OPINION RONALD LEE GILMAN, Circuit Judge.

After a bench trial in Michigan state court, Damon Hudson was convicted in September 2001 of assault with intent to commit murder, in violation of Mich. Comp. Laws § 750.83; possession of a firearm during the commission of a felony, in violation of Mich. Comp. Laws § 750.227b; and armed robbery, in violation of Mich. Comp. Laws § 750.529. These convictions were based on the fact that Hudson robbed Keith Bradley at gunpoint at an automatic teller machine (ATM) and shot Bradley as the latter drove away. Hudson is in a state prison serving a maximum sentence of 52 years for these crimes.

After exhausting his direct appeals and postconviction relief in the state courts, Hudson filed a habeas corpus petition in federal district court that asserted several constitutional claims. The district court denied his habeas petition and denied his request for a certificate of appealability (COA). This court then granted Hudson a COA on his claims that (1) the evidence was insufficient to support the conviction, and (2) the admission of the gun found in his car was an error rising to the level of a due process violation. Hudson now appeals the denial of his habeas petition, arguing that the writ should issue based on these two claims. For the reasons set forth below, we AFFIRM the judgment of the district court.

I. BACKGROUND

As noted above, Hudson's three convictions were based on his robbing Bradley at gunpoint at an ATM and shooting Bradley as the latter drove away. Bradley's version of the relevant events is as follows: At about 4:00 a.m. on April 8, 2001, he was depositing a check and withdrawing money at an ATM on John R Street in Detroit, Michigan. A stranger came from around the ATM and stuck a revolver through Bradley's window and against Bradley's chest. Bradley feared for his life. The gunman told Bradley not to do anything stupid and requested Bradley's personal identification number (PIN). Bradley pushed his ATM card into the machine, entered his PIN, and told the gunman to withdraw money from his savings account. As the gunman turned toward the ATM to withdraw the money, Bradley put his car into gear and drove off, attempting to escape. The gunman shot at Bradley as he pulled away, hitting him in the forearm and thigh. Although Bradley collided with a tree during his escape, he managed to drive to a hospital where he was treated. More than $100 was withdrawn from Bradley's bank account after he drove away.

Sometime after 6:00 a.m. on the same day, a police officer interviewed Bradley at the hospital. Although Bradley was suffering from the gunshot wounds, he was able to explain what had happened and describe the suspect.

Bradley later attended a lineup, but was unable to identify anyone. He described the suspect as a 5'10" tall male, weighing 180 to 200 pounds, and having a dark complexion. Although Bradley told the police that the suspect had short hair, he admitted at trial that a picture of the suspect at the ATM showed that the suspect wore something on his head that covered his hair.

Hudson told a very different story. He testified that he knew Bradley as "Whitey," Bradley's street name, and that Bradley had purchased cocaine from Hudson on several prior occasions. During the early morning hours in question, Hudson said that he met Bradley near a whore-house through Angie, a prostitute. Bradley allegedly wanted to buy more cocaine, but he already owed Hudson $200 from a previous drug purchase, and Bradley needed to pay Angie. Hudson and Bradley then drove to the ATM in separate cars so that Bradley could get money to pay Hudson back and buy more drugs. Deandre Matchett, also called Jay Rock, accompanied Hudson. Hudson carried the cocaine that Bradley wanted to buy in a brown manilla envelope.

According to Hudson, Bradley activated his ATM card and instructed Hudson to withdraw $300 from his account. Hudson tried to withdraw the money, but Bradley's account had insufficient funds. Bradley then drove away and, as he did so, Hudson contends that the envelope containing the cocaine fell inside Bradley's car. Hudson remained at the ATM for about eight seconds after that, unsuccessfully trying to withdraw money. Hudson denied having a gun, shooting Bradley, or knowing how Bradley got shot. He also testified that he did not see Matchett with a gun and that Matchett did not shoot Bradley either. Matchett was not called as a witness by either party.

