
608 F.3d 963 (2010)
Tyrone HOLMES, Petitioner-Appellant,
v.
Marcus HARDY, Warden, Respondent-Appellee.
No. 09-1293.
United States Court of Appeals, Seventh Circuit.
Argued May 21, 2010.
Decided June 11, 2010.
*964 Robert J. Palmer, Attorney, Victoria R. Wolf (argued), Attorney, May, Oberfell & *965 Lorber, Mishawaka, IN, for Petitioner-Appellant.
Michael M. Glick, Attorney, Katherine D. Saunders (argued), Attorney, Office of the Attorney General, Chicago, IL, for Respondent-Appellee.
Before EASTERBROOK, Chief Judge, and BAUER and TINDER, Circuit Judges.
BAUER, Circuit Judge.
After a bench trial, an Illinois court found Tyrone Holmes guilty of murder and sexual assault. Now, more than twenty years later, Holmes seeks federal relief from his life sentence, claiming that the state prosecution withheld exculpatory evidence and suborned perjury. But Holmes procedurally defaulted his claims and cannot otherwise show either that he was insufficiently informed to raise them earlier or that the newly discovered evidence he presents exonerates him. Therefore, we affirm.

I. BACKGROUND
After an Illinois court convicted Tyrone Holmes for murder and sexual assault, the state appellate court affirmed Holmes' convictions and sentence and the Illinois Supreme Court denied his petition for leave to appeal. Then from 1993 to 2004, Holmes filed five different state petitions for post-conviction relief. He asserted various challenges in these petitions but has since abandoned all but the two he pursues in this court: (1) that the prosecution withheld exculpatory evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by failing to turn over serologist Pamela Fish's handwritten notes regarding preliminary test results for the presence of blood on Holmes' clothing; and (2) that the prosecution knowingly used testimony by Fish that was false. Holmes first raised these claims in his fourth post-conviction petition, and the state appellate court found them waived. See Illinois v. Holmes, No. 1-02-3303, at 8, 348 Ill.App.3d 1087, 311 Ill.Dec. 438, 868 N.E.2d 1099 (Ill.App.Ct. June 16, 2004) (finding Holmes unable to meet his burden to show that he could not have raised the claims until the fourth petition, because "it is unclear if defendant learned of the notes prior to or after the filing of his third petition").
The district court in turn found the two claims procedurally defaulted, because the state court "rejected both based on the independent and adequate state ground of waiver." Holmes v. Pierce, No. 04 CV 8311, 2009 WL 57460, at *4 (N.D.Ill. Jan.7, 2009). The district court further found that Holmes pointed to no cause for his procedural default. Id. at *6. Finally, the district court declined to excuse Holmes' procedural default on the ground that he is actually innocent, because Holmes presented no new evidence establishing that "it was more likely than not that no reasonable juror would have convicted him in light of the new evidence." Id. at **6-8 (quoting Gomez v. Jaimet, 350 F.3d 673, 679 (7th Cir.2003)). Holmes appeals each of these findings.

