GRUENDER, Circuit Judge.

The petitioner, Quanartis Turnage, was convicted of first-degree murder in connection with the death of Wa Vang, a twentyone-year-old man whose body was discovered in a field next to a commercial storage facility in West St. Paul, Minnesota. The petitioner's co-defendants, Quantez Turnage (his brother, whom we will call "Quantez") and Damien Robinson (his friend and former roommate), both pled guilty to second-degree murder and testified as State's witnesses at the petitioner's trial. Quantez and Robinson each minimized his own role in the murder and asserted that the other two men had attacked and killed Vang. The state trial court sentenced the petitioner to life in prison without the possibility of parole. On direct appeal, the Minnesota Supreme Court affirmed the petitioner's conviction and sentence. Turnage v. State (Turnage I), 708 N.W.2d 535 (Minn. 2006).

While the direct appeal was pending, Quantez recanted his trial testimony in a handwritten affidavit, which reads as follows:

This letter is written to inform that the testamoney [sic] given at the trail [sic] of Quanartis Turnage was lies given only because of a promise of less time. I was told what needed to be said and said it because I feared if I did not I'd recieve [sic] a life sentence. After sitting and reflecting on what I did I feel it is only right that I at least try to fix this situation.

Quanartis Turnage had no knowlage [sic] of this crime other then [sic] what I told him after it became public.

No one has in anyway [sic] made or persuaded me to write this. I just feel its [sic] the right thing to do.

After the Minnesota Supreme Court decided Turnage I, the petitioner sought postconviction relief based on his brother's recantation. The trial court denied the petitioner's request for a new trial without holding an evidentiary hearing, and the Minnesota Supreme Court affirmed, State v. Turnage (Turnage II), 729 N.W.2d 593 (Minn. 2007).

The petitioner then filed this action in federal district court under 28 U.S.C. § 2254, seeking a writ of habeas corpus. The case was assigned to a magistrate judge, who recommended granting an evidentiary hearing to determine whether the state courts violated the petitioner's federal constitutional rights in denying postconviction relief based on Quantez's recantation. The district court rejected this recommendation and dismissed the petition in its entirety. The district court did, however, grant a certificate of appealability, see 28 U.S.C. § 2253(c), on the question whether "the state court erred by failing to hold an evidentiary hearing on the credibility of the eyewitness's i.e., Quantez's] recantation of his trial testimony."

Before seeking habeas corpus relief under § 2254, a prisoner ordinarily must "fairly present" his federal claims to the state courts. See, e.g., Baldwin v. Reese, 541 U.S. 27, 29, 124 S.Ct. 1347, 158 L.Ed.2d 64 (2004). This requirement serves the salutary purpose of giving states the "opportunity to pass upon and correct alleged violations of [their] prisoners' federal rights." Duncan v. Henry, 513 U.S. 364, 365, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995) (per curiam) (internal quotation marks omitted) (quoting Picard v. Connor, 404 U.S. 270, 275, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971)). The onus rests on the prisoner to present the substance of his federal claims "in each appropriate state court (including a state supreme court with powers of discretionary review)." Baldwin, 541 U.S. at 29, 124 S.Ct. 1347; see also Henry, 513 U.S. at 365-66, 115 S.Ct. 887 ("If state courts are to be given the opportunity to correct alleged violations of prisoners' federal rights, they must surely be alerted to the fact that the prisoners are asserting claims under the United States Constitution."). It is not enough to recite "only . . . the facts necessary to state a claim for relief," Gray v. Netherlands 518 U.S. 152, 163, 116 S.Ct. 2074, 135 L.Ed.2d 457 (1996) (citing Picard, 404 U.S. 270, 92 S.Ct. 509, 30 L.Ed.2d 438), or to "make a general appeal to a constitutional guarantee as broad as due process," id. (citing Anderson v. Harless, 459 U.S. 4, 103 S.Ct. 276, 74 L.Ed.2d 3 (1982) (per curiam)). Likewise, "[m]ere similarity between . . . state law claims and . . . federal habeas claims is insufficient" to satisfy the fair presentation requirement. Carney v. Fabian, 487 F.3d 1094, 1097 (8th Cir. 2007) (alteration in original) (quoting McCall v. Benson, 114 F.3d 754, 757 (8th Cir. 1997)). Thus, we have held that "[i]n order to fairly present a federal claim to the state courts, the petitioner must have referred to a specific federal constitutional right, a particular constitutional provision, a federal constitutional case, or a state case raising a pertinent federal constitutional issue in a claim before the state courts." Id. at 1096 (internal quotation marks omitted) (quoting McCall, 114 F.3d at 757). If a prisoner fails to present his federal claims to the state courts, those claims are generally considered procedurally defaulted. See, e.g., Barrett v. Acevedo, 169 F.3d 1155, 1161 (8th Cir. 1999) (en banc) (citing Abdullah v. Groose, 75 F.3d 408, 411 (8th Cir. 1996) (en banc)).

