OPINION
OWENS, Circuit Judge:
Marcos Reis-Campos appeals from the district court’s order denying his petition for writ of habeas corpus challenging his 2007 second-degree murder conviction. He correctly argues that the prosecution concealed evidence that could have bolstered his self-defense claim. However, the immensely deferential standard of review mandates that we affirm the district court.
I. Factual Background and Procedural History
On June 26, 2004, Reis-Campos — a Nor-teño gang member — killed Luis Guillermo Fuentes — the head of the local (and rival) MS-13 gang. The shooting occurred in Norteño territory in San Francisco, where Reis-Campos encountered Fuentes and his six-year-old son walking down the sidewalk. Fuentes wore blue shoes, MS-13’s color. Reis-Campos was not wearing or displaying anything red, his gang’s color. Reis-Campos shot Fuentes six times, hitting him in the face, back of the head, and back. After the shooting, Reis-Campos ran away, tossed the gun, and entered a laundromat, where he was arrested.
A. Trial
1. The Prosecution Case
Reis-Campos was charged with first-degree murder in violation of California Penal Code § 187. In his July 2007 jury trial, the prosecution argued that Reis-Campos executed Fuentes to gain status in the Norteño gang, and that Fuentes disrespected the Norteños by wearing blue shoes in Norteño territory. The prosecution also contended that Fuentes was an easy target because his six-year-old son was present. While the prosecution acknowledged that Fuentes belonged to MS-13, it downplayed his violent history, at one point characterizing Fuentes as “a family man,” emphasizing that “[h]e has kids and he’s a [house] painter.” The prosecution contended that Reis-Campos’ self-defense claim was “fabricated” and that his testimony about Fuentes’ prior threats was not credible.
To support its case, the prosecution called, among other witnesses: (1) Fuentes’ son; (2) an eyewitness to the shooting; and (3) Reis-Campos’ cellmate, who testified that Reis-Campos confided that he had confronted Fuentes, and after Fuentes pulled a knife and told him to leave him alone, chased down and shot Fuentes.
The prosecution also called San Francisco Police Sergeant Mario Molina, the case investigator and gang expert. Molina testified about various gang practices. He opined that the killing benefitted Reis-Campos by helping him rise in the Nor-teño ranks, and the Norteños by providing recognition and warning rival gangs.
In addition, Molina testified about his relationship with Fuentes. He claimed that he knew Fuentes primarily from soccer games at a local playground, and did not know of Fuentes’ high rank in MS-13 until after Fuentes was shot. On direct examination, when asked about the March 2004 Norteño killing of an MS-13 member, Molina agreed that this killing could lead to MS-13 retaliation against Norteños. When asked whether he knew of any such retaliation, Molina first said that he did not recall any. Asked again, Molina said that
he could not “think of any incident right now.” And on cross-examination, he again denied any knowledge of retaliation: “I am not sure there was any specific retaliation for his death that said we are going to go kill somebody because [of the March 2004 killing]. I don’t have that information.” Consistent with his professed lack of knowledge, Molina said he was unaware of any specific MS-13 calls to kill Norteños.
2. The Defense Case
Reis-Campos testified in his own defense, and claimed that Fuentes was out to get him. While the two had started out on friendly terms, their relationship quickly deteriorated once Reis-Campos rejected Fuentes’ attempt to recruit him to MS-13. Reis-Campos’ dating a woman who was carrying the child of another MS-13 member only made things worse. Reis-Campos claimed that by December 2003, he was told that MS-13 wanted to kill him, so he shortly thereafter joined the Norteños for protection.
Reis-Campos also claimed that Fuentes threatened his life on several occasions before the June 2004 shooting. These incidents included: (1) in March 2004, an MS-13 member shot at him (wounding his female companion); (2) in May 2004, Fuentes and his associates driving in a car chased down Reis-Campos and his associates and shot at them; (3) in early June 2004, Fuentes pointed a long-barreled gun at Reis-Campos outside a pizzeria; and (4) shortly after the pizzeria incident, Reis-Campos encountered Fuentes at the Hall of Justice, where Fuentes and an associate flashed gang tattoos and colors at Reis-Campos.
