{"id":"digit-sum-terminates","text":"Each iteration of the `while len(s) > k` loop produces a strictly shorter string (summing `d` digits yields at most `ceil(log10(9d+1))` characters, which is less than `d` for `d >= 2`), guaranteeing termination for valid inputs.","truth_value":"IN","source":"entries/2026/06/06/calculate-digit-sum-of-a-string-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"digit-sum-terminates","truth_value":"IN","reason":"premise"}]}}