The dispositive question in this case is whether the petitioner presented any federal claims to the Minnesota Supreme Court on appeal from the trial court's denial of postconviction relief. We find that the answer is "no." Simply comparing the arguments made in the petitioner's briefs to this court and the arguments made in the petitioner's brief to the Minnesota Supreme Court shows that the petitioner is attempting to raise a new claim in federal court that he failed to present in state court.

The petitioner's briefs to this court contain three principal arguments, which appear to be variations on a single federal claim: namely, that the denial of his requests for postconviction relief either directly violated or failed to remedy an existing violation of his due process rights under the Fourteenth Amendment. The first argument centers on a line of cases, stretching back to Mooney v. Holohan, 294 U.S. 103, 55 S.Ct. 340, 79 L.Ed. 791 (1935) (per curiam), in which the U.S. Supreme Court has held that "a conviction obtained by the knowing use of perjured testimony is fundamentally unfair, and must be set aside if there is any reasonable likelihood that the false testimony could have affected the judgment of the jury," United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) (footnotes omitted). See also, e.g., Pyle v. Kansas, 317 U.S. 213, 63 S.Ct. 177, 87 L.Ed. 214 (1942); Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959); Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). The petitioner contends that applying the rule prohibiting the knowing use of perjured testimony to the facts revealed in Quantez's affidavit demonstrates that he is entitled to a new trial, or at least an evidentiary hearing.

The petitioner's second argument builds on the first. While the precise contours of this argument are difficult to define, the crux seems to be that precedents such as Pyle and Giglio establish that an evidentiary hearing must be held to test the verity of a witness's recantation, at least in circumstances where the recantation introduces the possibility of a due process violation. Therefore, according to the petitioner, the state courts were obligated under federal law to hold an evidentiary hearing to assess Quantez's recantation, or to grant his request for a new trial outright.

The petitioner's third argument posits that the Minnesota Supreme Court deprived him of due process in his appeal from the denial of postconviction relief by applying the test set out in Larrison v. United States, 24 F.2d 82 (7th Cir. 1928). Under Larrison, as it has been interpreted by the Minnesota Supreme Court, a prisoner may be granted a new trial based on a witness's recantation if two conditions are met: "(1) the court is reasonably well-satisfied that the testimony given by a material witness was false; [and] (2) . . . without the testimony, the jury might have reached a different conclusion." Turnage II, 729 N.W.2d at 597 (ellipsis in original) (quoting Williams v. State, 692 N.W.2d 893, 896 (Minn. 2005)). The petitioner notes that a majority of federal courts of appeals, including the Seventh Circuit (where Larrison originated), have rejected the Larrison test in favor of a "probability" test, which we have said "require[s] a petitioner seeking a new trial to show [that] the jury would have `probably' or `likely' reached a different verdict had the perjury not occurred," Evenstad v. Carlson, 470 F.3d 777, 783 n. 6 (8th Cir. 2006) (collecting cases from the First, Second, Fourth, Seventh, Eighth, Ninth, Tenth, and D.C. Circuits). But see id. (collecting cases from the Third, Fourth, and Sixth Circuits that apply the "might have" or "possibility" standard set out in Larrison). Based on this trend away from Larrison in the federal courts of appeals, combined with the purported similarity between the "probability" test and the "any reasonable likelihood" standard that applies to the knowing use of perjured testimony, the petitioner suggests that the Minnesota Supreme Court should have repudiated the Larrison test and granted him relief.