Bradley and Hudson's encounter at the ATM was captured on a video-surveillance system. The prosecution introduced 29 photographs taken from the ATM's surveillance video into evidence. Unfortunately, these photographs are not part of the record on appeal because the police were unable to locate the file and the state trial court no longer has the pictures. What these photographs show, or do not show, is therefore necessarily based on the trial testimony of Bradley and Hudson.

Bradley testified that the man pictured outside his car in the photographs is the man who robbed and shot him. Hudson admitted that he was the person standing outside of Bradley's car and that he was wearing a black nylon "do-rag" (a head covering). Although Bradley admitted that the pictures did not show Hudson holding a gun, the testimony establishes only that Hudson's left hand is visible, not his right. Both parties acknowledge that the pictures showed Hudson holding a small object that looks like an envelope in his left hand. Hudson claimed that this was the envelope containing the cocaine.

Two days after the robbery, Hudson was apprehended. He was in a car with Matchett that the police stopped on John R Street. The officers arrested the two men. Sergeant Benito Mendoza impounded the car and conducted an inventory search of its contents. The search revealed a loaded revolver and Hudson's identification in the trunk and a do-rag in the back seat. Both the gun and the do-rag were admitted into evidence. Hudson testified that the gun and do-rag recovered from his car belonged to Matchett, who had borrowed his car the previous night.

During closing argument, Hudson's attorney argued that the photographs supported Hudson's version of events and undercut Bradley's because no gun appeared in the pictures. The attorney also argued that there was a reasonable probability that someone else shot Bradley because Bradley was involved in drugs, a dangerous habit. Finally, the attorney argued that even if Hudson shot Bradley, Hudson lacked the intent to kill that is necessary to convict Hudson of assault with intent to commit murder.

The state trial judge credited Hudson's testimony that he was a street thug who dealt in drugs and prostitution, but the judge stated that he did not believe anything else that Hudson said. At the end of the trial, the judge found that Hudson accosted Bradley at the ATM, attempted to rob him, and shot Bradley as the latter drove away. Accordingly, the judge found Hudson guilty of assault with intent to commit murder, possession of a firearm during the commission of a felony, and armed robbery.

Hudson was sentenced to a term of 25 to 50 years in prison for the armed robbery, a concurrent sentence of 25 to 50 years for assault with intent to commit murder, and a consecutive sentence of 2 years for possession of a firearm during the commission of a felony. The trial judge later granted Hudson's motion for resentencing, amending his sentence on the armed-robbery conviction to 17 years, 6 months. Hudson's overall maximum sentence remained at 52 years.

In December 2002, Hudson filed a delayed application for leave to appeal with the Michigan Court of Appeals, arguing (1) that the evidence was insufficient to support his conviction, and (2) that admitting the gun into evidence was prejudicial error. The Michigan Court of Appeals denied the leave to appeal in March 2003 in a summary order "for lack of merit in the grounds presented." Hudson then raised the same two claims before the Michigan Supreme Court, which also denied leave to appeal in a summary order "because [it was] not persuaded that the questions presented should be reviewed by [it]."

Next, Hudson raised five issues of alleged error in a motion for relief from judgment under Michigan Court Rules (MCR) 6.500 et seq. (Hudson actually raised nine issues counting the sub-issues.) In broad terms, Hudson alleged that he was denied his right to the effective assistance of trial and appellate counsel; that his sentence was based on inaccurate information; that he was actually innocent; and that the trial court deprived him of his constitutional rights in a variety of ways, including the making of clearly erroneous findings of fact. The trial court denied this motion for two reasons: (1) Hudson had not satisfied MCR 6.508(D)(3)'s threshold requirement that he show good cause for failing to raise those claims on appeal and show actual prejudice resulting from the alleged errors; and (2) the claims were wholly without merit. Hudson appealed the trial court's decision, but both state appellate courts denied leave to appeal because Hudson failed to meet the burden of establishing entitlement to relief under MCR 6.508(D).

