{"id":"kth-missing-monotonic-invariant","text":"The binary search is valid because `arr[i] - (i + 1)` (count of missing positives before index i) is monotonically non-decreasing for a strictly increasing array of positive integers.","truth_value":"IN","source":"entries/2026/06/06/kth-missing-positive-number-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"kth-missing-monotonic-invariant","truth_value":"IN","reason":"premise"}]}}