The petitioner's brief to the Minnesota Supreme Court contained three principal arguments, and none of them matches any of the arguments presented to this court. The petitioner first argued that the trial court improperly reached a conclusion concerning the veracity of Quantez's recantation without holding an evidentiary hearing to evaluate his credibility. The petitioner asserted, among other things, that the trial court's approach was contrary to the rule established in Opsahl v. State, 677 N.W.2d 414 (Minn. 2004). See id. at 423-24 (holding that a trial court misapplied the Minnesota statute governing hearings on petitions for postconviction relief, Minn. Stat. § 590.04, and therefore abused its discretion, in "concluding that [witness] recantations were unreliable without first evaluating the credibility of the witnesses at an evidentiary hearing").

The petitioner next argued that the trial court misapplied the "second prong" of the Larrison test. In particular, the petitioner found fault with the trial court's conclusion that "if Quantez Turnage had not testified at the [petitioner's] trial, the jury would still have had a sufficient factual basis to reach the same verdict." The sufficiency of the other evidence was beside the point, the petitioner claimed, because the Larrison test required him to show only that without Quantez's testimony the jury might have reached a different verdict.

The petitioner's final argument was that considering Quantez's recantation under the correct legal standards would yield the conclusion that he was entitled to a new trial, or at least an evidentiary hearing. Notably, the petitioner stated that the applicable legal standard for granting a new trial was the "test articulated in Larrison v. United States." And the petitioner asserted that the standard for granting an evidentiary hearing was less burdensome than the standard for granting a new trial, citing Opsahl and King v. State, 649 N.W.2d 149 (Minn. 2002), both of which discuss the Minnesota statute governing hearings on petitions for postconviction relief. See King, 649 N.W.2d at 156 ("A postconviction court must hold a hearing on the petition `[u]nless the petition and the files and records of the proceeding conclusively show that the petitioner is entitled to no relief.'" (alteration in original) (quoting Minn. Stat. § 590.04, subd. 1)); see also Opsahl, 677 N.W.2d at 423 ("We have interpreted [section 590.04] . . . to require the petitioner to allege facts that, if proven, would entitle him to the requested relief." (citing Ferguson v. State, 645 N.W.2d 437, 446 (Minn. 2002))).

The Minnesota Supreme Court considered the three arguments that we have just recited and affirmed the denial of postconviction relief. See Turnage II, 729 N.W.2d at 597-600. We need not recapitulate the details of the Minnesota Supreme Court's analysis, for what counts here is that the court's analysis was confined to matters of state law. This is patently obvious regarding the petitioner's claimed right to an evidentiary hearing under section 590.04 of the Minnesota Statutes, as interpreted in cases such as Opsahl and King. It is perhaps less obvious that the petitioner's claimed right to a new trial under Larrison also involved a matter of state law; Larrison, after all, is a federal case. Nevertheless, Larrison has no readily discernible constitutional underpinnings. See United States v. Huddleston, 194 F.3d 214, 219 (1st Cir. 1999) ("The Seventh Circuit adopted the possibility standard [in Larrison] without any developed reasoning."). And the courts that later adopted the Larrison test apparently did so "in the exercise of their supervisory powers." United States ex rel. Rice v. Vincent, 491 F.2d 1326, 1332 (2d Cir. 1974). Now that the Larrison test has been rejected by a majority of federal courts of appeals, including the Seventh Circuit, the notion that Larrison announced a mandatory federal standard would be virtually impossible to maintain. We are convinced, then, that the Minnesota Supreme Court's application of the Larrison test, as the test has been interpreted in cases such as Opsahl and Williams v. State, 692 N.W.2d 893 (Minn. 2005), was entirely a matter of state law.

