{"id":"subset-xor-closed-form","text":"The sum of XOR totals over all subsets equals `reduce(or_, nums) * 2^(len(nums)-1)`, reducing subset XOR summation from O(n·2^n) enumeration to O(n) time and O(1) space.","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":"subset-xor-closed-form","truth_value":"IN","reason":"premise"}]}}