{"id":"nim-game-mod4-characterization","text":"The first player wins Nim (1–3 stones per turn) if and only if `n % 4 != 0`; this is a complete characterization derived from the Sprague-Grundy theorem, not heuristic.","truth_value":"IN","source":"entries/2026/06/06/nim-game-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"nim-game-mod4-characterization","truth_value":"IN","reason":"premise"}]}}