
553 F.3d 230 (2009)
Robie J. DRAKE, Petitioner-Appellant,
v.
L.A. PORTUONDO, Superintendent, Shawangunk Correctional Facility, Respondent-Appellee.
Docket No. 06-1365-pr.
United States Court of Appeals, Second Circuit.
Argued: April 1, 2008.
Decided: January 23, 2009.
*232 Sally Wasserman, New York, NY, for Petitioner-Appellant.
Thomas H. Brandt, Assistant District Attorney (Matthew J. Murphy, Niagara County District Attorney, on the brief) Lockport, NY, for Respondent-Appellee.
Before: JACOBS, Chief Judge, KEARSE, and POOLER, Circuit Judges.
POOLER, Circuit Judge:
Robie J. Drake appeals from a judgment of the United States District Court for the Western District of New York (Elfvin, J.), on remand, denying a writ of habeas corpus pursuant to 28 U.S.C. § 2254. Drake is currently incarcerated for his 1982 conviction, *233 after a jury trial, in New York State Supreme Court, Niagara County, on two counts of second degree murder for the shooting of a young couple in a parked car. At Drake's trial, in order to compensate for the lack of evidence of motive, the prosecution, at the last minute, called an expert, Richard D. Walter. Walter testified regarding a fictional syndrome of sexual dysfunction, dubbed "picquerism," which is, "medically speaking, nonsense," but appeared to account for the particular, gruesome circumstances of the shooting. Drake v. Portuondo ("Drake I"), 321 F.3d 338, 346 (2d Cir.2003). In 2001, the district court rejected Drake's claim on habeas corpus review that his due process rights under the Fourteenth Amendment were violated because the prosecution knew or should have known that Walter was testifying falsely. On appeal, we vacated the district court's judgment and remanded for discovery and, if necessary, a hearing on whether the prosecution knew that Walter was testifying falsely. Id. at 347.
On remand, the parties deposed Walter and prosecutor Peter L. Broderick, now a Niagara County Court Judge. See Deposition of Richard D. Walter, July 30, 2003 ("Walter Dep."); Deposition of Judge Peter L. Broderick, Aug. 21, 2003 ("Broderick Dep. I"); Deposition of Judge Peter L. Broderick, Nov. 26, 2003 ("Broderick Dep. II"). After completion of depositions, the district court found that the prosecution was not aware of Walter's false statements, and that Walter's false testimony was not material to the jury's verdict. Drake v. Portuondo ("Drake II"), No. 99 Civ. 0681 (W.D.N.Y. Mar. 16, 2006). We now conclude that the district court erred in failing to consider direct evidence that the prosecution was aware that Walter misstated the extent of his preparation for trial and strong circumstantial evidence that the prosecution was aware that Walter testified falsely regarding his credentials. Walter's false statements likely contributed to the jury's decision to credit Walter's highly prejudicial testimony on the sole issue in the caseDrake's intent to commit murder. Accordingly, we reverse the judgment of the district court and remand for the entry of a judgment conditionally granting the writ of habeas corpus.

