EASTERBROOK, Circuit Judge.

Someone bludgeoned Bennie Ervin to death in her home and stole her jewelry plus other valuables. A jury convicted Joel Buie of these crimes; the judge sentenced him to life imprisonment. The evidence supporting this verdict includes Buie’s confession, the fact that he was hard up for money (shortly after the murder he tried to exchange a gold chain for cocaine, and Ervin’s husband testified that she always wore such a chain), and the fact that there were no signs of forced entry. Buie and Ervin lived a few doors apart, and he had agreed to install a hook for a flower pot in her home. The prosecutor’s theory is that, when Ervin admitted Buie for this purpose, he pushed her down the basement stairs and used the hammer on her rather than the hardware. Police found a metal hook on the floor near the bottom of the stairs.

Though Buie later contended that his confession to this sequence of events had been obtained unlawfully, the state judge found that Buie lied about what had occurred in the police station. He contended, for example, that the police severely beat him, but medical personnel found no bruises or scratches on his body. The confession also was consistent with statements of Buie’s girlfriend and a neighbor’s recollection that Buie related that he had visited the Ervin home to install a hook.

The state’s appellate court affirmed Buie’s conviction and sentence. People v. Buie, 238 Ill.App.3d 260, 179 Ill.Dec. 447, 606 N.E.2d 279 (1st Dist.1992). A collateral attack in state court was abandoned after counsel concluded that it was frivolous. The federal district judge denied Buie’s petition for relief under 28 U.S.C. § 2254. United States ex rel. Buie v. Page, 2002 U.S. Dist. LEXIS 16034 (N.D.Ill. Aug. 22, 2002). A motions panel declined to vacate the district judge’s certificate of appealability; although the panel concluded that the certificate failed to identify any substantial constitutional issue, see 28 U.S.C. § 2253(c)(2), it held that there was some potential for constitutional argument notwithstanding the certificate’s defects. Buie v. McAdory, 322 F.3d 980 (7th Cir.2003).

Buie’s principal argument is that the trial judge violated the due process clause by permitting an expert witness to overstate the strength of her conclusion. Police found some strands of hair on Ervin’s clothing and among shards of glass on the basement floor. (Ervin had been beaten with a bottle as well as a hammer.) Maria Pulling, who Buie acknowledges to be a legitimate expert in hair analysis, testified that the hair “exhibited characteristics that were the same as Joel Buie’s head hair standards.” After detailing for the jury the respects in which the hairs matched, Pulling testified: “Within a reasonable degree of scientific certainty I would say that the hair came from Joel Buie.” She told the jury that her methods did not exclude the possibility that the hairs came from someone else but that she thought this probability low. She repeated these limitations on cross-examination. Buie presented a hair expert of his own; this expert testified that Pulling had overstated the degree of confidence allowed by tests available at the time. He did not, however, examine the hairs himself, conclude that they came from someone other than Buie, or even opine that the *625 set of potential donors for these strands was particularly large.

According to Buie, the Constitution forbids any expert witness to misstate scientific conclusions in a criminal prosecution. It is far from clear that Pulling did this; she and the defense expert debated the accuracy of hair analysis, and Buie does not cite any scientific literature establishing that Pulling was in the wrong. “Reasonable degree of scientific certainty” is a plastic phrase. Let us assume, however, that Buie’s expert had the better of the argument. Still, to obtain collateral relief, Buie must show that the state’s decision “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). No decision of the Supreme Court “clearly establishes” that experts (or any other witnesses) must be right; the constitutional rule is that the defendant is entitled to a trial that will enable jurors to determine where the truth lies. That a witness may give false or mistaken testimony therefore is not an independent constitutional violation. See, e.g., Herrera v. Collins, 506 U.S. 390, 398-405, 113 S.Ct. 853, 122 L.Ed.2d 203 (1993). What the Constitution provides is assurance that evidence may be tested by cross-examination and by contrary proofs. Whether a given expert witness overstated her conclusion is mete for cross-examination, and no one impaired Buie’s ability to elicit from her just how likely (or unlikely) a “reasonable degree of scientific certainty” was in her vocabulary. The state paid for an expert witness to evaluate the issue and testify on behalf of the defense. See Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985).

The state’s appellate court did not apply any of these principles unreasonably in holding that the jury was entitled to hear Pulling’s testimony. And if state law contains the principle for which Buie contends, and the state court therefore should have struck this portion of Pulling’s testimony — well, an error of state evidence law cannot be the basis of federal collateral relief. See Estelle v. McGuire, 502 U.S. 62, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). See also Gilmore v. Taylor, 508 U.S. 333, 113 S.Ct. 2112, 124 L.Ed.2d 306 (1993). Although the federal Constitution may be offended when probative exculpatory evidence is pointlessly excluded, see Chambers v. Mississippi 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), no comparable rule condemns the admission of evidence that the defendant deems untrustworthy, as long as the state affords the defendant the means to demonstrate its weaknesses (and its use does not violate the confrontation clause). Informants may be lying, eyewitnesses may be tricked by their own memories, and experts may produce flawed analyses. The tools of the adversary process supply the means to expose these testimonial shortcomings. The Constitution does not impose Fed. R.Evid. 702 on the states, let alone require that federal courts scrutinize line by line the state-court testimony of experts conceded to be competent.