This led Hudson to file a habeas corpus petition in federal district court in accordance with 28 U.S.C. § 2254. Hudson alleged, among other things, that the evidence was insufficient to support his conviction and that admitting the gun into evidence was prejudicial error. The State asserted that several of Hudson's claims were procedurally defaulted, but the district court analyzed all of Hudson's claims on the merits without considering the procedural-default issues because it found that approach more efficient. Applying the standards set forth in the Antiterrorism and Effective Death Penalty Act (AEDPA), which is codified in part at 28 U.S.C. § 2254(d), the court denied habeas relief.

Hudson then filed a motion for a COA, which the district court denied in August 2008. In March 2009, a single judge of the Sixth Circuit also denied Hudson a COA. But Hudson petitioned for a rehearing of the Sixth Circuit's ruling and, in August 2009, this court granted him a COA on two issues: (1) "whether the evidence was sufficient to support the convictions," and (2) "whether the admission of the gun found in Hudson's car was an error rising to the level of a due process violation." In accordance with this COA, Hudson now appeals the district court's rulings.

II. ANALYSIS

Hudson argues that we should grant the writ of habeas corpus for three reasons: (1) the evidence was insufficient to convict him of the three offenses because the photographs prove that he did not have a gun during the incident; (2) even assuming that he had a gun, the evidence was insufficient to prove that he had the intent to kill Bradley, which is an essential element of the crime of assault with intent to commit murder; and (3) admitting the gun recovered from Hudson's car into evidence was an error that denied him his right to a fundamentally fair trial.

Before turning to the merits of these claims, we would ordinarily decide the exhaustion and procedural-default issues raised by the State. But the federal courts can bypass these threshold inquiries if they decide the merits against the petitioner, especially where analyzing the merits is less complex than analyzing the procedural issues. See 28 U.S.C. § 2254(b)(2) ("An application for a writ of habeas corpus may be denied on the merits, notwithstanding the failure of the applicant to exhaust the remedies available in the courts of the State."); Lambrix v. Singletary, 520 U.S. 518, 525, 117 S.Ct. 1517, 137 L.Ed.2d 771 (1997) (reasoning that the federal courts may ignore a complicated "procedural-bar issue" where the merits are "easily resolvable against the habeas petitioner"). Because we conclude that Hudson's claims lack merit, we will not analyze any exhaustion or procedural-default issues.

A. Standard of review

We review a district court's legal conclusions in a habeas case de novo and its factual findings under the clear-error standard. Lovell v. Duffey, 629 F.3d 587, 593-94 (6th Cir. 2011). In addition, federal courts review state-court decisions in habeas proceedings under the standards set forth in AEDPA ( 28 U.S.C. § 2254(d)). Section 2254(d) provides as follows:

(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim —

(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or

(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.

Section 2254(d) creates a "`highly deferential standard for evaluating state-court rulings,' which demands that state-court decisions be given the benefit of the doubt." Woodford v. Visciotti 537 U.S. 19, 24, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (quoting Lindh v. Murphy, 521 U.S. 320, 333 n. 7, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997)). A state-court decision is contrary to clearly established federal law under § 2254(d)(1) only if "the state court arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law or if the state court decides a case differently than [the Supreme Court] has on a set of materially indistinguishable facts." Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). "A state-court decision is an unreasonable application of clearly established federal law if it `correctly identifies the governing legal rule but applies it unreasonably to the facts of a particular prisoner's case.`" Parker v. Renico, 506 F.3d 444, 448 (6th Cir. 2007) (quoting Williams, 529 U.S. at 407-08, 120 S.Ct. 1495).

"When assessing unreasonableness, `a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable.`" Id. (quoting Williams, 529 U.S. at 411, 120 S.Ct. 1495).

With respect to § 2254(d)(2), "factual determinations by state courts are presumed correct absent clear and convincing evidence to the contrary, § 2254(e)(1), and a decision adjudicated on the merits in a state court and based on a factual determination will not be overturned on factual grounds unless objectively unreasonable in light of the evidence presented in the state-court proceeding."