BACKGROUND

I. The Trial
It was undisputed at trial that around midnight on December 5, 1981, Drake, a high school senior, shot and killed two other high school students, Amy Smith and Stephen Rosenthal. We recounted the pertinent trial testimony in Drake I:
[Smith and Rosenthal] were in Rosenthal's rusty 1969 Chevy Nova in the parking lot of a factory in the Town of North [Tonawanda], New York. The factory parking lot was adjacent to a junkyard with abandoned vehicles. [Smith and Rosenthal] were using the spot as a lovers' lane....
In a confession, Drake said that he left home at approximately 11:30 p.m., dressed in military fatigues and armed with a loaded Marlin .22 caliber semi-automatic rifle, a loaded Winchester .22 caliber high powered rifle, extra ammunition and two hunting knives, and that he went to the junkyard looking for abandoned vehicles to use in target practice. He said that the first vehicle he came across was the parked Nova, that he believed the car to be abandoned because the engine was off and no noise came from within, and that he opened fire on the passenger side window of the car with his semi-automatic rifle.
Drake claimed that he did not intend to kill Smith and Rosenthal, and insisted *234 that he learned of their deaths only when he inspected the car, heard Rosenthal groaning, and opened the door to find the two bodies. According to Drake, he stabbed Rosenthal twice, in a fit of panic, to stop him from groaning, but ... he "didn't mean to kill him or anything." Trial Transcript at 267. According to Drake, Rosenthal was fully clothed, Smith not. Unsure of what to do, he drove the Nova car to a secluded spot down the road from the parking lot, and put Rosenthal's body in the trunk. Surprised by a passing car, Drake got back in the car and drove to the Niagara County dump in the neighboring town of Wheatfield, where he was putting Smith's body into the trunk when he was spotted by two police officers on routine patrol.
321 F.3d at 341.
The only issue at trial was whether Drake had the intent requisite for second degree murder. Although an announcement was made over the high school's public address system requesting that any student with information about Drake and the victims come forward, only one witness testified as to any such informationthat she had overheard Drake and Rosenthal exchange profanity on one occasion in the cafeteria. Thus, the prosecution advanced the theory that the shooting was a sex-crime, based on the following evidence:
The emergency room physician who pronounced the victims dead testified concerning sexual trauma to Smith, including a bruised rectum, and mud near her private parts. The medical examiner who performed the autopsies noted a bite-mark on Smith's left breast, with hemorrhaging so minor as to indicate that the bite had been inflicted post-mortem. The prosecution's medical forensic witness found no evidence of semen anywhere except on Drake's underwear. Forensic experts who performed a second autopsy following the exhumation of Smith's body a month after her death, confirmed that the bite on Smith's [left] breast was inflicted post-mortem, and also found a post-mortem bite mark on the other breast. Dr. Lowell Levine, a dentist and forensic odontologist with experience in bite marks, confirmed the presence of the two post-mortem marks on each breast. Over a defense objection, Dr. Levine opined that bite marks are often present in "sexually [sic] or demented type[s] of crimes." Trial Transcript at 671.
Id. at 341-42.
Notwithstanding this circumstantial evidence in support of the sex crime theory, the prosecution evidently concluded that more evidence of motive was needed. The Erie County Medical Examiner had initially told Broderick that traces of semen, which were believed to have come from Drake, were found on a slide from Smith's rectal cavity. However, when defense counsel asked to examine the semen evidence, the medical examiner could not find the slide. The next day, the medical examiner informed Broderick that he had found the slide, but there was no evidence of sperm. The pathologist who had taken the slide had been mistaken about the semen and had been "let go." Broderick Dep. I at 36.
At that point, Broderick sought another means of convincing the jury of Drake's motive for intentional murder. The prosecutor explained his thinking as follows:
I had people who caught this defendant in the act of putting a naked girl in the trunk of a car and all I needed was some reasonable explanation for why this thing happened and when I lost the sperm evidence a couple of weeks before trial, I was just looking for somebody to give an explanation to the jury as to why *235 this happened. Not that I needed to but I think juries are always interested in knowing why.
Broderick Dep. II at 26; see also Trial Tr. at 750 (Broderick explaining, "when I lost that evidence which I thought in my own conventional mind was the evidence I sought or would need to prove the sexual assault. I had to look elsewhere and I consulted with [Walter]....").
Broderick called Dr. Levine, the forensic dentist, and explained that he had lost the semen evidence. Dr. Levine "said the guy that you've got to talk to is Dr. Walter," a prison psychologist in Michigan. Broderick Dep. I at 38-39. Dr. Levine called Walter on October 7, 1982, approximately two weeks before trial.[1] That same day, Broderick also called Walter, and the two had a telephone conversation lasting 52 minutes. During that 52 minute conversation, Broderick never "got into [Walter's] real credentials." Id. at 43. Rather, Broderick gave Walter "a thumbnail sketch of the evidence in the case, the type of crime that was involved," and discussed the "bite mark question," "the bandoliers of ammunition," and the facts that Drake was "carrying two guns that night" and "dressed in military garb, camouflage." Id. at 38; Broderick Dep. II at 37-38. Walter told Broderick that he needed some time to think about the case before he could give Broderick his opinion.
At some point after that telephone call, Walter called Broderick back and said that he believed "picquerism" was involved. Broderick responded, "what the hell is picquerism," because he "had never heard of that term before." Broderick Dep. I at 44. Picquerism is a purported syndrome or criminal profile in which the perpetrator realizes sexual satisfaction from penetrating a victim by sniper activity or by stab or bite wounds. As we explained in Drake I, the word picquerism comes from "a derivative misspelling of the French verb `piquer,' which means, among other things, to stick or poke," 321 F.3d at 342, and is "medically speaking, nonsense," id. at 346.[2] Walter explained "picquerism" to Broderick and sent him two books that referred to the concept. Broderick did not independently investigate Walter's credentials or contact any other mental health professional to inquire about picquerism.
Although he had discussed picquerism with Walter approximately two weeks before trial, Broderick did not inform defense counsel of his intention to call Walter until Thursday, October 21, 1982, the day before Walter was to take the stand. The trial judge had already advised the parties that due to an out-of-town judicial commitment, the trial would have to conclude no later than the following Tuesday, October 26. Under the announced schedule, defense counsel would have no more than a weekend to find a competing expert and prepare his cross-examination.
Walter testified at trial to the following credentials: (1) he received a Bachelors *236 and a Masters degree in psychology from Michigan State University and had done post-graduate work in criminal justice at California State University; (2) he had been employed by the Los Angeles County Coroner's office, where he "had personal involvement with at least" 5,000 to 7,500 cases, in which he "consulted with the prosecutors, the police agencies and various investigative agencies ... and the pathologists related to moding [sic] cause of death and profiling for possible leads ... also leads in terms of investigation for the resolution of the case"; (3) he had been a prison psychologist for the Michigan Department of Corrections for four and a half years; (4) he was an "adjunct lecturer" at Northern Michigan University; (5) he had written "papers or articles" in his field; (6) he had testified as an expert witness before in both Los Angeles and Pasadena, California; and (7) he was a member of a number of professional associations and had lectured to various groups. Trial Tr. at 783-92.
Walter testified at trial that the only person with whom he had ever discussed the case was Broderick. He also claimed that his testimony was based only upon the information he had received regarding the case between his arrival in New York the night before and the time he testified the very next day, when he reviewed the trial exhibits and grand jury transcript, and spoke with Broderick. When asked by defense counsel whether he had formulated his opinion based only on his investigation beginning the previous evening, Walter responded in the affirmative, and commented that "it was not [a] difficult" case. Id. at 814. On direct examination, after Walter had summarized the documentary evidence he had reviewed, the prosecutor asked whether "this case fits into one of the psychological profiles?" and Walter replied emphatically: "Oh yes it does." Id. at 793.
To achieve verisimilitude, Walter's testimony on picquerism was laden with technical jargon, see id. at 796-805 (using terms including "erotication," "machoism," "coital continuum" "fetish," and "phallution"), alluded to a spurious body of research, see id. at 793-94 (describing a typology of "lust murders" and picquerism's place "within that structure" as "a pathological condition"), and gave the impression of familiarity with a large number of case studies, see id. at 795 ("It's not uncommon to see cases where they will ...."); id. at 797 ("What generally happens, particularly [in] these types of cases...."). Walter began by giving an elaborate analysis of the psychological profile and upbringing of a picquerist, for instance, claiming that in order to fulfill a fantasy of superiority, a piquerist may use "machoism, such as weaponry, such as sniper activity." Id. at 795-96. Walter explained that picquerism involves eroticism, but this is not sexuality "in the conventional sense," rather a picquerist "would use the breast, would use symbolic things of sexuality rather than direct sexuality." Id. at 797.
Walter then testified that Drake's crime was a clear case of picquerism. He suggested that nearly every fact in the case was highly suggestive of picquerism, and that this went directly to intent (the sole issue at trial).
[T]he pattern of the gunshot wounds, the bite mark and its location, and the, having an anal assault, then when you see that whole big picture of what the intent is, then you look in at the secondary characteristics and you look at the bite mark. .... In this particular case I found it to be sexual.
Id. at 802-03 (emphasis added). In response to the prosecutor's invitation for Walter to "tell the jury what it is [he] relied on in coming to [the] conclusion," id. *237 at 803, that Drake was a picquerist, Walter gave this summary:
Again the location of the bite marks bilaterally on both breasts. The indication of suckling going on, also ... you find the penetration in the gunshot wound to the head, and the whole notion of stealing the honor of the normal .... the sort of destruction of the whole power center is the whole sense of sight, the whole sense of learning.... You come to the breast and ... the relationship and in terms of acting out not sex per se ... but kind of a mock form of sexuality in terms of power control, dominance expressed through rage, anger. You find the location again highly, highly significant. Again in terms of timing, it's not uncommon to move from the destruction of the power center ... and then start working out your fantasy system.
Id. at 803-04. Walter further testified that it was significant that the bites were post-mortem: "[i]n picquerism it's almost always post-mortem, after the person has been deceased. Because you see the threat ... that ... they're trying to surmount over, [and] that is in their way so they have to kill first." Id. at 804-05. To explain the evidence of rectal bruising, Walter stated that a picquerist, "incidently, derives the sexual satisfaction through the shooting which is quite common.... You can also derive sexual satisfaction through any form of physical assault to the person whether it be in the vagina or whether it be in the rectum or any other created orifice." Id. at 800. To explain the lack of evidence of seminal fluid on the victim, Walter stated that "in these types of cases," one would "[n]ot at all" expect to find sperm, because "what they're really after is the satisfaction that they can control and that they can degrade and that they can annihilate and consume others." Id. at 798-99. Overcoming the evidentiary gap created by Drake's apparent unfamiliarity with the victims, Walter explained that "[m]any times if the victim is known to the perpetrator it's incidental." Id. at 799. He then testified that a picquerist carries a psychological "murder kit" at all times, and provided his theory of what Drake did that night: "[H]e carries a murder kit with him ... [;] he may not feel as though he was going out to murder a specific person but when the opportunity strikes he can impl[e]ment it all the way through." Id.
On the Monday following Walter's testimony, defense counsel informed the trial judge that despite his attempts over the weekend to retain a rebuttal psychologist, he could not find any expert who had ever heard of "picquerism." Id. at 953. The defense requested a two-week continuance to find a psychologist with the expertise required. The prosecution opposed a continuance and the judge ruled in the prosecution's favor. Drake was found guilty of two counts of second degree murder and sentenced to two consecutive terms of twenty years to life by the state court.

