How does the statute of limitations apply when a petitioner has filed a timely petition and then amended to replace the original petition with new claims?

Where a petitioner has filed a timely petition and then amends to replace the original claims with new claims, but does so after expiration of the statute of limitations, those new claims are only timely if they "relate back" to the claims in the original timely petition. See Mayle v. Felix, 545 U.S. 644, 654-55 (2005). In order for claims to relate back, they must be "tied to a common core of operative facts." Id. at 664. Simply arising out of the same "trial, conviction, or sentence" is insufficient. Id. A claim "does not relate back (and thereby escape AEDPA's one-year time limit) when it asserts a new ground for relief supported by facts that differ in both time and type from those the original pleading set forth." Id. at 650.