On the night of the shooting, Reis-Cam-pos said that he was walking towards a tattoo parlor in Norteño territory when he saw Fuentes, in blue shoes, walking with his son. His son then walked away, leaving the two alone. Fuentes, “looking mad,” approached Reis-Campos and backed him up towards a wall. A few feet away from Reis-Campos, Fuentes bent over. Fearing that Fuentes was reaching for a weapon, Reis-Campos pulled out his gun. And when Fuentes reached for Reis-Campos’ gun, Reis-Campos opened fire. He testified that he acted in self-defense, and not to boost his profile among the Norteños. As Reis-Campos put it: “Could be me or him. He had tried to kill me in the past.” He said he shot Fuentes because “[h]e could take the gun away from me and kill me. He was bigger and stronger than me.”
The jury rejected Reis-Campos’ claim of self-defense, and found him guilty of second-degree murder (with enhancements for acting for the benefit: of a criminal street gang and using a firearm),
as well as active participation in a street gang.
3. Post-Trial Motions
In November 2007, Reis-Campos filed a motion for a new trial. Before filing its opposition, the prosecution sent this letter to defense counsel:
It has come to my attention that there may be a federal informant who provided information to the Daly City Police Department about a shooting and that this informant provided information that “Memo” [Fuentes] was the purported driver of the vehicle. I have nothing in writing regarding this.
I have contacted Inspector Draper of the Daly City Police Department who declined to provide any documentation concerning this as there is an ongoing investigation.
I am sharing this information with you in an abundance of caution.
After this disclosure, Reis-Campos filed a motion for an evidentiary hearing based on this new information about Fuentes’ violent past. The trial court denied both motions in January 2008, and sentenced Reis-Campos to 50 years to life.
B. State Court Appeal and Habeas Proceedings
Reis-Campos timely appealed in March 2008. Among other arguments, he contended that: (1) the prosecution suppressed material information favorable to the defense and the trial court erred in denying him a related evidentiary hearing, violating his rights to due process and a fair trial under
Brady v. Maryland,
373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and (2) the trial court erroneously curtailed his cross-examination of Officer Molina. The California Court of Appeal rejected his claims in a reasoned decision in December 2010, and the California Supreme Court denied review in March 2011.
Through defense investigative efforts, Reis-Campos obtained new information about Fuentes’ violent past and Molina’s knowledge of it prior to trial. First, Reis-Campos discovered that Molina participated in a multi-agency investigation into MS-13 (“Operation Devil Horns”), which lasted from 2005 to 2008 and led to a multi-count and multidefendant indictment. While working on Operation Devil Horns and prior to his testimony, Molina learned from an informant that Fuentes orchestrated the murder of a Norteño in Daly City to avenge the March 2004 killing of an MS-13 member by a Norteño. This information about the Daly City murder conflicted with Molina’s trial testimony, where he claimed no knowledge of any MS-13 retaliation in response to the March 2004 killing. According to Reis-Campos, not only did the prosecution withhold this exculpatory evidence, but Molina perjured himself when he stated that he was unaware of any retaliation for the March 2004 murder, and the prosecutor failed to correct his false testimony.
Second, Reis-Campos learned new information concerning a redacted FBI report about Fuentes that was disclosed prior to trial. The report stated that an informant revealed Fuentes had posed as a homeless person to kill unsuspecting rival gang members, and had taught fellow gang members this technique. The prosecution convinced the trial court to prohibit the defense from cross-examining Molina with the report, reasoning that the report was unreliable because the source was unknown. After learning about Operation Devil Horns, Reis-Campos argued that Molina knew who the source was — the same informant who revealed Fuentes’ role in avenging the March 2004 murder. Reis-Campos argued that he could have cross-examined Molina with the report to establish Fuentes’ reputation for violence, and also called the informant to testify about Fuentes’ homeless murder ruse and the Daly City killing, again evincing Fuentes’ violent nature.
