{"id":"counting-vs-simulation-for-origin-return","text":"`judgeCircle` determines origin return by counting opposing moves (`L==R` and `U==D`) rather than simulating coordinates, exploiting the mathematical insight that horizontal and vertical axes are independent.","truth_value":"IN","source":"entries/2026/06/06/robot-return-to-origin-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"counting-vs-simulation-for-origin-return","truth_value":"IN","reason":"premise"}]}}