II. Walter's False Statements
In 1995, many years after he had exhausted his direct appeals, Drake moved to vacate his conviction and sentence pursuant to N.Y.Crim. Proc. Law § 440.10 on the basis of newly discovered evidence that Walter had lied about his credentials. From his research in prison, Drake discovered that Walter's job at the Los Angeles County Medical Examiner's Office was to clean and maintain the forensic lab, not criminal profiling; Walter was never on the payroll of Northern Michigan University; and there was no record that Walter had testified as an expert witness in any criminal proceedings while he worked at the Los Angeles County Medical Examiner's Office. Drake I, 321 F.3d at 342-43.
*238 The Supreme Court, Niagara County, summarily denied the motion without a hearing, finding that Drake had made no showing that the prosecution knew or should have known about Walter's perjury. Drake exhausted his state court appeals and filed a federal habeas petition, which was denied by the district court.
On appeal in Drake I, we held that it was apparent that Walter's testimony contained significant falsehoods in addition to the improbability of his testimony as to the scientific validity of "picquerism." Id. Because the state courts did not permit the development of the factual record as to whether the prosecution knew Walter's testimony to be perjured, and the Appellate Division relied on that incomplete record, there were "no findings of fact requiring deference," and there was "no way for a federal habeas court to assess whether the Appellate Division's conclusion represented an unreasonable application of federal law." Id. at 345.[3] We concluded that Drake should be permitted to develop the record further and therefore remanded the case to the district court "for limited discovery on the circumstances surrounding Walter's perjured testimony." Id. at 346.
Walter's deposition on remand confirms that he grossly exaggerated most of his qualifications and outright lied about some of them. He testified at trial that he prepared criminal profiles at the Los Angeles County Medical Examiner's Office "to help the pathologist and the investigating agencies figure out what happened, but also then towards leads in resolving the case." Trial Tr. at 791. But "[a]ccording to Walter's supervisors there, he was employed as a lab assistant responsible for cleaning and maintaining the forensic lab." Drake I, 321 F.3d at 343. Walter confirmed at his deposition that he had been a student employee whose job in the lab was "grunt work" for which he was paid "[t]hree dollars and something" an hour. Walter Dep. at 91, 117. Although he may have discussed his opinions with detectives, he never prepared any written reports and was not aware of whether any investigating agency ever relied on his oral opinions in prosecuting any cases. In short, Water was no more than an avid student volunteer.
Walter's deposition also revealed that, although he was in fact a "prison psychologist" for the Michigan Department of Corrections, Trial Tr. at 783, he had only a "limited license," Walter Dep. at 80. Because he did not have a doctorate degree in psychology, he was only authorized to provide psychological services in the setting of a governmental institution or under the supervision of a fully-licensed psychologist.
Additionally, although Walter had answered "yes" to the prosecution's narrowly framed question as to whether he had "written" any "papers or articles in his field," Trial Tr. at 784 (emphasis added), he had not actually published any such writings, Walter Dep. at 34, 42-43.
We observed in Drake I that there "seem[ed] to be no record that Walter was ever on the payroll of Northern Michigan University, where he claimed to be an adjunct professor." 321 F.3d at 343. At Walter's deposition, he acknowledged that his use of the term "adjunct lecturer" was misleading; in fact, he had only been asked to lecture as a guest by a professor *239 at Northern Michigan University. Walter Dep. at 70-72 (emphasis added).
With respect to his testimony at Drake's trial that he had previously testified as an "expert witness" in two California jurisdictions, Trial Tr. at 785 (emphasis added), Walter had in fact only testified once before the Drake trial, and not as an expert in psychology or criminal profiling, but rather, as a lab technician on a chain of custody issue related to his handling of evidence at the Los Angeles County Coroner's office, Walter Dep. at 85-88.
Additionally, contrary to his trial testimony that his familiarity with the case came from the documents he reviewed and his discussions with Broderick on the eve and morning of his testimony, Walter acknowledged at his deposition that he had spoken with both Dr. Levine and Broderick nearly two weeks before trial, and that his conversation with Broderick had lasted 52 minutes.
Despite new evidence coming to light in Walter and Broderick's depositions, the district court granted Respondent's motion for summary judgment without conducting a hearing on the grounds that (1) there was no evidence that the prosecutor knew or should have known of Walter's false testimony, and (2) Walter's false statements did not render the trial constitutionally defective.