With this new information, Reis-Campos filed a habeas petition in state court. He argued that the new information supported his claims that the prosecution had suppressed evidence, presented false testimony, and failed to correct false testimony in violation of his federal constitutional rights
under
Brady v. Maryland,
373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963),
Alcorta v. Texas,
355 U.S. 28, 78 S.Ct. 103, 2 L.Ed.2d 9 (1957), and
Napue v. Illinois,
360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959).
Reis-Campos also filed a federal habeas petition which contained both exhausted claims (rejected on direct appeal) and unexhausted claims (founded on the new evidence that surfaced after the direct appeal became final). The district court stayed proceedings for him to exhaust his state court remedies. The California Court of Appeal summarily denied his state ha-beas petition, as did the California Supreme Court.
The district court then permitted Reis-Campos to reopen the case, and he filed an amended federal habeas petition in April 2013. The district court ultimately denied the petition on materiality grounds, holding that: (1) his
Brady
claim failed because the state court could have reasonably concluded that the evidence concerning Fuentes’ involvement in the Daly City killing and the FBI report was not material to Reis-Campos’ defense; and (2) his
Napue
claim failed because, assuming Officer Molina had committed perjury that the prosecutor knowingly left uncorrected, this too was not material to Reis-Campos’ defense. The district court issued a certificate of appealability for all of Reis-Campos’ claims, and he timely appealed. We have jurisdiction under 28 U.S.C. § 2253(a).
II. Discussion
A. Standard of Review
We review the district court’s denial of a petition for habeas relief de novo, and its findings of fact for clear error.
Christian v. Frank,
595 F.3d 1076, 1080 (9th Cir. 2010).
The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA) limits our review of Reis-Campos’ claims. AED-PA mandates 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) (per curiam) (quoting
Lindh v. Murphy,
521 U.S. 320, 333 n.7, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997)). Under AEDPA, to obtain habeas relief a petitioner must demonstrate that the last reasoned state court decision on the merits was either: (1) “contrary to, or involved an unreasonable application of, clearly established Federal law” or (2) “based on an unreasonable' determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d).
Because the state courts summarily denied all of Reis-Campos’ post-conviction claims, the last reasoned state court decision was on direct appeal. This impacts our review in several ways. First, we presume that the state courts adjudicated Reis-Campos’ habeas claims on the merits.
See Harrington v. Richter,
562 U.S. 86, 99, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011) (“When a federal claim has been presented to a state' court and the state court has denied relief, it may be presumed that the state court adjudicated the claim on the merits.”). Second, under California law, we assume that the factual allegations in Reis-Campos’ habeas petition are true.
See Cullen v. Pinholster,
563 U.S. 170, 188 n.12, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011) (citing
People v. Duvall,
9 Cal.4th 464, 37 Cal.Rptr.2d 259, 886 P.2d 1252, 1258-59 (1995) (en banc)) (explaining that under California law, a summary dismissal indicates that the court found the factual allegations, taken as true except for wholly conclusory allegations, did not establish a prima facie case for relief).
Finally, with respect to evaluating the state court’s reasoning, where a feder
al claim has been adjudicated in a reasoned decision, we “look through” subsequent summary denials and review the last reasoned decision.
See Ylst v. Nunnemaker,
501 U.S. 797, 803, 111 S.Ct. 2590, 115 L.Ed.2d 706 (1991) (“Where there has been one reasoned state judgment rejecting a federal claim, later unexplained orders upholding that judgment or rejecting the same claim rest upon the same ground.”). However, where there is no reasoned decision on a particular claim, a petitioner must show that “there was no reasonable basis for the state court to deny relief.”
