his claims were not barred by California claim preclusion weighs against finding Furnace’s suit “malicious” or “frivolous.”