STANDARD OF REVIEW

I. State Court Decisions
"When a state court adjudicates a habeas petitioner's claim on the merits, we must afford that decision the deferential standard of review established by the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA") in 28 U.S.C. § 2254(d)." Hawkins v. Costello, 460 F.3d 238, 242 (2d Cir.2006). Applying AEDPA deference, a federal court may grant a writ of habeas corpus if the state court's adjudication on the merits "was contrary to, or involved an unreasonable application of, clearly established, Federal law as determined by the Supreme Court of the United States." 28 U.S.C. § 2254(d)(1). "Clearly established Federal law ... refers to the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision." Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).[4] A state court's findings of fact are "presumed to be correct" unless rebutted "by clear and convincing evidence." 28 U.S.C. § 2254(e)(1); see also Drake I, 321 F.3d at 345. In this case, we have already held that no deference to the state courts' conclusions is required because the state courts did not permit the development of the factual record. Drake I, 321 F.3d at 345-47.

II. District Court Decision
We review a district court's legal conclusions in denying a habeas petition de novo and its factual findings for clear error. Hawkins, 460 F.3d at 242. Clear error review requires examination of factual findings to determine whether "the district court's account of the evidence is plausible in light of the record viewed in its entirety." Anderson v. City of Bessemer, 470 U.S. 564, 573-74, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). "The reviewing court may reverse ... when, although there is *240 evidence to support the finding, `on the entire evidence [the court] is left with the definite and firm conviction that a mistake has been committed.'" Doe v. Menefee, 391 F.3d 147, 164 (2d Cir.2004) (quoting Anderson, 470 U.S. at 573, 105 S.Ct. 1504). A district court's factual findings may be clearly erroneous "where the court ... failed to synthesize the evidence in a manner that accounts for conflicting evidence or the gaps in a party's evidentiary presentation[;]... incorrectly assessed the probative value of various pieces of evidence [; or] failed to weigh all of the relevant evidence before making its factual findings." Id. at 164.

DISCUSSION

I. Clearly Established Federal Law on a Conviction Obtained Through Use of False Evidence
Since at least 1935, it has been the established law of the United States that a conviction obtained through testimony the prosecutor knows to be false is repugnant to the Constitution. See Mooney v. Holohan, 294 U.S. 103, 112, 55 S.Ct. 340, 79 L.Ed. 791 (1935). This is so because, in order to reduce the danger of false convictions, we rely on the prosecutor not to be simply a party in litigation whose sole object is the conviction of the defendant before him. The prosecutor is an officer of the court whose duty is to present a forceful and truthful case to the jury, not to win at any cost. See, e.g., Jenkins v. Artuz, 294 F.3d 284, 296 n. 2 (2d Cir.2002) (noting the duty of prosecutors under New York law "to seek justice, not merely to convict").
Shih Wei Su v. Filion, 335 F.3d 119, 126 (2d Cir.2003). Supreme Court holdings have long "established that a conviction obtained through use of false evidence, known to be such by representatives of the State, must fall under the Fourteenth Amendment." Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959) (emphasis added); see also United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976); Giglio v. United States, 405 U.S. 150, 153, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). "The same result obtains when the State, although not soliciting false evidence, allows it to go uncorrected when it appears." Napue, 360 U.S. at 269, 79 S.Ct. 1173.
Agurs identified the test as whether "the prosecution knew, or should have known, of the perjury." 427 U.S. at 103, 96 S.Ct. 2392. In Agurs, however, there was no allegation that the prosecutor should have known of any false statements. 427 U.S. at 104, 96 S.Ct. 2392. Thus, in Drake I, we identified the "should have known" language in Agurs as dicta. We did not rule on the contours of clearly established precedent on the level of culpability, short of actual knowledge, a prosecutor must have for a violation under Napue. 321 F.3d at 345. In Giglio, the Supreme Court held that, even though the specific prosecutor on the case did not have actual knowledge of the facts giving the lie to a prosecution witness's testimony at trial, he was charged with the knowledge of another prosecutor because a prosecutor's office has a duty to "insure communication of all relevant information on each case to every [prosecutor] who deals with it." 405 U.S. at 154, 92 S.Ct. 763. However, neither Giglio nor any other Supreme Court case decided prior to Drake's trial "clearly established," by its holding, that a prosecutor's failure to investigate testimony by a state witness that the prosecutor has reason to believe may be false is an error under Napue.[5]
*241 "[T]he [Supreme] Court has consistently 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." Agurs, 427 U.S. at 103, 96 S.Ct. 2392 (footnote omitted); see also Shih Wei Su, 335 F.3d at 129. In United States v. Wallach, we summarized the materiality standard under Napue, explaining that the "question is whether the jury's verdict `might' be altered." 935 F.2d 445, 456 (2d Cir. 1991) (quoting Sanders v. Sullivan, 863 F.2d 218, 225 (2d Cir.1988)). We have interpreted Supreme Court precedent as holding that "if it is established that the government knowingly permitted the introduction of false testimony reversal is virtually automatic." Shih Wei Su, 335 F.3d at 127 (quoting Wallach, 935 F.2d at 456)). This "strict standard of materiality" is appropriate "not just because [such cases] ... involve prosecutorial misconduct, but more importantly because they involve a corruption of the truth-seeking function of the trial process." Agurs, 427 U.S. at 104, 96 S.Ct. 2392.[6]
Thus, the clearly established Supreme Court precedent relevant to this habeas petition is that the conviction must be set aside if (1) the prosecution actually knew of Walter's false testimony, and (2) there is any reasonable likelihood that the false testimony could have affected the judgment of the jury.

