{"id":"bit-position-independence-principle","text":"In XOR-subset problems, each bit position contributes independently to the total sum — if any element has bit b set, exactly half of all 2^n subsets have that bit survive XOR.","truth_value":"IN","source":"entries/2026/06/06/sum-of-all-subset-xor-totals-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"bit-position-independence-principle","truth_value":"IN","reason":"premise"}]}}