Harrington,
562 U.S. at 98, 131 S.Ct. 770.
1.
Brady Claim
Reis-Campos’ Brady-related claim has a muddled procedural history.
Ultimately, as the state court effectively rejected Reis-Campos’ evidentiary hearing claim based on a substantive analysis of the potential
Brady
material, we employ the “look through” approach here.
See, e.g., Shackleford v. Hubbard,
234 F.3d 1072, 1079 n.2 (9th Cir. 2000) (“The California Supreme Court denied review of [the] direct appeal and habeas petition without comment. In this circumstance, we ‘look through’ the unexplained ... decisions to the last reasoned decision, the state appellate court’s decision, as the basis for the state court’s judgment.”).
Additionally, our review under § 2254(d)(1) is “limited to the record that was before the state court that adjudicated the claim on the merits.”
Pinholster,
563 U.S. at 181, 131 S.Ct. 1388. As Reis-Cam-pos provided further evidence in support of his claim to the state habeas court, we review “the reasonableness of the California Supreme Court’s decision by the evidence that was before it, and [use] the Court of Appeal’s reasoning in accordance with our usual practice of ‘looking through’ summary denials to the last reasoned decision.”
Cannedy v. Adams,
706 F.3d 1148, 1159 n.5 (9th Cir. 2013) (emphasis omitted). We do this because “[h]ad the state supreme court intended different reasoning because of the newly added facts, the court could have provided it.”
Id.
2.
Napue
Claim
There is no reasoned state court decision on the
Napue
claim because it was not raised on direct appeal. As such, if there were any reasonable basis for the California Supreme Court to deny the
Napue
claim, habeas relief is unwarranted.
See Harrington,
562 U.S. at 102, 131 S.Ct. 770 (“Under § 2254(d), a habeas court must determine what arguments or theories supported or, as here, could have supported, the state court’s decision; and then it must ask whether it is possible fairmind-ed jurists could disagree that those argu-
merits or theories are inconsistent with the holding in a prior decision of this Court.”).
B. No AEDPA Error in Rejecting
Brady
Claim
Under
Brady,
“suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment.” 373 U.S. at 87, 83 5.Ct. 1194. It follows that there are three elements to a
Brady
violation: (1) “the evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching,” (2) “that evidence must have been suppressed by the State, either willfully or inadvertently,” and (3) “prejudice must have ensued.”
Strickler v. Greene,
527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). With respect to the prejudice element, “evidence is material only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.”
United States v. Bagley,
473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). “A ‘reasonable probability’ is a probability sufficient to undermine confidence in the outcome.”
Id.
Materiality is considered “collectively, not item by item.”
Kyles,
514 U.S. at 436, 115 S.Ct. 1555.
Reis-Campos alleges that the state suppressed two pieces of evidence in violation of
Brady:
(1) information possessed by Officer Molina that Fuentes participated in the Daly City revenge killing, and (2) information that the prosecution knew and trusted the informant identified in the FBI report. As described above, we assume that the prosecution should have disclosed this additional information about Fuentes’ violent nature, and the State has no good answer as to why it did not. Indeed, the government’s attempts to explain the letter that the prosecutor sent to Reis-Cam-pos&emdash;both in its briefing and at oral argu- ment&emdash;have fallen short of what we expect. Still, the more difficult
issue is whether, under AEDPA’s extremely deferential standard, this error mandates relief&emdash;i.e., whether it sufficiently prejudiced Reis- Campos’ defense. Ultimately, we conclude it does not. First, the jury heard expert testimony
that Fuentes was the “shot caller” of MS- 13, a vicious street gang responsible for murders and violence in San Francisco. The jury learned that to become the shot caller, Fuentes necessarily had a “readiness to use violence.” And as the shot caller, Fuentes would have initiated and organized gang killings. While the prosecutor’s closing argument portraying Fuentes as a “family man” and a “painter” was a poor attempt to whitewash his true nature, we cannot say that it was unreasonable for the state court to conclude that the jury had still heard sufficient information regarding Fuentes’ history of violence.