II. Application of Clearly Established Federal Law
Based on the discovery on remand, Drake argues that there is now a factual basis for his claim for relief. We agree.

A. The Prosecutor's Knowledge of Walter's False Testimony
On remand, the district court concluded that there was "no evidence that the prosecution knew ... of Walter's false testimony." Drake II, slip op. at 34. Upon review of the evidence assessed by the district court, considered in its entirety, we are left with the firm conviction that this finding is clearly erroneous.
The main falsehood that now requires reversal  uncovered for the first time during the depositions on remand  is Walter's false testimony that he learned about the facts of the case the night before his testimony. Walter's trial testimony was offered on October 22, 1982. At trial, during cross-examination, Walter gave the jury, the court, and defense counsel the impression that he had become substantively involved in the case only the night before and that his testimony was based entirely on what he had learned beginning the previous day:
[Defense Counsel]: When did you first get involved with this case timewise?

*242 [Walter]: I arrived in Buffalo last night at about 8.30.
[Defense Counsel]: Oh, I see. When's the first time you read anything like a Grand Jury transcript or anything having to do with this case?
[Walter]: I read the Grand Jury this morning.
[Defense Counsel]: This morning?
[Walter]: Yes.
. . . .
[Defense Counsel]: Well, who did you talk to before you testified here about this case?
[Walter]: I consulted with the prosecutor.
[Defense Counsel]: You mean Mr. Broderick?
[Walter]: Right.
[Defense Counsel]: Who else?
[Walter]: As far as I know that's all.
[Defense Counsel]: What do you mean, did you come in here and look at the exhibit blackboard?
[Walter]: Last night about 9:30.
. . . .
[Defense Counsel]: Okay. Now just so I understand ..., you came in last night.
[Walter]: Yes.
[Defense Counsel]: You looked, you talked to Mr. Broderick.
[Walter]: Uh huh.
[Defense Counsel]: And you looked at some things.
[Walter]: Uh huh.
[Defense Counsel]: And based upon that and that alone you've given your testimony this afternoon. Is that right?
[Walter]: Yes, it was not difficult.