Although the petitioner insists that he fairly presented his federal "habeas claims" to the state courts, that proposition is incorrect. The petitioner's brief to the Minnesota Supreme Court did not cite Mooney, Pyle, Napue, Giglio, Agurs, or any other case raising a pertinent federal constitutional issue. Nor did the petitioner's brief specifically refer to a provision of the U.S. Constitution or a right arising thereunder. Cf. Carney v. Fabian, 487 F.3d 1094, 1096 (8th Cir. 2007) ("In order to fairly present a federal claim to the state courts, the petitioner must have referred to a specific federal constitutional right, a particular constitutional provision, a federal constitutional case, or a state case raising a pertinent federal constitutional issue in a claim before the state courts." (internal quotation marks omitted) (quoting McCall v. Benson, 114 F.3d 754, 757 (8th Cir. 1997))). The petitioner certainly did not contend that applying the Larrison test would deprive him of due process; on the contrary, the petitioner stated unequivocally that the "test articulated in Larrison "was the applicable legal standard for granting a new trial.

Notwithstanding these deficiencies in his fair presentation argument, the petitioner seems to think it is particularly relevant that both the state and federal proceedings revolve around Quantez's affidavit. We cannot agree, since a petitioner does not fairly present the substance of a federal claim merely by reciting the underlying facts. See Gray v. Netherlands 518 U.S. 152, 163, 116 S.Ct. 2074, 135 L.Ed.2d 457 (1996) (citing Picard v. Connor, 404 U.S. 270, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971)). The petitioner also points out that he has consistently demanded an evidentiary hearing to investigate Quantez's bona fides. But this too is inapposite, since in the Minnesota Supreme Court the petitioner sought an evidentiary hearing as a matter of state law. While the petitioner now asserts that federal law required the state court to grant the requested hearing, asking for the same relief on different grounds does not retroactively convert the state law claim presented in the petitioner's brief to the Minnesota Supreme Court into a federal claim. Any similarity between the petitioner's state and federal claims regarding the need for a hearing on Quantez's credibility is not alone sufficient to satisfy the fair presentation requirement. See Carney, 487 F.3d at 1097. Finally, the petitioner identifies a single mention of the term "due process" in his state court filings, but it comes in his petition for postconviction relief, not in his brief to the Minnesota Supreme Court, and it is followed closely by references to the state law standards for granting an evidentiary hearing under section 590.04 and for granting a new trial under Larrison. Even assuming that the state petition contained more than a "general appeal" to the constitutional guarantee of due process, see Gray, 518 U.S. at 163, 116 S.Ct. 2074 (citing Anderson v. Harless, 459 U.S. 4, 103 S.Ct. 276, 74 L.Ed.2d 3 (1982) (per curiam)), the petitioner abandoned the issue on appeal to the Minnesota Supreme Court by not referring to the Due Process Clause as an independent ground on which relief could be granted.

The Minnesota Supreme Court did not address any federal claims because none were fairly presented in the petitioner's brief to that court. Although the petitioner raises a federal due process claim in his briefs to this court, his failure to present that claim to the Minnesota Supreme Court means that it is procedurally defaulted, along with any other potential federal claims relating to Quantez's recantation. See, e.g., Scruggs v. State, 484 N.W.2d 21, 24 n. 1 (Minn. 1992) (holding that a claim not presented on appeal is "deemed waived" (citing Balder v. Haley, 399 N.W.2d 77, 80 (Minn. 1987))); Melina v. Chaplin, 327 N.W.2d 19, 20-21 (Minn. 1982) (collecting cases applying the waiver rule); see also Wooten v. Norris, 578 F.3d 767, 777 (8th Cir. 2009) ("A claim is procedurally defaulted if a habeas petitioner failed to raise it in state proceedings."). The petitioner does not attempt to show that he could revive the defaulted due process claim in the state courts, and we are satisfied that such an effort would be unsuccessful. See Powers v. State, 731 N.W.2d 499, 501 (Minn. 2007) ("Matters . . . known but not raised in an earlier petition for postconviction relief will generally not be considered in subsequent petitions for postconviction relief." (citing Spears v. State, 725 N.W.2d 696, 700 (Minn. 2006))).