Second, and more importantly, the jury
heard from Reis-Campos about why he was so scared of Fuentes, and a police officer corroborated one of the incidents at trial. Assuming that California law permits a defendant to introduce a victim’s prior bad acts to corroborate a defendant’s be- little to undermine the prosecution’s attempt
lief that the victim was violent, the ultimate effect of that evidence here is not enough to warrant relief. The most persuasive evidence that Reis-Campos felt compelled to shoot Fuentes in self-defense necessarily came from Reis-Campos. The fact that Fuentes, on other occasions, was a violent person has more limited application to Reis-Campos’ state of mind at the time of the shooting.
Third, the overall evidence in the case supports the state court’s determination. Reis-Campos shot Fuentes, a rival gang member, six times in Norteño territory, even though Fuentes was walking with his six-year-old son. No weapon was recovered from Fuentes, and no other witness corroborated Reis-Campos’ testimony that Fuentes initiated their encounter or reached for Reis-Campos’ gun.
Cf. Benn v. Lambert,
283 F.3d 1040, 1062 (9th Cir. 2002) (explaining that undisclosed evidence was material where it “would have substantially undermined the state’s principal theory of motive and its main support for the aggravating factor ..., as well as its contention that the killings were premeditated”).
Finally, contrary to Reis-Campos’ contention, the withheld evidence had inadequate impeachment value. Assuming that the undisclosed evidence would have impeached Molina’s somewhat equivocal testimony, it was not unreasonable for the state court to determine that it would not have sufficiently undermined his testimony or credibility. As the state court observed, Molina “did not testify that Fuentes was nonviolent or deny that Fuentes was involved in gang activity” — he was brought in to opine whether the killing was gang related. While Molina discussed the violent activities and tendencies of gang members, including Fuentes, the undisclosed evidence would not have “lent significant force to [Reis-Campos’] impeachment of Officer Molina.”
Cf. Horton v. Mayle,
408 F.3d 570, 578-79 (9th Cir. 2005) (holding that failing to disclose a leniency deal was material because the witness’s testimony was “central to the prosecution’s case” and “the deal would have provided powerful and unique impeachment evidence demonstrating that [the witness] had an interest in fabricating his testimony”).
In sum, the state court did not err under AEDPA in rejecting Reis-Campos’
Brady
claim and concluding that it would be extremely unlikely that Fuentes would launch an unarmed attack against a rival (and likely armed) gang member, placing his own child in danger. Reis-Campos’ additional evidence did not “undermine confidence in the outcome” of the trial.
Bagley,
473 U.S. at 682, 105 S.Ct. 3375.
C. No AEDPA Error in Rejecting
Napue
Claim
“[A] criminal defendant is denied due process of law when a prosecutor either knowingly presents false evidence or fails to correct the record to reflect the true facts when unsolicited false evidence is introduced at trial.”
Hayes v. Brown,
399 F.3d 972, 984 (9th Cir. 2005) (en banc);
see also Napue,
360 U.S. at 269, 79 S.Ct. 1173;
Alcorta,
355 U.S. at 29-30, 78 S.Ct. 103.
“A claim under
Napue
will succeed when ‘(1) the testimony (or evidence) was actually false, (2) the prosecution knew or should have known that the testimony was actually false, and (3) the false testimony was material.’ ”
Jackson v. Brown,
513 F.3d 1057, 1071-72 (9th Cir. 2008) (quoting
Hayes,
399 F.3d at 984). The
Napue
materiality standard is less demanding than
Brady.