Ayers v. Hudson, 623 F.3d 301, 308 (6th Cir. 2010) (brackets omitted) (quoting Miller-El v. Cockrell, 537 U.S. 322, 340, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003)).

Under AEDPA's strictures, we review the last state-court decision to reach the merits of the particular claim being considered. Phillips v. Bradshaw, 607 F.3d 199, 209 (6th Cir. 2010). As to the claims that Hudson raised on direct appeal, the Michigan Court of Appeals was the last state court to reach the merits. The last state-court to reach the merits of the claims that Hudson raised in his state postconviction proceedings was the trial court.

Because both of these courts issued summary opinions that do not discuss their reasoning, "we defer only to the result reached, not the reasoning used by the state court." Lovell, 629 F.3d at 595 (brackets and internal quotation marks omitted); accord Harris v. Stovall, 212 F.3d 940, 943 n. 1 (6th Cir. 2000) (holding that where a state court decides an issue in summary fashion, "a habeas court should then focus on the result of the state court's decision"). We conduct a "careful and independent review of the record and applicable law." Lovell, 629 F.3d at 595 (internal quotation marks omitted). But this independent review "is not a full, de novo review of the claims." Id. (internal quotation marks omitted). Our review instead "remains deferential because [we] cannot grant relief unless the state court's result is not in keeping with the strictures of the AEDPA." Id. (internal quotation marks omitted). The focus of our review, in other words, is "to determine whether, under the AEDPA standard, the state court decision is contrary to federal law, unreasonably applies clearly established law, or is based on an unreasonable determination of the facts in light of the evidence presented." Howard v. Bouchard, 405 F.3d 459, 467 (6th Cir. 2005).

B. Sufficiency of the evidence

In Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), the Supreme Court set forth the standard for challenges based on sufficiency of the evidence, holding that "the relevant question is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Id. at 319, 99 S.Ct. 2781 (emphasis in original). This standard is applied "with explicit reference to the substantive elements of the criminal offense as defined by state law." Id. at 324 n. 16, 99 S.Ct. 2781. Under this standard, a reviewing court does not reweigh the evidence, redetermine witness credibility, or substitute its judgment for the factfinder's. Brown v. Konteh, 567 F.3d 191, 205 (6th Cir. 2009).

"[A] federal habeas corpus court faced with a record of historical facts that supports conflicting inferences must presume — even if it does not affirmatively appear in the record — that the trier of fact resolved any such conflicts in favor of the prosecution, and must defer to that resolution." Jackson, 443 U.S. at 326, 99 S.Ct. 2781. "The mere existence of sufficient evidence to convict therefore defeats a petitioner's claim." Matthews v. Abramajtys, 319 F.3d 780, 788-89 (6th Cir. 2003). Because the Jackson standard and AEDPA both apply to a habeas petitioner's sufficiency-of-the-evidence claims, we review Hudson's arguments under a double layer of deference. See Tucker v. Palmer, 541 F.3d 652, 656 (6th Cir. 2008).

Hudson first argues that the evidence was insufficient to convict him of the three offenses because the photographs from the ATM surveillance video showed that he did not possess a gun during the incident. He asserts that even Bradley admitted that the photographs showed both of Hudson's hands and that he did not have a gun in either hand. This is the basis for his argument that the state trial court's finding that Hudson had a gun was unreasonable, thus entitling him to habeas relief in accordance with § 2254(d)(2).

Hudson's argument is unpersuasive because its premise — that the photographs conclusively established that he did not possess a gun during the incident — is false. Bradley first testified that the gun was in Hudson's left hand. But after examining the photos, he testified that the gun was in Hudson's right hand and explained the discrepancy by remarking: "Well, you have to understand, I was scared for my life because I had a gun at my sternum." Hudson denied having a gun. But the trial judge found that Hudson did have a gun, so the judge credited Bradley's testimony instead of Hudson's.