Although the state must not withhold exculpatory evidence or use testimony that the prosecutor knows is false, see Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972); Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), these closely related decisions do not offer Buie any support. (The district judge thought that arguments based on Giglio had been forfeited in state court, while arguments based on Brady had been preserved. Yet these two decisions reflect the same fundamental principle, which therefore is open to consideration in this collateral attack.) Illinois did not try to conceal the limitations of hair analysis. Scientific literature is published *626 for all to read, and the state furnished Buie with an expert to assist in the understanding and application of this knowledge. If Pulling should have been more cautions than she was, this was known to the defense as well as to the prosecutor. Giglio does not license a federal court to determine whether particular testimony in a state trial was good or bad substantively; that decision condemns only subornation of perjury. The Illinois appellate court did not act unreasonably in concluding that the prosecutor’s behavior was above board. He asked a series of questions that enabled Pulling to describe the tests she performed and the conclusions she drew. Buie does not contend that the prosecutor had, but concealed, some private knowledge suggesting that Pulling had not performed the tests about which she testified, or that she did not actually hold the conclusions she articulated. Thus we are back to the claim that Pulling made a statement more confident than the science supports, and that is neither a Brady nor a Giglio problem. It is just a reason why defendants have the right to cross-examine witnesses and present evidence of their own.

Buie’s other contention is that his lawyer in the state proceedings furnished constitutionally ineffective assistance. This claim was defaulted, as the district judge held. It was not presented to the state judiciary on direct appeal or pursued to conclusion on collateral attack. See O’Sullivan v. Boerckel, 526 U.S. 838, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999). Buie does not contend that he has any cause for this omission. See Wainwright v. Sykes, 433 U.S. 72, 97 S.Ct. 2497, 53 L.Ed.2d 594 (1977). Instead, he says, this claim should be adjudicated despite the default in order to vindicate the rights of a person who is actually innocent. See Herrera, 506 U.S. at 404, 113 S.Ct. 853; Sawyer v. Whitley, 505 U.S. 333, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992). Yet it is hard to see how one who has confessed can assert actual innocence. Buie’s challenge to that confession was rejected in state court on factual grounds that are uncontested today.

According to Buie, his innocence is established by the fact that his fingernails were intact when he was arrested. This seemingly mundane fact acquires significance, Buie’s lawyer insists, when combined with the fact that a fingernail fragment was retrieved from the bottom of the basement stairs in Ervin’s house, tested, and found not to be Ervin’s. If it was not Ervin’s, and could not have been his, then someone else must have committed the crime, Buie contends. The problem with this argument is that the record does not show how old the fragment was when collected and how many other people may have broken a fingernail in the Ervin basement within the available time. Without that information, the fact that it could not have come from Buie on the day of the murder reveals nothing about who committed that crime.

Nothing else in the record implies actual innocence. We say this cognizant of the fact that the record in this collateral attack is only a subset of the record assembled in state court. It contains some pages of the transcript, but not the full thing. At oral argument, Buie’s lawyer said that he had made informal inquiries and been told that much of the transcript had been lost in the lengthy time (more than a decade) since the trial, and that the court reporter was unavailable to recreate it. At this point counsel let matters drop. He did not ask the federal judge to require the state to locate or recreate a complete transcript, nor did he raise this as an issue on appeal (which, given the lack of request in the district court, could not have been much of an appellate issue). A defendant who asserts actual innocence as a reason to excuse a procedural default must demonstrate innocence; the burden is his, not the *627 state’s, for the state has the benefit of the jury’s verdict. See Schlup v. Delo, 513 U.S. 298, 324-38, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995). Congress codified the requirement in 28 U.S.C. § 2254(e)(2)(B), which says that, when a prisoner fails to develop the factual basis of a position in state court (as Buie failed to develop his ineffective-assistance claim) and an eviden-tiary hearing in federal court would be necessary to prevail, the default may be overcome only if “the facts underlying the claim would be sufficient to establish by clear and convincing evidence that but for constitutional error, no reasonable factfin-der would have found the applicant guilty of the underlying offense.” Buie could not prevail without an evidentiary hearing into his ineffective-assistance claim, yet he has not come close to establishing innocence by clear and convincing evidence. It was not the task of the district judge (or this court) to attempt that task for him by augmenting the record, when Buie has been content to receive a decision on the record as it stands.

Affirmed.