The U.S. Supreme Court has established that "federal habeas review of [defaulted] claims is barred unless the prisoner can demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law, or demonstrate that failure to consider the claims will result in a fundamental miscarriage of justice." Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). Here, the petitioner makes no attempt to show cause for failing to present his federal due process claim to the Minnesota Supreme Court, so he may obtain review of that claim "only if he falls within the `narrow class of cases . . . implicating a fundamental miscarriage of justice.'" Schlup v. Delo, 513 U.S. 298, 314-15, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995) (ellipsis in original) (quoting McCleskey v. Zant, 499 U.S. 467, 494, 111 S.Ct. 1454, 113 L.Ed.2d 517 (1991)); see also Murray v. Carrier, 477 U.S. 478, 496, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986) ("[I]n an extraordinary case, where a constitutional violation has probably resulted in the conviction of one who is actually innocent, a federal habeas court may grant the writ even in the absence of a showing of cause for the procedural default."). While the petitioner comes close to arguing that Quantez's affidavit proves that he is innocent, he does not invoke the miscarriage-of-justice exception or otherwise acknowledge the burden he would face in making a gateway claim of actual innocence. See Schlup, 513 U.S. at 316, 115 S.Ct. 851 (explaining that the miscarriage-of-justice exception requires prisoners to present "evidence of innocence so strong that a court cannot have confidence in the outcome of the trial unless the court is also satisfied that the trial was free of nonharmless constitutional error"). In any event, given the other evidence introduced at trial, including several tape-recorded conversations in which the petitioner showed clear consciousness of guilt, see Turnage II, 729 N.W.2d at 596, 600; Turnage I, 708 N.W.2d at 541, the petitioner's scattered assertions concerning his alleged innocence are unconvincing. We therefore conclude that the petitioner has failed to demonstrate either cause and prejudice or a fundamental miscarriage of justice that would permit us to review his defaulted federal claim.

We must tie up two more loose ends before concluding. First, it should go without saving that this court cannot review the Minnesota Supreme Court's adjudication of the petitioner's state law claims. As we have said time and again, "we lack authority to review . . . state courts' interpretation and application of state law." Evenstad v. Carlson, 470 F.3d 777, 782 (8th Cir. 2006). Thus, we express no opinion about whether the Minnesota Supreme Court correctly interpreted and applied state law in affirming the denial of post-conviction relief.

Second, at oral argument, counsel for the petitioner informed us that the petitioner's other codefendant, Damien Robinson, has now also recanted his trial testimony in a handwritten affidavit. Counsel subsequently reported that the state trial court granted the petitioner's request for an evidentiary hearing regarding Robinson's alleged recantation. In its order, the court scheduled the hearing for May 10, 2010, asked the public defender's office to appoint someone to serve as counsel for Robinson, and announced that "[a]ny issue regarding the alleged recantation of the trial testimony by Quantez Turnage is reserved." Although the petitioner's counsel has promised to keep us apprised of developments in the new state court proceeding, counsel has not asked this court to hold the present appeal in abeyance. A survey of the caselaw shows that other circuits have found in similar circumstances that the pendency of parallel state court proceedings does not necessarily prevent federal courts from adjudicating § 2254 petitions containing fully exhausted federal claims. See, e.g., Slutzker v. Johnson, 393 F.3d 373, 384 (3d Cir. 2004); Nowaczyk v. Warden of N.H. State Prison, 299 F.3d 69, 77 (1 st Cir. 2002); Carter v. Estelle, 677 F.2d 427, 436 n. 4 (5th Cir. 1982); see also Jimenez v. Fla. Dep't of Corr., 481 F.3d 1337, 1342 n. 3 (11th Cir. 2007) (finding that filing motions and petitions in state court after filing an application for habeas corpus under § 2254 did not affect "the determination of issue exhaustion in [the federal] application"). Thus, we see no good reason to withhold our decision pending the outcome of the parallel state court proceeding.

In summary, the petitioner in his briefs to this court raises a federal due process claim relating to Quantez's recantation, but that claim is procedurally defaulted because the petitioner did not present it to the Minnesota Supreme Court. We do not reach the merits of the defaulted claim because the petitioner has failed to show either cause and prejudice or a fundamental miscarriage of justice that would permit us to do so. And we cannot review the Minnesota Supreme Court's adjudication of the petitioner's state law claims relating to Quantez's recantation. Though Robinson has now allegedly recanted, the pendency of a new state court proceeding concerning Robinson's recantation does not require this court, sua sponte, to enter an order holding the present appeal in abeyance. Accordingly, we affirm the dismissal of the petition.