II. DISCUSSION
As an initial matter, the government seeks to quash Holmes' appeal by arguing that he failed to address this court about the merits of his two prosecutorial-misconduct claims. The constitutional claims are waived, argues the government, because Holmes addressed only the antecedent procedural question in his opening brief.
We disagree because Holmes did exactly as we instructed him. Our order granting a certificate of appealability from the district court's ruling invited the parties only to brief the procedural issue. Indeed, it stated that "Holmes has made a substantial *966 showing [on the constitutional claims].... The parties must first, however, address the antecedent issue of procedural default." Holmes v. Mathy, No. 09-1293 (7th Cir. May 4, 2009) (order granting certificate of appealability). The government made no effort to construe this language as requiring the parties to additionally address the constitutional questions in their briefs. The government's waiver argument is thus waived. See Fed. R.App. P. 28(a)(9)(A) and 28(b) (requiring the appellee to state not only its contentions, but also its "reasons for them, with citations to the authorities and parts of the record on which the appell[ee] relies."); cf. Supreme Court Rule 14.1(a) (providing a more lenient standard in that the issue need only be "fairly included" in the parties' briefs).
Even were the government correct that the certificate of appealability is defective for failure to require the parties to brief the constitutional issues, "[a] litigant whose lawyer is misled by the language of a judicial order should not suffer ill consequences." Beyer v. Litscher, 306 F.3d 504, 507 (7th Cir.2002). And in any event, the certificate of appealability is not defective. The requirement that not only procedural but also constitutional claims always be addressed is directed not at advocates' briefs, but at judges' issuances of certificates of appealability. See id. at 505-07 (citing 28 U.S.C. § 2253(c)(3) and Slack v. McDaniel, 529 U.S. 473, 483-85, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)) ("[N]either Congress nor the Supreme Court has required advocates to cook up constitutional issues in briefs.... Slack imposes duties on judges rather than lawyers, and thus never requires any particular question to be briefed.") (emphasis in original). The cases the government cites for the proposition that Holmes was additionally required to address his constitutional claims either: (1) involve certificates of appealability that, unlike the one in this case, instructed the petitioner to address those claims, see Modrowski v. Mote, 322 F.3d 965, 967 (7th Cir.2003) ("[T]he district court granted a certificate of appealability on the equitable tolling question and on all but one of Modrowski's substantive claims."); Anderson v. Litscher, 281 F.3d 672, 675 (7th Cir. 2002) ("Also certified for appeal were two constitutional issues."), or (2) excused the petitioner's failure to brief the constitutional issues. See Beyer, 306 F.3d at 507.
More generally, in the typical case where we find an issue waived, there is no prior finding that the issue has "substantial" merit, and to rule on the unbriefed issue would be to engage in a form of judicial activism contrary to our normal mode of operation. See United States v. Lanzotti, 205 F.3d 951, 957 (7th Cir.2000) (quoting Carducci v. Regan, 714 F.2d 171, 177 (D.C.Cir.1983) (Scalia, J.)) ("The premise of our adversarial system is that appellate courts do not sit as self-directed boards of legal inquiry and research, but essentially as arbiters of legal questions presented and argued by the parties before them."); see also Sarah M.R. Cravens, Involved Appellate Judging, 88 Marq. L.Rev. 251 (2004); Adam A. Milani & Michael R. Smith, Playing God: A Critical Look at Sua Sponte Decisions by Appellate Courts, 69 Tenn. L.Rev. 245 (2002). By contrast, here we found in our order granting a certificate of appealability that Holmes had already made a substantial showing as to the constitutional claims, and certified the appeal as to the complex procedural question only. We did so on the theory that we would prefer to allow the district court to decide the constitutional issues in the first instance were Holmes to win this appeal on the procedural one, which as we discussed above is entirely within our power. See Beyer, 306 F.3d at 505-07. Here we decide an issue that has been fully briefed. This is hardly judicial activism.
*967 Thus we arrive at the procedural question we certified for appeal. We review de novo each of the district court's rulings that Holmes procedurally defaulted his constitutional claims, Smith v. Gaetz, 565 F.3d 346, 351 (7th Cir.2009), that he could show no cause for the procedural default, Tolliver v. Sheets, 594 F.3d 900 (6th Cir.2010), and that he is not otherwise excused from the procedural default because he failed to establish that no reasonable juror would convict him in light of the new evidence he presented. Gomez v. Jaimet, 350 F.3d 673, 679 (7th Cir.2003).

A. Procedural Default
A federal court will not review a question of federal law decided by a state court if the decision of the state court clearly and expressly relied on the petitioner's failure to meet a state procedural requirement as an independent basis for its disposition of the case. Harris v. Reed, 489 U.S. 255, 261-62, 109 S.Ct. 1038, 103 L.Ed.2d 308 (1989) (citing Caldwell v. Mississippi, 472 U.S. 320, 327-28, 105 S.Ct. 2633, 86 L.Ed.2d 231 (1985)); Moore v. Bryant, 295 F.3d 771, 774 (7th Cir.2002). Here the state court disposed of Holmes' case by finding that he failed to meet his burden of showing that he could not have raised his claims of prosecutorial misconduct until the fourth petition. Indeed, the court noted that Holmes "states in his brief that he first learned of Fish's notes... before the filing of his third post-conviction petition." Holmes, No. 1-02-3303, at 8.
More fundamentally, any fair reading of the state court's opinion reveals that it clearly, expressly, and only relied on Holmes' procedural failure, without deciding the substantive claims. Holmes disagrees, arguing that the state court reached the merits of his constitutional claims when it considered the "actual innocence" exception to his state procedural misstep, that is, when it judged the weight of Fish's notes and the likelihood Holmes would have succeeded on the merits had the notes been included. But to decide whether a case's outcome would have been different given a different mix of evidence is not to review a case's merits. Cf. Serafinn v. Local 722, Int'l Bhd. of Teamsters, 597 F.3d 908, 917 (7th Cir.2010) (distinguishing between Fed.R.Civ.P. 60(b)(2)'s requirement of showing that the new evidence is likely to change the outcome and Fed.R.Civ.P. 56(c)(2)'s standard for entering summary judgment). In any event, a state court that separately reaches the merits of a substantive claim may also produce an independent procedural ruling that bars federal habeas review. The test to avoid procedural default in federal court is whether the state court's decision rests on the substantive claims primarily, that is, whether there is no procedural ruling that is independent. Moore, 295 F.3d at 774 (citing Coleman v. Thompson, 501 U.S. 722, 735, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991)). Here, the state court's procedural ruling was primary, and a fortiori independent. Thus, the district court decided correctly that Holmes procedurally defaulted his claim in federal court.

