{"id":"hamming-xor-popcount","text":"`hammingDistance` computes Hamming distance as popcount of XOR (`bin(x ^ y).count('1')`); any change to either the XOR or the popcount step would break correctness.","truth_value":"IN","source":"entries/2026/06/06/hamming-distance-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"hamming-xor-popcount","truth_value":"IN","reason":"premise"}]}}