Does the Due Process Clause require a more rigorous standard of review for judicial fact-finding beyond Georgia's 'any evidence' standard?

QUESTIONS PRESENTED CAPITAL CASE After receiving the trial court’s instructions not to discuss the case with anyone, one of the jurors who sentenced Mr. Esposito to death sought advice from her pastor about how to reconcile her Christian faith with her civic duty to serve on a capital trial. Her pastor’s guidance and the Bible verses he recommended allayed her concerns about imposing the death penalty and gave her peace of mind about serving on the jury. Mr. Esposito presented this misconduct in state habeas proceedings, with compelling proof of the juror’s misconduct. Nonetheless, the habeas court denied relief in an opinion at odds with the overwhelming weight of the evidence. The Georgia Supreme Court, in turn, denied review, even though it had recently granted certiorari in another case to determine whether its application of the “any evidence” standard for reviewing judicial fact-finding should be replaced by a more rigorous standard of review—a critical issue in this case. These facts give rise to the following questions: 1. Given the risk that meritorious federal constitutional claims will be denied due to an appellate court’s excessively deferential review of judicial factfinding, does the Due Process Clause require application of the federal clearly erroneous standard, i.e., whether, “although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed,” United States v. United States Gypsum Co., 333 U.S. 364, 395 (1948), or some another standard more probing that Georgia’s “any evidence” standard of review? 2. Whether the state court misapplied federal constitutional law and wrongly concluded that the juror had not engaged in prejudicial misconduct because she did not discuss the specifics of the case and her pastor did not recommend the sentence she should impose but merely sanctioned a decision to impose the death penalty as consistent with her Christian faith. il