{"id":"negation-trick-requires-integers","text":"The tiebreaker `-x` only produces correct descending order for numeric types; applying this pattern to strings or other non-numeric types would fail.","truth_value":"IN","source":"entries/2026/06/06/sort-array-by-increasing-frequency-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"negation-trick-requires-integers","truth_value":"IN","reason":"premise"}]}}