COOK, Circuit Judge.
Following a bench trial, Milton Harris was convicted of second-degree homicide for killing Sammy Wright. On appeal from the denial of his petition for habeas corpus, he claims that insufficient evidence supports his conviction. We affirm.
I. Facts and Procedural History
When Milton Harris walked by Sammy Wright’s house one night in 1999, Wright made threatening or harassing statements to Harris while allegedly brandishing a gun. Harris went to his own house, and, some time later, returned to Wright’s house with a shotgun. Wright was still on his porch and continued to threaten or harass Harris, and eventually Harris shot and killed Wright.
Michigan tried Harris for the shooting, and, after a bench trial, the state court found Harris guilty of second-degree murder (though the prosecution had pressed the first-degree offense). The court began [321]*321its discussion of Harris's mental state by noting, “The only issue really is that of intent because for first-degree murder ... the defendant must have actually intended to kill the victim.” In concluding that Hands lacked the intent necessary for first-degree murder, the court repeatedly referred to Harris’s “anger,” and concluded that he lacked “actual intent ... to kill,” but still concluded that he “knowingly created a very high risk of death or great bodily harm knowing that death could result from his actions.” The court further concluded that Harris’s actions “were not justified.” Toward the end of its discussion, the court explained that “one of the words we used to hear is hot blood and I think this was a shooting which came from hot blood.” The court, however, had previously stated,
Now, in this case there was time [between Wright accosting Harris and Harris returning to shoot Wright.] The defendant was home, he was in a position of safety, he could have stayed there. If he felt he had been treated badly or dissed, in today’s language, he could have chosen to ignore it. If he felt he had been threatened, he could have called the police.... ”
Ultimately, the court rejected the first-degree offense and instead found Harris guilty of second-degree murder.
Harris appealed, claiming that the trial court’s inconsistent findings on his intent failed to support the second-degree offense; that is, because the trial court mentioned “hot blood,” it should have convicted him of voluntary manslaughter.1 The Michigan Court of Appeals affirmed, People v. Harris, No. 231398, 2002 WL 1424839 (Mich.Ct.App. June 28, 2002), but the Michigan Supreme Court vacated and remanded “for further findings of fact regarding the defendant’s intent,” People v. Harris, 468 Mich. 879, 659 N.W.2d 240 (Mich.2003) (table). On remand, the state trial court provided detailed findings of fact. The court explained that its “erroneous and unfortunate use of the phrase ‘that this was [a] shooting which came from hot blood[,]’ was in no way intended to mean that it meets the test for voluntary manslaughter.” It went on to explain at length why the record did not support a voluntary manslaughter conviction: in short, a reasonable person would not have been acting out of irresistible passion given the amount of time Harris had to “cool off” following Wright’s harassment. It then reiterated its finding that Harris “knowingly created a very high risk of death or great bodily harm, knowing that death or harm would be the likely result of his actions.” The trial court again found Hands guilty of second-degree murder. The Michigan Court of Appeals affirmed, People v. Harris, No. 231398, 2003 WL 21771746 (Mich. Ct.App. July 31, 2003) (mem.), and the Michigan Supreme Court denied leave to appeal, People v. Harris, 469 Mich. 989, 674 N.W.2d 155 (Mich.2003) (table).
Harris filed a habeas petition — rather than independently brief his claim, he attached a copy of the briefs he had previously presented to the state courts. A magistrate judge recommended denying the petition, and the district court adopted the magistrate’s report and denied the petition. Harris moved for a Certificate of Appealability, which the district court denied. On appeal this court granted a Certificate of Appealability but only as to Har[322]*322ris’s claim that “the evidence presented before the trial court regarding [his] intent required the reduction of his conviction from second-degree murder to voluntary manslaughter.”
II. Sufficiency of the Evidence as to Harris’s Intent
Harris claims that the state trial court erred by convicting him of second-degree murder when, according to Harris, the facts adduced at trial support only voluntary manslaughter.
The first question is whether Harris exhausted this claim in state court. We determine he did not. To satisfy the exhaustion requirement, a state prisoner must present his claim to the state courts, and he must present it as the denial of some federal constitutional right. Duncan v. Henry, 513 U.S. 364, 365-66, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995) (“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.”). The prisoner need not “cite book and verse on the federal constitution,” id. at 365, 115 S.Ct. 887; he need only “fairly present” his claim to the state court, see Picard v. Connor, 404 U.S. 270, 275, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971); Newton v. Million, 349 F.3d 873, 877 (6th Cir.2003). In this circuit, fair presentation generally depends on whether the prisoner has “(1) reli[ed] upon federal cases employing constitutional analysis; (2) reli[ed] upon state cases employing federal constitutional analysis; (3) phras[ed] the claim in terms of constitutional law or in terms sufficiently particular to allege a denial of a specific constitutional right; or (4) alleged] facts well within the mainstream of constitutional law.” Newton, 349 F.3d at 877 (quoting McMeans v. Brigano, 228 F.3d 674, 681 (6th Cir.2000)); see also Blackmon v. Booker, 394 F.3d 399, 400 (6th Cir.2004). “General allegations of the denial of rights to a ‘fair trial’ and ‘due process’ do not ‘fairly present claims’ that specific constitutional rights were violated.” McMeans, 228 F.3d at 681.