To demonstrate that this finding was unreasonable, the photographs would have had to show that Hudson's right hand was both visible and did not hold a gun. Otherwise the photographs could not exclude the possibility that Hudson held a gun in his right hand, which was simply not pictured. We must look to the testimony about the photographs to determine what they showed because the photographs are not in the record. Although witness testimony about the photographs establishes that Hudson's left hand was visible in the photographs and held no gun, the testimony does not establish that Hudson's right hand was visible — let alone that it was visible and did not hold a gun.

The closest the record comes to suggesting that Hudson's right hand is visible in the photographs is the following exchange between Hudson and his attorney:

Q: [Hudson's attorney] And what are you doing with your right hand, in that first picture?

A: [Hudson] With my right hand I'm pushing to see if-pushing the number amount, the dollar amount that he told me to push in the ATM machine, so that he could purchase the rocks.

But this exchange does not conclusively demonstrate that Hudson's right hand was visible. Hudson's right hand may have been outside the frame of the picture, in which case the question would simply have been seeking to establish what Hudson was doing with his hand that could not be seen. The trial judge had the benefit of examining the photos and judging the credibility of the witnesses, and his factual finding that Hudson had a gun is presumed correct absent clear and convincing evidence to the contrary. See 28 U.S.C. § 2254(e)(1). Because the testimony about the photographs does not overcome this presumption, Hudson has failed to show that the trial judge's verdict was based on an unreasonable determination of the facts.

Hudson next argues that admitting the gun later found in his car into evidence cannot "support the unreasonable conclusion that Hudson wielded a gun." This argument assumes that receiving the gun into evidence was necessary to support the finding that Hudson had a gun at the ATM. But this assumption is false. Bradley's testimony that Hudson had a gun is enough by itself to support that finding. See Tucker, 541 F.3d at 658 ("[T]his Court has long held that the testimony of the victim alone is constitutionally sufficient to sustain a conviction."). If a victim's testimony alone is sufficient to convict, then a victim's testimony alone must also be sufficient to support the factual findings that are necessary to convict. Otherwise, the testimony of a victim alone would not be sufficient.

Moreover, the admission of the gun was not the only evidence corroborating Bradley's testimony that Hudson wielded a gun at the ATM. Also relevant are the facts that Hudson admitted being at the ATM with Bradley and that Bradley was shot as he drove away. The trial judge was not unreasonable in linking these facts together to conclude that Hudson had a gun during the incident.

Hudson's final sufficiency-of-the-evidence claim is that even if he had a gun, the evidence was insufficient to prove that he had the intent to kill Bradley, which is an essential element of the crime of assault with intent to commit murder. We must first address whether Hudson waived this argument before reaching its merits. The State asserts that Hudson has waived this argument by failing to raise it before the federal district court in his habeas petition. But Hudson's petition does set forth the question whether his conviction for assault with intent to commit murder was based on sufficient evidence "due to the failure of the prosecution to show Petitioner had a specific intent to kill." This fact — combined with the rule that courts should liberally construe the allegations of a pro se habeas petition — defeats the State's waiver argument. See Franklin v. Rose, 765 F.2d 82, 84-85 (6th Cir. 1985) (holding that courts should liberally construe a pro se habeas petition "to encompass any allegation stating federal relief (internal quotation marks omitted)).

Turning to the merits of Hudson's argument, the elements in Michigan of "assault with intent to commit murder are (1) an assault, (2) with an actual intent to kill, (3) which, if successful, would make the killing murder." People v. Plummer, 229 Mich. App. 293, 581 N.W.2d 753, 759 (1998). The actual-intent-to-kill element does not need to be proved by "direct, positive, or independent evidence." People v. Taylor, 422 Mich. 554, 375 N.W.2d 1, 7 (1985) (internal quotation marks omitted). Rather, the intent may be shown by inference from any fact in evidence, provided that the inference is reasonable. Id. at 8. For example, the factfinder may infer the requisite intent from

the nature of the defendant's acts constituting the assault; the temper or disposition of mind with which they were apparently performed[;] whether the instrument and means used were naturally adapted to produce death[;] his conduct and declarations prior to, at the time, and after the assault[;] and all other circumstances calculated to throw light upon the intention with which the assault was made.

