A Notebook LLM review of a June 2025 United States Supreme Court syllabus and opinion in the case of Rivers v. Guerrero. This case addresses a crucial point in federal habeas corpus law, specifically defining when a second-in-time habeas petitionis considered "second or successive" under the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA). The Court's unanimous decision establishes that such a petition generally triggers the strict procedural requirements of AEDPA once a district court has issued its final judgment on an initial habeas petition, irrespective of whether an appeal of that first judgment is still pending. This ruling clarifies that the existence of a final judgment is the key determinant for applying these limitations on subsequent filings, promoting judicial efficiency and finality in state-court judgments.