In response to the government’s contention that he has not met this standard, Harris argues that his “claims of insufficiency of evidence ... [are] ‘well within the mainstream of the pertinent constitutional law.’ ” See id. We cannot agree, as Harris’s filings did not sufficiently apprise the state courts of the federal constitutional nature of his claims. In the brief submitted to the Michigan Court of Appeals (before the Michigan Supreme Court remanded for further findings on his intent), Harris argued that the trial court “failed to apply the correct rule of [state ] law” to its “specific findings of fact concerning the circumstances surrounding the killing,” in violation of Mich. Ct. R. 6.403.
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COOK, Circuit Judge.
Following a bench trial, Milton Harris was convicted of second-degree homicide for killing Sammy Wright. On appeal from the denial of his petition for habeas corpus, he claims that insufficient evidence supports his conviction. We affirm.
I. Facts and Procedural History
When Milton Harris walked by Sammy Wright’s house one night in 1999, Wright made threatening or harassing statements to Harris while allegedly brandishing a gun. Harris went to his own house, and, some time later, returned to Wright’s house with a shotgun. Wright was still on his porch and continued to threaten or harass Harris, and eventually Harris shot and killed Wright.
Michigan tried Harris for the shooting, and, after a bench trial, the state court found Harris guilty of second-degree murder (though the prosecution had pressed the first-degree offense). The court began [321]*321its discussion of Harris's mental state by noting, “The only issue really is that of intent because for first-degree murder ... the defendant must have actually intended to kill the victim.” In concluding that Hands lacked the intent necessary for first-degree murder, the court repeatedly referred to Harris’s “anger,” and concluded that he lacked “actual intent ... to kill,” but still concluded that he “knowingly created a very high risk of death or great bodily harm knowing that death could result from his actions.” The court further concluded that Harris’s actions “were not justified.” Toward the end of its discussion, the court explained that “one of the words we used to hear is hot blood and I think this was a shooting which came from hot blood.” The court, however, had previously stated,
Now, in this case there was time [between Wright accosting Harris and Harris returning to shoot Wright.] The defendant was home, he was in a position of safety, he could have stayed there. If he felt he had been treated badly or dissed, in today’s language, he could have chosen to ignore it. If he felt he had been threatened, he could have called the police.... ”
Ultimately, the court rejected the first-degree offense and instead found Harris guilty of second-degree murder.
Harris appealed, claiming that the trial court’s inconsistent findings on his intent failed to support the second-degree offense; that is, because the trial court mentioned “hot blood,” it should have convicted him of voluntary manslaughter.1 The Michigan Court of Appeals affirmed, People v. Harris, No. 231398, 2002 WL 1424839 (Mich.Ct.App. June 28, 2002), but the Michigan Supreme Court vacated and remanded “for further findings of fact regarding the defendant’s intent,” People v. Harris, 468 Mich. 879, 659 N.W.2d 240 (Mich.2003) (table). On remand, the state trial court provided detailed findings of fact. The court explained that its “erroneous and unfortunate use of the phrase ‘that this was [a] shooting which came from hot blood[,]’ was in no way intended to mean that it meets the test for voluntary manslaughter.” It went on to explain at length why the record did not support a voluntary manslaughter conviction: in short, a reasonable person would not have been acting out of irresistible passion given the amount of time Harris had to “cool off” following Wright’s harassment. It then reiterated its finding that Harris “knowingly created a very high risk of death or great bodily harm, knowing that death or harm would be the likely result of his actions.” The trial court again found Hands guilty of second-degree murder. The Michigan Court of Appeals affirmed, People v. Harris, No. 231398, 2003 WL 21771746 (Mich. Ct.App. July 31, 2003) (mem.), and the Michigan Supreme Court denied leave to appeal, People v. Harris, 469 Mich. 989, 674 N.W.2d 155 (Mich.2003) (table).
Harris filed a habeas petition — rather than independently brief his claim, he attached a copy of the briefs he had previously presented to the state courts. A magistrate judge recommended denying the petition, and the district court adopted the magistrate’s report and denied the petition. Harris moved for a Certificate of Appealability, which the district court denied. On appeal this court granted a Certificate of Appealability but only as to Har[322]*322ris’s claim that “the evidence presented before the trial court regarding [his] intent required the reduction of his conviction from second-degree murder to voluntary manslaughter.”
II. Sufficiency of the Evidence as to Harris’s Intent
Harris claims that the state trial court erred by convicting him of second-degree murder when, according to Harris, the facts adduced at trial support only voluntary manslaughter.