Id. (internal quotation marks omitted). "Because of the difficulty of proving an actor's state of mind, minimal circumstantial evidence" suffices to prove the intent to kill. People v. McRunels, 237 Mich. App. 168, 603 N.W.2d 95, 102 (1999).

Viewing the evidence in the light most favorable to the prosecution, a rational trier of fact could have found the requisite intent to kill. Bradley testified to the following: that the perpetrator stuck a revolver through Bradley's window and pushed it against Bradley's chest while attempting to rob him, that the perpetrator told him not to "do anything stupid," that Bradley feared for his life, and that the perpetrator shot at him as he drove away. The perpetrator's threats during the robbery, his use of a deadly weapon, and the fact that he carried out his threats and shot Bradley are all facts from which a rational factfinder could reasonably infer the requisite intent, especially when the evidence is viewed in the light most favorable to the prosecution. And to grant the writ under AEDPA, we would have to conclude that the state court unreasonably applied Jackson, not just that it incorrectly applied Jackson. See Tucker v. Palmer, 541 F.3d 652, 656 (6th Cir. 2008).

Hudson's argument to the contrary is unpersuasive because the principal case he relies on in arguing that he did not have the intent to kill — People v. Johnson, Nos. 278955, 279522, 2008 WL 4724317 (Mich. Ct.App. Oct.28, 2008) (per curiam) (unpublished opinion) — is distinguishable. In Johnson, defendant Jackson shot the victim, who was standing 10 to 15 feet away, in the shin. Id. at *4. The court reasoned that finding an intent to kill by Jackson would require the court to conclude that "Jackson shot [the victim] in the shin with the hope that a fatal injury would result," which is "contrary to logic." Id. Because no evidence suggested that some factor altered Jackson's shot — such as evidence that the victim was moving at the time — the court could not reasonably assume that Jackson aimed at the victim's head or torso. Id. And the court reasoned that it must be able to reasonably assume that Jackson aimed at one of these vital regions to conclude that Jackson intended to kill the victim. Id.

In the present case, the factfinder could reasonably assume that Hudson aimed at one of Bradley's vital regions because Hudson pressed the gun up against Bradley's chest at the ATM. And although the bullet passed through Bradley's forearm and thigh rather than a vital region, this can reasonably be explained by the fact that Bradley was driving away when he was shot. The evidence is thus sufficient for a rational factfinder to infer the requisite intent.

C. Admission of the gun

Finally, Hudson raises the issue whether admitting the gun recovered from his car into evidence was an error that violated his due process right to a fair trial. Erroneously admitting evidence under state evidence rules amounts to a due process violation in a federal habeas proceeding only in extraordinary cases. Schoenberger v. Russell, 290 F.3d 831, 836 (6th Cir. 2002). Federal courts undertaking a habeas review of due process claims based on the improper admission of evidence must take into account the Supreme Court's warning that "it is not the province of a federal habeas court to reexamine state-court determinations on state-law questions." Ege v. Yukins, 485 F.3d 364, 375 (6th Cir. 2007) (quoting Estelle v. McGwire, 502 U.S. 62, 68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991)). The standard of review is therefore very deferential on such claims. Id. An evidentiary ruling may violate due process — and thus warrant habeas relief — only where it "is so egregious that it results in a denial of fundamental fairness." Bugh v. Mitchell, 329 F.3d 496, 512 (6th Cir. 2003). "[T]he Supreme Court has defined `very narrowly' the category of infractions that violates `fundamental fairness.`" Bey v. Bagley, 500 F.3d 514, 522 (6th Cir. 2007) (quoting Dowling v. United States, 493 U.S. 342, 352, 110 S.Ct. 668, 107 L.Ed.2d 708 (1990)). Whether admitting "prejudicial evidence constitutes a denial of fundamental fairness turns upon whether the evidence is material in the sense of a crucial, critical[,] highly significant factor." Brown v. O'Dea, 227 F.3d 642, 645 (6th Cir. 2000) (internal quotation marks omitted).