Under
Napue,
a conviction must be set aside “whenever there is
‘any
reasonable likelihood that the false testimony
could
have affected the judgment of the jury.’ ”
Id.
at 1076 (quoting
Hayes,
399 F.3d at 985).
Reis-Campos did not adequately allege a violation of clearly established federal law with respect to his
Napue
claim. He alleged only that Molina knew the testimony was false, not that the
prosecutor
had such knowledge. While the Supreme Court has clearly established that the prosecution’s
Brady
duty encompasses evidence “known only to police investigators and not to the prosecutor,”
Kyles,
514 U.S. at 437-38, 115 S.Ct. 1555, it is
not
clearly established that a police officer’s knowledge of false testimony may be attributed to the prosecution under
Napue. See Briscoe v. LaHue,
460 U.S. 325, 326 n.1, 103 S.Ct. 1108, 75 L.Ed.2d 96 (1983) (noting that while the Supreme Court had “held that the prosecutor’s knowing use of perjured testimony violates due process,” the Court had “not held that the false testimony of a police officer in itself violates constitutional rights”). Several of our sister circuits have recognized this lack of clarity.
See, e.g., Smith v. Massey,
235 F.3d 1259, 1272 (10th Cir. 2000),
abrogated on other grounds by Neill v. Gibson,
278 F.3d 1044, 1057 (10th Cir. 2001);
Sargent v. Sec’y, Fla. Dep’t of Corr.,
480 Fed.Appx. 523, 530 (11th Cir.2012).
Even if we assume that Reis-Campos sufficiently alleged that Molina knowingly perjured himself and the prosecutor suborned such perjury, his claim still fails on materiality grounds for the same reasons we previously explained.
As we outlined in
Jackson,
analyzing collective prejudice for concurrent
Brady
and
Napue
violations requires a special framework because the materiality standards differ:
The
Napue
and
Brady
errors cannot all be collectively analyzed under
Napue’s
“reasonable likelihood” standard, as that would overweight the
Brady
violations. On the other hand, they cannot be considered in two separate groups, as that would fail to capture their combined effect on our confidence in the jury’s decision. To resolve this conflict, we first consider the
Napue
violations collectively and ask whether there is “any reasonable likelihood that the false testimony
could
have affected the judgment of the jury.” If so, habeas relief must be granted. However, if the
Napue
errors are not material standing aloné, we consider all of the
Napue
and
Brady
violations collectively and ask whether “there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding
Would
have been different.” At both stages, we must ask whether the defendant “received ... a trial resulting in a verdict worthy of confidence.”
513 F.3d at 1076 (eitatiohs omitted). The
Jackson
analysis does not change the result here. First, considering only the
Na-pue
violation, there is no “reasonable likelihood that the false testimony could have affected the judgment of the jury.”
Id.
(emphasis and citation omitted). Standing alone, Molina’s testimony, that he did not know of any retaliation for a particular
gang-related killing would not have affected the jury’s determination of whether Reis-Campos feared for his life when he encountered Fuentes, nor would the prosecutor’s correction of Molina’s perjury have cast significant doubt on Molina’s credibility or testimony. Second, even when combined with the
Brady
violations, there is no reasonable probability that the result- of the proceeding would have been different. As we previously explained, the jury already had heard significant testimony about Fuentes’ violent tendencies and status as the leader of a vicious gang, and the incentives for Reis-Campos to attack Fuentes to gain status in his own gang.
The prosecutor’s withholding of information and Molina’s false testimony are very troubling. Yet “troubling” is not the relevant standard. It is materiality, evaluated in light of AEDPA deference, that controls. Ultimately, these failures do not materially change the already negative and violent depiction of Fuentes. It was not unreasonable for the state court to determine that nothing that the government suppressed or falsely proffered addressed the most fundamental question before the jury — whether Reis-Campos shot Fuentes because he feared for his life on June 26, 2004. As such, though the prosecution’s tactics were suspect, the state court did not err under AEDPA in rejecting Reis-Campos’ claims.
For these reasons, we AFFIRM the district court’s denial of Reis-Campos’ petition for habeas relief.