B. Cause and Prejudice
One way to avoid procedural default is to show cause for the default. See Coleman, 501 U.S. 722, 111 S.Ct. 2546; Wainwright v. Sykes, 433 U.S. 72, 97 S.Ct. 2497, 53 L.Ed.2d 594 (1977). Holmes tries to show cause by asserting only that he could not have raised the issue of withholding Fish's notes in his third state petition because he did not have them by then. But as we noted, he admitted in state court that he did have them before filing the third petition. And he admits in this court that "it is unclear when Holmes discovered the existence of Ms. Fish's notes." Holmes thus continues to be unable to *968 meet his burden to show cause, just as he was unable to do in state court. Instead, he has shown only ambiguity. That is not enough.

C. Actual Innocence
The other way to avoid procedural default is to show actual innocence, that is, to show that "in light of new evidence, `it is more likely than not that no reasonable juror would have found petitioner guilty beyond a reasonable doubt.'" House v. Bell, 547 U.S. 518, 537, 126 S.Ct. 2064, 165 L.Ed.2d 1 (2006) (quoting Schlup v. Delo, 513 U.S. 298, 327, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995)). The new evidence Holmes presents here is twofold, each of which we will discuss in turn: (1) Fish's notes; and (2) results from recent blood and DNA testing.
As to Fish's notes, they do not preclude a finding of guilt by a reasonable juror. The notes indicated that Holmes' pants had "no stains identifiable as blood" and "several reddish brown stains neg PT"which might mean negative for blood after preliminary testing, but we cannot tell because no one has bothered to explain to us the meaning of "PT." Cf.  (visited May 26, 2010) (listing 172 possibilities). The notes also indicated that Holmes' boots were "pos PT by laces." Finally, the district court found that the notes "merely indicate that [Holmes'] coat was tested," but "do not indicate the result of the preliminary testing." Holmes, 2009 WL 57460, at *7. The notes as they have been provided to us are illegible as to the coat and the parties have provided us with no reason to find a clear error in the court's finding. In sum, Fish's notes indicated at best that preliminary testing results were negative for blood on the pants and positive for blood on the boots, and that the notes were inconclusive with respect to the coat.
Yet Fish testified that she found blood on all three items after conducting a "preliminary chemical test." Petitioner's Br. at 3-4 (quoting Tr. at 141-42). And "preliminary chemical test" might be the same thing as "PT," which would mean that Fish's testimony was inconsistent with her notes. But this possibility that Fish's testimony was inconsistent, even were Holmes to prove it, is not enough to show actual innocence. Rather, it impeaches Fish's testimony as to the pants, not to the coat and boots. A reasonable finder of fact still could have found credible Fish's testimony that she found blood on Holmes' coat and boots, notwithstanding Fish's inconsistent testimony about evidence in a prior case. See People v. Willis, No. 90 CR 23912 (cited in the parties' briefs, but no one gives us a court or a date). Moreover, Fish's testimony was hardly the lynchpin in the state's case, as there was so little blood that she could not test whether it belonged to the victim. The following evidence of guilt also was presented at trial: (1) Holmes' admission that he was with the victim about one hour before she was found in a stairwell; (2) his changing account of when he had last seen the victim; (3) eyewitness testimony placing him in the stairwell arguing with and holding the arm of the crying victim, who carried a fresh bruise on her chin; (4) a different witness who found the victim in the stairwell an hour later, thirty minutes after hearing a thumping sound; (5) semen in Holmes' underwear and in the victim; (6) Holmes' explanation for the semen in his underwear, that he had sex with someone else earlier that night, denied by the someone else; (7) and Holmes' fingerprint on the liquor bottle found next to the victim. This heap of evidence shows that Fish's notes, while troubling, at best show a mere possibility that a jury presented with the notes would have exonerated *969 Holmes, not a probability, as is required. House, 547 U.S. at 537, 126 S.Ct. 2064.
Neither does the new blood and DNA test results Holmes presents exonerate him. Cellmark Diagnostics performed testing ten years after trial on Holmes' coat, pants, and boots, and on a vaginal swab of the victim. It found no blood on the three items of clothing, but this is consistent with Fish's testimony that there were no portions left on the clothing to test after she had sampled the already minuscule amounts. The results also found that Holmes could not be excluded as the source of the DNA obtained from the sperm fraction of the vaginal swab although only 1 in 2900 people with Holmes' racial profile was consistent with that DNA. Finally, the results excluded Holmes "as the source of the DNA obtained from the non-sperm fraction of the vaginal swab." Respondent's Br., App. at 32 (emphasis added). Holmes interprets this to mean that Holmes is excluded as the source of the DNA obtained from the non-sperm fraction of the semen. But he relegated this argument to a footnote in his brief, without any explanation as to why the non-sperm fraction of the vaginal swab constituted semen and not, say, cells from the victim's vagina. When we asked Holmes' attorney at oral argument how we should interpret the report, she responded only with how she interpreted it and gave no reasons for her interpretation. This is insufficient a predicate on which to base any conclusion. We are left with a report from Cellmark Diagnostics about blood and DNA that, if anything, only confirms Holmes' guilt.

III. CONCLUSION
Holmes procedurally defaulted his habeas petition and cannot show cause for doing so. Moreover, the new evidence Holmes presents is too inconclusive and vague to show a reasonable probability that he is actually innocent. Therefore, we affirm.