Hudson argues that admitting the gun recovered from his car into evidence was an error that violated his due process right to a fair trial. He asserts that the gun had "absolutely no relevance" and that "there was absolutely no evidence linking the gun introduced into evidence to the gun allegedly used in the alleged crimes." Hudson further contends that there was no foundation for admitting the gun, which means that the gun was improperly admitted. From this premise he argues that the erroneously admitted evidence denied him a fair trial because it was the only evidence besides Bradley's testimony — which Hudson characterizes as uncorroborated, inconsistent, and "severely undermined by the photographic evidence" — that suggested that Hudson had a gun. He contends that the admission of the gun was "a crucial, critical, highly significant factor, in corroborating the claim that Mr. Hudson had a gun at the incident and was therefore guilty of the crimes charged."

Hudson's claims that the gun had no relevance and that no evidence linked it to the gun used in the robbery are unpersuasive. The gun and Hudson's identification were found in the trunk of Hudson's car, and a do-rag was found in the back seat. Hudson admitted that he was wearing a do-rag at the ATM during the incident in question. These facts provide evidence to link the gun to Hudson. And there is circumstantial evidence linking the gun recovered to the gun used because Sergeant Mendoza testified that the gun was a revolver, and Bradley said that the gun he was threatened with was a revolver. "Evidence of a defendant's possession of a weapon of the kind used in the offense with which he is charged is routinely determined by courts to be direct, relevant evidence of his commission of that offense." People v. Hall, 433 Mich. 573, 447 N.W.2d 580, 583 (1989).

Hudson may be correct, however, that there was not a sufficient foundation for the gun's admission despite its relevance. The court in Hall noted that the foundation for admitting the gun in that case was established in part by the victim's testimony "that the gun looked like the same gun defendant had used in [the charged] robbery." Id. There is no analogous testimony in the present case. Indeed, Bradley — the only person who could have possibly provided similar testimony — was never even shown the gun that was admitted into evidence.

This case appears more analogous to People v. Kramer, 103 Mich.App. 747, 303 N.W.2d 880 (1981). No witness in Kramer testified that the three shotguns admitted into evidence in that case were similar to the guns used in the charged crime. Id. at 886. Instead, a witness testified that a robber had used "some kind of a shotgun or rifle." Id. This testimony is similar to Bradley's testimony that his attacker used a revolver. And just as the Kramer court reasoned that the three shotguns "might have been the ones that were used," the gun recovered from Hudson's car might have been the gun used to shoot Bradley. Id. But the Kramer court reasoned that the shotguns, even if slightly probative, arguably should have been excluded under Rule 403 of the Michigan Rules of Evidence because the possibility of prejudice outweighed their probative value. Id. The court concluded, however, that reversal was not required even if the admission of the guns constituted error because the defendants would have been convicted anyway based on the other strong circumstantial evidence. Id.,

Based on Kramer, the most Hudson can show is that admitting the gun might have amounted to an error under the Michigan Rules of Evidence. This is not enough, however, for him to establish the necessary due process violation. An evidentiary ruling that might have violated state rules is, by definition, not an egregious violation of those rules.