Trial Tr. at 806-14 (emphases added).
The falsity of this testimony became clear when, at Walter's deposition, he acknowledged that a telephone bill from October 7, 1982  about two weeks before trial  showed a telephone call lasting 52 minutes that "very well" seemed to be between his office and the prosecutor's office. Walter Dep. at 48-52. Walter commented that he was "quite convinced that they called me on Thursday and that I testified on Friday ... but apparently it was a ten day lag there." Walter Dep. at 51.[7]
During that 52-minute telephone conversation, Broderick explained all of the details of the crime to Walter. Upon hearing the facts, Walter did not perceive a clear case of picquerism; rather "he hesitated at that point to render any opinion and said he would like to think about it and he'd call [Broderick] back." Broderick Dep. II at 4. This is flatly inconsistent with Walter's trial testimony that he first became substantively involved with the case the night before, when he arrived in Buffalo, looked at some exhibits, talked with the prosecutor, and based his testimony "upon that and that alone." Trial Tr. at 814. To the contrary, as Broderick now recounts, Walter learned the relevant facts two weeks prior to the trial. Obviously, Broderick knew that this portion of Walter's testimony was false, because the falsehood related to a conversation Walter had with Broderick.
*243 Even before the depositions on remand, there was inferential support for the conclusion that Broderick knowingly elicited Walter's false statements. The prosecutor's decision to spring Walter's testimony at the last minute and resist a continuance provided circumstantial evidence of the prosecutor's knowing complicity in Walter's false testimony. Drake I, 321 F.3d at 346. Broderick's depositions revealed that during his conversations with Walter approximately two weeks before trial, they spoke at length and even discussed picquerism. Yet Broderick only gave one day's notice of his plan to call Walter.
Although Broderick had never heard of picquerism until Walter mentioned it, he did not contact any other mental health professional to inquire about the concept. Broderick Dep. II at 26. Broderick did not ask Walter about his credentials until Walter arrived in New York the night before his trial testimony. At that time, Broderick recalled that he was impressed by Walter's claim to have handled 10,000 profiles for the Los Angeles County Medical Examiner. When asked about his reaction to this improbable number, Broderick admitted, "Well, now that I look at it, it seems like an extraordinary number." Broderick Dep. I at 41-42. But Broderick failed to ask Walter for a reference to verify the claim.
Broderick never asked Walter about the substance of his purported "expert" testimony in prior cases in California, although he admitted that it would have "obviously" been important to him to know that Walter had "testified as a witness on a chain of custody of a piece of evidence that had come into a lab, rather than ... as to psychological matters." Broderick Dep. II at 19.
The record strongly suggests that Broderick knew that Walter's testimony about his scholarship was intentionally misleading. Broderick took notes of his interview of Walter the morning Walter was to testify at trial. The notes contain the word "papers" crossed out. At his deposition, when asked to explain this notation, Broderick agreed that it was a fair assumption that he had asked whether Walter had written or published any papers, and the cross-out meant that the answer was negative. Walter provided further detail at his remand deposition: at the time of Drake's trial, the sum of his scholarship was one unpublished paper. Nevertheless, at trial Broderick asked Walter, "[h]ave you written any papers or articles in your field," to which Walter answered "[y]es." Trial Tr. at 784. Thus, aware that Walter was not a published scholar, Broderick trimmed the question to inquire only as to papers Walter had "written," as opposed to "published." The prosecutor plainly crafted the question to achieve literal accuracy while conveying the false impression that Walter's work had been validated through publication. By contrast, during his direct examination of Dr. Levine, Broderick asked not only, "Ever write any articles, Doctor?," but also, "Have you had them published?," and "How many articles have you had published in what type of publication[s]?" Id. at 668-69.
To be sure, eliciting literally accurate testimony is not a ground for a claim of subornation of perjury. Carefully phrased questions designed to elicit literally accurate testimony while not revealing weaknesses are grist for cross-examination. A prosecutor who asks such questions on direct takes a chance of damaging his case if defense counsel follows with a cross that brings out these weaknesses. In this case, however, defense counsel had only one night to investigate Walter's qualifications or scholarship, and Broderick successfully opposed the request for a continuance that *244 would have allowed the defense to investigate the new witness.

