{"id":"quarter-gap-proves-frequency-in-sorted-array","text":"In a sorted array, `arr[i] == arr[i + len(arr)//4]` proves that element appears at least `len(arr)//4 + 1` times, because all values between those indices must be identical.","truth_value":"IN","source":"entries/2026/06/06/element-appearing-more-than-25-in-sorted-array-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"quarter-gap-proves-frequency-in-sorted-array","truth_value":"IN","reason":"premise"}]}}