Nor was the gun a crucial or critical factor in Hudson's conviction because Bradley's testimony alone is sufficient for a factfinder to conclude that Hudson had a gun. See Tucker v. Palmer, 541 F.3d 652, 658 (6th Cir. 2008) ("[T]his Court has long held that the testimony of the victim alone is constitutionally sufficient to sustain a conviction."). To be sure, an erroneous-admission-of-evidence claim is different than a sufficiency-of-evidence claim. But when federal courts decide whether a state evidentiary error amounts to a due process violation, they consider the strength of the other evidence of guilt. See Ege v. Yukins, 485 F.3d 364, 376-78 (6th Cir. 2007) (reasoning that the court must assess the strength of the other evidence to decide whether the evidentiary error rose to the level of a due process violation). Conclusions about the sufficiency of the other evidence are relevant in assessing this factor and in deciding whether the challenged evidence is a crucial or critical factor in the conviction. Broimi, v. O'Dea, 227 F.3d 642, 645 (6th Cir. 2000) (holding that the challenged evidence was not a crucial or critical factor in the petitioner's conviction, in part because the state court had twice concluded that the other evidence against the petitioner was sufficient to justify his conviction).

Moreover, Hudson's reliance on Snowden v. Singletanj, 135 F.3d 732 (11th Cir. 1998), does not strengthen his argument. The challenged evidence in Snowden, a child-abuse case, was the expert witness's testimony "that 99.5% of children tell the truth and that the expert, in his own experience with children, had not personally encountered an instance where a child had invented a lie about abuse." Id. at 737.

The Eleventh Circuit had several concerns about this testimony. First, the improper nature of this evidence could "hardly be disputed" because it invaded the province of the jury by directly bolstering the credibility of the victims. Id. at 738. The testimony was also stressed by the prosecutor "[o]ver and over again." Id. Finally, "[t]he case against Snowden was based almost entirely upon the stories told by three, young-children witnesses." Id. Accordingly, the court concluded that allowing the expert to boost the credibility of the children victims through his testimony violated Snowden's right to due process. Id. at 739.

This case is distinguishable from Snowden. In Snowden, the challenged evidence not only told the jury that the children were extremely likely to be credible; it also provided a mathematical number for how credible the children were likely to be. The challenged evidence (the gun) in the present case is both qualitatively and quantitatively different. Admitting the gun did not speak directly to the credibility of Bradley and thus did not invade the province of the factfinder. Rather, admitting the gun bolstered the credibility of Bradley indirectly by corroborating a detail of his testimony — the fact that a gun was present — that makes it more likely that his testimony is truthful. The factfinder, however, was still free to draw his own conclusion as to how much that corroborative detail bolstered Bradley's credibility. Another difference is that the admitted gun in this case might have been improper, whereas the improper nature of the expert's testimony in Snowden could "hardly be disputed." Id. at 738.

The gun as an admitted exhibit was also not extensively discussed at trial. Sergeant Mendoza described the gun and where he got it from, and Hudson answered a few questions about it. Unlike the prosecutor in Snowden, who constantly mentioned the expert's testimony, the prosecutor in this case did not refer to the gun over and over again. The prosecutor in fact never claimed that the gun admitted was the gun used to shoot Bradley. And finally, other evidence besides Bradley's testimony supported the case against Hudson. Key among this other evidence is that Hudson himself admitted being at the ATM with Bradley on the night in question, plus the undisputed fact that Bradley was shot as he pulled away from the ATM. And the farfetched nature of Hudson's version of the events also likely served to enhance the Bradley's credibility. The other evidence in this case is thus stronger than the other evidence in Snowden. So unlike the challenged evidence in Snowden, admitting the gun here did not make Hudson's trial fundamentally unfair. The trial court's decision to admit the gun therefore did not amount to a due process violation that warrants habeas relief.

Hudson also argues that his trial counsel provided ineffective assistance by failing to object to the admission of the gun. The government appears to misconstrue this argument's purpose as being a separate basis for relief, rather than as an attempt by Hudson to demonstrate the "cause" and "prejudice" necessary to overcome the procedural bar created by failing to contemporaneously object. In any event, Hudson cannot prevail on an ineffective-assistance-of-counsel claim because a COA was not granted on this issue. See Phillips v. Bradshaw, 607 F.3d 199, 205 (6th Cir. 2010) (holding that habeas claims for which a COA has not been granted are not properly before this court).

III. CONCLUSION

For all of the reasons set forth above, we AFFIRM the judgment of the district court.