Before HIGGINBOTHAM, DENNIS, and ELROD, Circuit Judges. PATRICK E. HIGGINBOTHAM, Circuit Judge: We deny Quintin Jones’s motions for authorization to file a successive federal habeas petition under 28 U.S.C. § 2244 and for a stay of execution. I Jones was convicted of capital murder by a Texas jury in 2001 for killing his aunt. The jury found that Jones was likely to commit future acts of violence that would constitute a continuing threat to society and found insufficient mitigating circumstances to warrant a life sentence. Accordingly, the trial court sentenced Jones to death. His conviction and sentence were affirmed by the Texas Court of Criminal Appeals,[1] and the Supreme Court denied certiorari.[2] In 2014, Jones filed an amended federal habeas petition, raising six claims. The district court denied relief in 2016. Jones then sought a certificate of appealability (“COA”) on two of the denied claims, and this Court granted a COA on one.[3] We affirmed the district court’s denial of relief and denied Jones’s subsequent petition for rehearing.[4] The Supreme Court denied certiorari.[5] In the fall of 2020, Jones’s execution was scheduled for May 19, 2021. In May 2021, Jones filed a new state application for habeas relief arguing that he is intellectually disabled per Moore v. Texas, 137 S. Ct. 1039 (2017), and that the State introduced false and misleading testimony relying on the Hare Psychopathy Checklist (PCL-R). The Texas Court of Criminal Appeals dismissed his application as an abuse of the writ on May 12, finding that Jones failed to make a prima facie showing on any of his allegations. Jones now moves for a stay of execution and authorization to file a successive federal habeas petition based on claims of intellectual disability and false and misleading testimony.[6] II We review a motion to authorize the filing of a successive habeas application to determine if it makes a prima facie showing of satisfying the requirements of § 2244(b)(3)(C).[7] A prima facie showing is “simply a sufficient showing of possible merit to warrant a fuller exploration by the district court.”[8] A person in custody under a state-court judgment who moves to file a successive application for a writ of habeas corpus in federal court must demonstrate that the claim or claims presented in a second or successive habeas application were not presented in a prior application.[9] Claims not presented in a prior application shall still be dismissed unless: (A) the applicant shows that the claim relies on a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable; or (B)(i) the factual predicate for the claim could not have been discovered previously through the exercise of due diligence; and (ii) the facts underlying the claim, if proven and viewed in light of the evidence as a whole, would be sufficient to establish by clear and convincing evidence that, but for constitutional error, no reasonable factfinder would have found the applicant guilty of the underlying offense.[10] The applicant must also demonstrate the timeliness of a successive petition.[11] Section 2244(d)(1) provides a one-year period of limitations, which runs from the latest of: the date on which the judgment became final by the conclusion of direct review or the expiration of the time for seeking such review; the date on which the impediment to filing an application created by State action in violation of the Constitution or laws of the United States is removed, if the applicant was prevented from filing by such State action; the date on which the constitutional right asserted was initially recognized by the Supreme Court, if the right has been newly recognized by the Supreme Court and made retroactively applicable to cases on collateral review; or the date on which the factual predicate of the claim or claims presented could have been discovered through the exercise of due diligence.[12] III Even if Jones establishes a prima facie showing under § 2244(b)(2), he fails to demonstrate that either claim is within the one-year period of limitations provided in § 2244(d). While the one-year time limitation may be equitably tolled, Jones makes no argument that equitable tolling is warranted here.[13] Jones’s claim of intellectual disability is based on Moore v. Texas, which he contends establishes a new rule of constitutional law made retroactive to cases on collateral review. Alternatively, he argues that his claim is based on Atkins v. Virginia, 536 U.S. 304 (2002), but only became available to Jones following Moore. “But even if we count Moore as the starting date” for Jones’s intellectual disability claim, “the statutory time limit for asserting this claim is one year following Moore,” which was decided in 2017.[14] And even if we consider the Supreme Court’s second decision in Moore in 2019 as the starting date, Jones’s 2021 petition is still time-barred.[15] Jones points to no factual predicate discovered in the last year that could not have been discovered earlier through the exercise of due diligence to support his intellectual disability claim.[16] Thus, this claim is untimely. Jones’s second ground for relief is that the State introduced false and misleading testimony from Dr. Price, who relied on the PCL-R to testify that Jones was a psychopath. Jones introduces an April 2021 affidavit from Dr. John Edens explaining flaws with the PCL-R, but Dr. Edens’s affidavit itself relies on scientific studies casting doubts on the PCL-R’s reliability from the last decade. The most recent study criticizing the PCL-R that Jones includes is from January 2020, also outside the one-year period. Because the necessary factual predicate for Jones’s false and misleading testimony claim could have been discovered through due diligence more than a year ago, this claim is also untimely. Jones moves for a stay of execution on the basis that his motion to file a successive habeas petition is meritorious. “Because [Jones] has failed to set up a basis for filing a successive habeas petition, we have no authority to grant a stay of execution.”[17] We deny both Jones’s motion for authorization to file a successive habeas petition and his motion for a stay of execution.