{"id":"shift-grid-k-mod-optimization","text":"`k` is reduced modulo `m*n` before any list operations, making runtime independent of `k`'s magnitude — standard for cyclic operations in this repo.","truth_value":"IN","source":"entries/2026/06/06/shift-2d-grid-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["modular-arithmetic-eliminates-simulation"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"shift-grid-k-mod-optimization","truth_value":"IN","reason":"premise"}]}}