B. Materiality
The question in this case is whether the evidence was so overwhelming that there is no "reasonable likelihood" that Walter's false testimony, of which the prosecutor was aware, could have "affected the judgment of the jury." Napue, 360 U.S. at 271, 79 S.Ct. 1173. Walter explicitly testified that the brevity of his review of the evidence confirmed that this "was not [a] difficult" case. Trial Tr. at 814. Walter testified that this case was replete with the tell-tale signs of picquerism  the nature of the bullet wounds, the stabbing, the lack of sperm found on the slides from Smith's rectal cavity, the anal bruising, the breast bite marks, the commando clothing. Given these overwhelming and obvious indicia of picquerism, Walter suggested, a trained expert could conclude in a short evening's work that this was a textbook case, with sufficient confidence in that conclusion to testify under oath to a jury in a murder trial. Indeed, Walter explicitly made this point by emphasizing that this case was "not difficult."
As Broderick knew, however, the truth was quite different: Walter learned the facts in significant detail (including the bite marks, the camouflage, the bandolier of ammunition, and the guns) two weeks before he testified.[8] When Walter learned these facts, he did not come up with an opinion on the "spur of the moment"; rather, he told Broderick he would need time to think about it. Broderick Dep. I at 44.
Walter then had two weeks to conjure up his quackery. His direct testimony on picquerism, which spans twelve pages of trial transcript, consisted largely of uninterrupted and prolix exposition, weaving the complicated facts of the case into a seemingly coherent narrative, all pointing to the symptoms of the fictive syndrome called picquerism. Walter even adapted the symptoms of the syndrome to remedy any potential weaknesses in the prosecution's theory of Drake's motive, for example, the lack of semen evidence. Given that, as Walter admitted during his deposition, the literature on picquerism is obscure, it must have taken Walter some time to concoct his description of the picquerist syndrome in a manner that (1) incorporated all the facts in Drake's case and (2) made picquerism sound as if it were well-known to psychologists. If picquerism were indeed a well-known diagnosis, it would not be surprising that Walter would have looked at this case the night before, come to the easy conclusion that Drake was a picquerist, and delivered a virtually impromptu lecture on the topic the next day. The jury, therefore, would have been much more likely to believe that picquerism was a real syndrome if, as Walter testified, he learned the facts of this case only the night before. Walter had no time to make all this up. Thus, the supposed brevity of Walter's contact with the facts of the case was perhaps the strongest reason for the jury to conclude that Walter was not fabricating this sophisticated story.
There is a strong likelihood that this falsehood was vitally important to the *245 jury's decision to credit Walter's testimony. And "[t]he principle that a State may not knowingly use false evidence, including false testimony, to obtain a tainted conviction, implicit in any concept of ordered liberty, does not cease to apply merely because the false testimony goes only to the credibility of the witness." Napue, 360 U.S. at 269, 79 S.Ct. 1173. The jury's estimate of the truthfulness of Walter's testimony may well have been determinative of the single issue at trial  Drake's intent.
The prosecutor virtually conceded the materiality of Walter's testimony in acknowledging that he called Walter to compensate for problems revealed with his theory of the case after it turned out that there was no evidence of semen in Smith's rectal cavity. Walter's testimony filled the gap in the prosecution's theory of intent with a sensationalistic and pseudo-scientific explanation of motive. As we observed in Drake I, "the jury was likely to be impressed (if not inflamed) by testimony that the defendant was a `picquerist' who killed, mutilated, and abused his victims to satisfy a warped sexual urge." 321 F.3d at 346. In response to defense counsel's objection at trial that Walter was "a breath away" from proclaiming Drake guilty, Broderick pointed out that, in light of Walter's testimony, it was impossible to "avoid the analogy that in fact the defendant is the killer in a one-issue case." Trial Tr. at 818, 824.
We have held that "at least for purposes of a collateral attack, a defendant is normally required to exercise due diligence in gathering and using information to rebut a lying prosecution witness." Shih Wei Su, 335 F.3d at 127 (citing United States v. Helmsley, 985 F.2d 1202, 1208 (2d Cir. 1993)). But where the prosecutor engages in conduct designed to inhibit the defense in this regard, for example, by objecting to efforts at impeachment, bolstering false testimony in summation, or, as in this case, contriving a scheduling crisis, it "sharpen[s] the prejudice." See, e.g., Jenkins, 294 F.3d at 294. As we held in Drake I, the prejudice was compounded by the fact that the trial court "denied the defendant a continuance to afford the defense an opportunity to confirm counsel's grounded suspicion (later confirmed) that the witness was a charlatan, and that his testimony was, medically speaking, nonsense." 321 F.3d at 346. Had defense counsel been informed that Broderick and Walter spent nearly an hour discussing the case two weeks before trial, and that Walter had raised the idea of "picquerism" with Broderick on that day or the next, defense counsel would have had a much stronger argument for a continuance or exclusion of Walter' testimony.
Respondent now argues that the evidence of Drake's guilt is so overwhelming that there is no reasonable likelihood that Walter's misstatements had any effect on the jury. Respondent points to testimony at trial supporting its argument that Smith's body had been abused after her death. A physician, Dr. Bich Nguyen, testified that she examined decedent Smith's body for signs of rape, found Smith's anus to be dilated, and observed a bruise on the interior wall of Smith's rectum. However, Dr. Nguyen was not a pathologist and had never before performed a rape examination on a deceased person. Dr. Nguyen could not testify as to the cause of the anal dilation, or whether the bruising had occurred pre-or postmortem. Dr. Nguyen also testified that she found "mud and dirt.... between the anus and the vulva." Trial Tr. at 606. This evidence does not compel the conclusion that sexual assault occurred; it may have resulted when Drake dropped Smith's body on the ground as he attempted to move her body to the trunk of the car.
*246 Dr. Justin Uku, the pathologist who examined the bite marks testified that it was his opinion that they had been inflicted post-mortem. But Dr. Uku's examination occurred after the body was exhumed more than one month after the crime. The basis for his conclusion was the lack of white blood cells or broken blood vessels around the injury. But he testified on cross examination that it was possible that "a trauma inflicted within an hour of death might also show a lack of white blood cells," id. at 658, and that a lack of broken blood vessels could also indicate a premortem trauma that was not severe, id. at 654-55. Dr. Levine, who also testified that the bite marks were inflicted post-mortem, was not a pathologist and the basis for his opinion was Dr. Uku's examination.
The witness who testified as to the evidence of seminal fluid found on Drake's undergarments could not state "with any reasonable degree of scientific certainty when the seminal fluid was deposited ..." Id. at 529 (emphasis added).
Respondent also argues that the following evidence demonstrates that Drake shot at the Nova with the intent to commit murder: (1) contrary to Drake's statement that he was ten to fifteen feet away from the car, experts testified that he may have been closer, possibly within eight feet; (2) Drake described the windows as "fogged," a condition that would have occurred only if the car were occupied;[9] (3) the car had license plates and registration inspection stickers, which would have been visible due to street lights; (4) the location of the shooting was not in the dump where abandoned cars were generally found but rather, one half mile away; and (5) despite Drake's statement that he wanted to destroy the car, the only bullet holes were in the passenger's side window. This evidence, however, is also consistent with Drake's statement that as he was walking down the road, he made a "turn, approached, went over what appeared to be debris and a pile of leaves, dirt," and "opened fire" upon the car without pausing to check whether the car was occupied. Id. at 266-67. A prosecution expert testified that Drake could have fired all nineteen rounds of ammunition into the car in 3 to 4.5 seconds, supporting Drake's statement that he had fired in the spur of the moment. No prosecution witness disputed that the rusted Nova was in poor condition.
Respondent also points to the fact that a jailhouse informant testified at trial that Drake had admitted to stabbing Rosenthal in a panic in order to "wipe him out." Id. at 723 (testifying that the exact words Drake had used were "I had to wipe him out. Something in that order."). However, it was established that the stabbing was not the cause of Rosenthal's death. Moreover, these statements are consistent with Drake's confession that he stabbed Rosenthal as a result of "panic[ ]." Id. at 271.
Respondent also argues that a witness, Theresa Weslowski, testified that Drake exchanged profanity with Rosenthal on one occasion in the high school cafeteria. But the evidence of any prior connection between Drake and Rosenthal was extremely thin. A police officer testified at trial that an announcement was made over the high school's public address system asking that students come forward with any information about Drake, Smith, or Rosenthal, and out of over 1,500 students at the high *247 school, only Weslowski came forward with testimony.
Because the evidence on Drake's intent was not conclusive, the issue of the validity of Walter's testimony on piquerism was no extraneous matter. In sum, we conclude that the evidence of Drake's intent was not sufficiently overwhelming that there is no "reasonable likelihood" that Walter's false testimony could have "affected the judgment of the jury." Napue, 360 U.S. at 271, 79 S.Ct. 1173. The district court clearly erred in finding that Walter's false statements were not material.