The first question is whether Harris exhausted this claim in state court. We determine he did not. To satisfy the exhaustion requirement, a state prisoner must present his claim to the state courts, and he must present it as the denial of some federal constitutional right. Duncan v. Henry, 513 U.S. 364, 365-66, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995) (“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.”). The prisoner need not “cite book and verse on the federal constitution,” id. at 365, 115 S.Ct. 887; he need only “fairly present” his claim to the state court, see Picard v. Connor, 404 U.S. 270, 275, 92 S.Ct. 509, 30 L.Ed.2d 438 (1971); Newton v. Million, 349 F.3d 873, 877 (6th Cir.2003). In this circuit, fair presentation generally depends on whether the prisoner has “(1) reli[ed] upon federal cases employing constitutional analysis; (2) reli[ed] upon state cases employing federal constitutional analysis; (3) phras[ed] the claim in terms of constitutional law or in terms sufficiently particular to allege a denial of a specific constitutional right; or (4) alleged] facts well within the mainstream of constitutional law.” Newton, 349 F.3d at 877 (quoting McMeans v. Brigano, 228 F.3d 674, 681 (6th Cir.2000)); see also Blackmon v. Booker, 394 F.3d 399, 400 (6th Cir.2004). “General allegations of the denial of rights to a ‘fair trial’ and ‘due process’ do not ‘fairly present claims’ that specific constitutional rights were violated.” McMeans, 228 F.3d at 681.
In response to the government’s contention that he has not met this standard, Harris argues that his “claims of insufficiency of evidence ... [are] ‘well within the mainstream of the pertinent constitutional law.’ ” See id. We cannot agree, as Harris’s filings did not sufficiently apprise the state courts of the federal constitutional nature of his claims. In the brief submitted to the Michigan Court of Appeals (before the Michigan Supreme Court remanded for further findings on his intent), Harris argued that the trial court “failed to apply the correct rule of [state ] law” to its “specific findings of fact concerning the circumstances surrounding the killing,” in violation of Mich. Ct. R. 6.403. He relied exclusively on state-court cases, all of which concern only the state of mind required to support different degrees of homicide as a matter of state law. In his 2003 application for leave to appeal to the Michigan Supreme Court, he continued to question the application of Michigan homicide law to the facts of his case. Review of the record does not reveal any other briefs submitted by Harris, and a habeas petitioner bears the burden of establishing that he has exhausted in state court. See Caver v. Straub, 349 F.3d 340, 345 (6th Cir.2003) (citing Rust v. Zent, 17 F.3d 155, 160 (6th Cir.1994)). Because Harris has no remaining state court avenue in which to properly exhaust this claim, it is procedurally defaulted, and he has not attempted to show cause and prejudice sufficient to excuse the default. See Martin v. Mitchell, 280 F.3d 594, 603 (6th Cir.2002).
[323]*323Even if we were to find this claim exhausted, Harris still could not prevail. He cannot establish that the evidence was insufficient to support his conviction for second-degree murder. Under Jackson v. Virginia, Harris must show that “no rational trier of fact could have found proof of guilt [of second-degree murder] beyond a reasonable doubt.” 443 U.S. 307, 324, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979). After the Michigan Supreme Court’s remand, the trial court clarified any ambiguity in its earlier findings and found the facts necessary to support every element of a conviction for second-degree murder. See, e.g., People v. Smith, 478 Mich. 64, 731 N.W.2d 411, 414-15 (2007) (defining the elements of second-degree murder as “(1) a death, (2) the death was caused by an act of the defendant, (3) the defendant acted with malice, and (4) the defendant did not have lawful justification or excuse for causing the death”); People v. Neal, 201 Mich.App. 650, 506 N.W.2d 618, 620 (1993) (defining “malice” as “an intent to kill, an intent to do great bodily harm, or an intent to create a high risk of death or great bodily harm with knowledge that such is the probable result”).
Finally, to the extent Harris claims that the trial court’s initial findings compelled a conviction of voluntary manslaughter under Michigan homicide law, his claim is not cognizable on federal habeas review, as “it is not the province of a federal habeas court to reexamine state-court determinations on state-law questions.” Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991); see also Ege v. Yukins, 485 F.3d 364, 375 (6th Cir.2007).
III. Double Jeopardy Clause
Harris also invokes the Double Jeopardy Clause to complain of the state courts’ findings regarding his mental state. He claims that both the trial court and the Michigan Supreme Court (in its remand order) either explicitly or implicitly acquitted him of second-degree murder by finding the evidence legally insufficient, and therefore, the trial court on remand could not constitutionally convict him of that offense. Given that this issue lacks certification, even implicitly, we decline to address either exhaustion or the merits of the claim. See 28 U.S.C. § 2253(c).
IV. “Right to Present a Defense”
We treat likewise Harris’s argument — concededly uncertified for review— that the state trial court violated his federal constitutional “right to present a meaningful defense” when it denied his motion for a continuance to locate a res gestae witness after the prosecution had endorsed the witness but failed to produce him for trial.
V. Conclusion
We affirm the judgment of the district court.