Typically, a petition for review must be received by the clerk's office of the federal appeals court within 30 days of the agency's final decision. However, a detainee or inmate need only show that mailed his petition by the 30th day, in accordance with the detention facility's procedures for mailing legal documents. In the instant case, the Ninth Circuit granted a motion to file new evidence (an extremely unusual procedure at a federal appeals court) to allow a detainee to prove that he had complied with this rule, and thus, that the Court had jurisdiction to review his appeal even though the petition for review was received by the clerk's office five days after the 30 day deadline. The court noted that when a detainee's declaration of compliance with the mailbox rule is presented after his petition for review, the court has the discretion to refuse to consider the declaration.
The full text of Barrientos v. Lynch can be found here:
http://cdn.ca9.uscourts.gov/datastore/opinions/2016/07/19/14-73178.pdf