III. Relief
Because the main facts requiring a grant of habeas relief were uncovered for the first time on remand to the district court, the state court's factual findings and conclusions of law do not require deference under AEDPA. See Drake I, 321 F.3d at 345-47. Respondent argues that the doctrine of exhaustion requires rejection of Drake's arguments on remand regarding Broderick's knowledge of Walter's false statements, because the facts supporting those arguments were not presented to the state courts. But the Supreme Court has "never held that presentation of additional facts to the district court, pursuant to that court's directions, evades the exhaustion requirement when the prisoner has presented the substance of his claim to the state courts." Vasquez v. Hillery, 474 U.S. 254, 257-58, 106 S.Ct. 617, 88 L.Ed.2d 598 (1986); see also Pinholster v. Ayers, 525 F.3d 742, 765 (9th Cir.2008). Respondent does not dispute that Drake presented the substance of his Napue claim to the state courts. In Drake I, we held that Drake had made a showing of good cause that the state courts failed to provide Drake with the opportunity to develop the record. 321 F.3d at 345-46. We now conclude that, based on the record developed by Drake, the district court erred in denying habeas relief.[10]
Ordinarily, where an appellant demonstrates that a district court denied habeas relief erroneously without holding a hearing, we would remand to the district court for proceedings on the ultimate merits of the appellant's claim. In the present matter, however, neither party seeks remand. We hold, based on the record before us, that the district court committed clear error in reaching its findings with respect to Broderick's knowledge of Walter's false testimony and that the district court erred in its determination with respect to the materiality of the false testimony. Respondent has had a full opportunity to develop the record and brief the issues in response to Drake's claims. Because there is no basis for requiring additional proceedings, we conclude that reversal, not vacatur, of the district court's judgment is warranted, and direct the district court to enter judgment for Drake conditionally granting the writ of habeas corpus. See Henry v. Poole, 409 F.3d 48, 72 (2d Cir.2005).

CONCLUSION
For the foregoing reasons, the judgment of the district court is REVERSED and *248 REMANDED for the entry of judgment conditionally granting the writ of habeas corpus and ordering Drake's release unless the State provides him a new trial within 90 days.
NOTES
[1]  Although Broderick referred to Walter as "Dr. Walter" during his deposition, Walter had neither a medical nor any other doctorate degree.
[2]  We are troubled that Respondent continues to assert that picquerism "appears in numerous, serious, criminal investigative works," of which Respondent seems to be able to locate only four examples from the past 50 years. Resp. Br. at 59. Walter himself admitted it is fair to say that "the canon concerning picquerism is not large." Walter Dep. at 140. Picquerism, a concept wildly sensational and pseudo-scientific, was once the subject of an episode of a network television crime drama. But picquerism is not now and never has been recognized in the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders. Support for the idea is primarily anecdotal, popping up in the literature on "lust murder" and "serial killings," alongside names like Jack the Ripper.
[3]  We rejected Drake's argument that his rights to due process under the Fourteenth Amendment and compulsory process under the Sixth Amendment were violated because Walter's surprise testimony, coupled with the trial court's refusal to grant a continuance to allow defense counsel to find a competing expert, deprived Drake of the opportunity to present a meaningful defense. Drake I, 321 F.3d at 344.
[4]  Under Section 2254(d)(2), relief is also available if the state court made "an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(2). The terms of Section 2254(d)(2) do not limit a federal court's power to grant a writ to situations in which a state court acted in violation of "clearly established Federal law." However, Drake has not invoked Section 2254(d)(2).
[5]  United States v. Wallach found constitutional error where the government "should have known" that its witness was committing perjury but, given the importance of the witness's testimony to their case, "the prosecutors may have consciously avoided recognizing the obvious." 935 F.2d 445, 457 (2d Cir. 1991). However, Wallach was not a habeas case and therefore did not address the question at issue here  whether this principle was clearly established federal law, defined as a Supreme Court holding in existence at the time of the relevant state-court decision. Williams, 529 U.S. at 412, 120 S.Ct. 1495.
[6]  Respondent argues that relief is warranted only if the alleged constitutional errors had a substantial and injurious effect or influence in determining the jury's verdict. However, certain types of habeas claims, such as errors under Napue, are analyzed under their own harmless error standard. See, e.g., Shih Wei Su, 335 F.3d at 129 (analyzing Napue claim for whether there was any reasonable likelihood that the false testimony could have affected the judgment of the jury).
[7]  Respondent argues that there is no proof that Walter willfully intended to provide false testimony, and that his false testimony may have been the result of confusion or mistake. Napue held that there was constitutional error where a prosecutor knew of "false evidence." Napue, 360 U.S. at 269, 79 S.Ct. 1173. The question of whether the witness's "untruthfulness... constituted perjury" makes no "material difference" where the issue is a conviction "on tainted testimony." Mesarosh v. United States, 352 U.S. 1, 9, 77 S.Ct. 1, 1 L.Ed.2d 1 (1956) (cited in Napue, 360 U.S. at 269, 79 S.Ct. 1173)).
[8]  The morning of Walter's testimony, Broderick did acknowledge during a bench conference that he had contacted Walter "within the past two weeks." Trial Tr. at 750. However, Broderick did not disclose the relevant falsehood in Walter's subsequent testimony: that he had a 52-minute conversation with Walter in which he detailed the factual background of the case. At the end of that conversation, Walter said that he could not give an immediate opinion.
[9]  From the record, it is not clear whether Drake first saw fog on the windows before or after the shooting.
[10]  Respondent also argues that Drake waived the specific point regarding Broderick's knowledge of the 52-minute phone conversation by failing to raise it before the district court or in his initial submissions to this Court. But Drake presented the facts and his argument that the prosecutor was aware that certain portions of Walter's testimony were false. Even if Drake did not state this issue with precision, that does not amount to waiver. See Claudio v. Scully, 982 F.2d 798, 802 n. 3 (2d Cir. 1992) (issue was not "waived" because it was not a "new claim," rather, it was merely "an additional argument relating to a point already under dispute").
