本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261108-r01-finite-group-orbit-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0}。請依 [point, orbit, group_order, certificate] 欄序回答。
(0, [0, 1], 2, all_group_elements_enumerated)
Wave6第二層核對=(0, [0, 1], 2, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]],"point":1}。請依 [point, orbit, group_order, certificate] 欄序回答。
(1, [0, 1, 2], 3, all_group_elements_enumerated)
Wave6第二層核對=(1, [0, 1, 2], 3, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2, 3], 4, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2, 3], 4, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"point":3}。請依 [point, orbit, group_order, certificate] 欄序回答。
(3, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)
Wave6第二層核對=(3, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"point":4}。請依 [point, orbit, group_order, certificate] 欄序回答。
(4, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)
Wave6第二層核對=(4, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [2], 2, all_group_elements_enumerated)
Wave6第二層核對=(2, [2], 2, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2], 3, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2], 3, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2, 3], 4, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2, 3], 4, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [2], 2, all_group_elements_enumerated)
Wave6第二層核對=(2, [2], 2, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]],"point":1}。請依 [point, orbit, group_order, certificate] 欄序回答。
(1, [0, 1, 2], 3, all_group_elements_enumerated)
Wave6第二層核對=(1, [0, 1, 2], 3, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]],"point":0}。請依 [point, orbit, group_order, certificate] 欄序回答。
(0, [0, 1, 2, 3], 4, all_group_elements_enumerated)
Wave6第二層核對=(0, [0, 1, 2, 3], 4, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]],"point":6}。請依 [point, orbit, group_order, certificate] 欄序回答。
(6, [6], 5, all_group_elements_enumerated)
Wave6第二層核對=(6, [6], 5, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]],"point":6}。請依 [point, orbit, group_order, certificate] 欄序回答。
(6, [6], 6, all_group_elements_enumerated)
Wave6第二層核對=(6, [6], 6, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]],"point":0}。請依 [point, orbit, group_order, certificate] 欄序回答。
(0, [0, 1], 2, all_group_elements_enumerated)
Wave6第二層核對=(0, [0, 1], 2, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]],"point":4}。請依 [point, orbit, group_order, certificate] 欄序回答。
(4, [4], 3, all_group_elements_enumerated)
Wave6第二層核對=(4, [4], 3, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]],"point":3}。請依 [point, orbit, group_order, certificate] 欄序回答。
(3, [0, 1, 2, 3], 4, all_group_elements_enumerated)
Wave6第二層核對=(3, [0, 1, 2, 3], 4, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)
Wave6第二層核對=(2, [0, 1, 2, 3, 4], 5, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]],"point":1}。請依 [point, orbit, group_order, certificate] 欄序回答。
(1, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)
Wave6第二層核對=(1, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]],"point":2}。請依 [point, orbit, group_order, certificate] 欄序回答。
(2, [2], 2, all_group_elements_enumerated)
Wave6第二層核對=(2, [2], 2, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]],"point":0}。請依 [point, orbit, group_order, certificate] 欄序回答。
(0, [0, 1, 2], 3, all_group_elements_enumerated)
Wave6第二層核對=(0, [0, 1, 2], 3, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]],"point":6}。請依 [point, orbit, group_order, certificate] 欄序回答。
(6, [6], 4, all_group_elements_enumerated)
Wave6第二層核對=(6, [6], 4, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]],"point":5}。請依 [point, orbit, group_order, certificate] 欄序回答。
(5, [5], 5, all_group_elements_enumerated)
Wave6第二層核對=(5, [5], 5, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-of-point；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]],"point":4}。請依 [point, orbit, group_order, certificate] 欄序回答。
(4, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)
Wave6第二層核對=(4, [0, 1, 2, 3, 4, 5], 6, all_group_elements_enumerated)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-of-point · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1]], [0, 1], 是, 是)
Wave6第二層核對=([[0, 1]], [0, 1], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2]], [0, 1, 2], 是, 是)
Wave6第二層核對=([[0, 1, 2]], [0, 1, 2], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3]], [0, 1, 2, 3], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3]], [0, 1, 2, 3], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4]], [0, 1, 2, 3, 4], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4]], [0, 1, 2, 3, 4], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4, 5]], [0, 1, 2, 3, 4, 5], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4, 5]], [0, 1, 2, 3, 4, 5], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1], [2]], [0, 1, 2], 是, 是)
Wave6第二層核對=([[0, 1], [2]], [0, 1, 2], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2], [3]], [0, 1, 2, 3], 是, 是)
Wave6第二層核對=([[0, 1, 2], [3]], [0, 1, 2, 3], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3], [4]], [0, 1, 2, 3, 4], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3], [4]], [0, 1, 2, 3, 4], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4, 5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4, 5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1], [2], [3]], [0, 1, 2, 3], 是, 是)
Wave6第二層核對=([[0, 1], [2], [3]], [0, 1, 2, 3], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2], [3], [4]], [0, 1, 2, 3, 4], 是, 是)
Wave6第二層核對=([[0, 1, 2], [3], [4]], [0, 1, 2, 3, 4], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4, 5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4, 5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1], [2], [3], [4]], [0, 1, 2, 3, 4], 是, 是)
Wave6第二層核對=([[0, 1], [2], [3], [4]], [0, 1, 2, 3, 4], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2], [3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)
Wave6第二層核對=([[0, 1, 2], [3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3], [4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3], [4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4], [5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4], [5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4, 5], [6], [7], [8]], [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4, 5], [6], [7], [8]], [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1], [2], [3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)
Wave6第二層核對=([[0, 1], [2], [3], [4], [5]], [0, 1, 2, 3, 4, 5], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2], [3], [4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)
Wave6第二層核對=([[0, 1, 2], [3], [4], [5], [6]], [0, 1, 2, 3, 4, 5, 6], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3], [4], [5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3], [4], [5], [6], [7]], [0, 1, 2, 3, 4, 5, 6, 7], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4], [5], [6], [7], [8]], [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4], [5], [6], [7], [8]], [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-orbit-partition；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]]}。請依 [orbits, covered_points, pairwise_disjoint, partition_certificate] 欄序回答。
([[0, 1, 2, 3, 4, 5], [6], [7], [8], [9]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, 是)
Wave6第二層核對=([[0, 1, 2, 3, 4, 5], [6], [7], [8], [9]], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-orbit-partition · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"x":0,"y":1}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(0, 1, [1], 是, [0, 1], [0, 1], 是)
Wave6第二層核對=(0, 1, [1], 是, [0, 1], [0, 1], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]],"x":1,"y":2}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(1, 2, [1], 是, [0, 1, 2], [0, 1, 2], 是)
Wave6第二層核對=(1, 2, [1], 是, [0, 1, 2], [0, 1, 2], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)
Wave6第二層核對=(2, 3, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"x":3,"y":4}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(3, 4, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)
Wave6第二層核對=(3, 4, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"x":4,"y":5}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(4, 5, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)
Wave6第二層核對=(4, 5, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"x":2,"y":0}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 0, [], 否, [2], [0, 1], 是)
Wave6第二層核對=(2, 0, [], 否, [2], [0, 1], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [], 否, [0, 1, 2], [3], 是)
Wave6第二層核對=(2, 3, [], 否, [0, 1, 2], [3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)
Wave6第二層核對=(2, 3, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)
Wave6第二層核對=(2, 3, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)
Wave6第二層核對=(2, 3, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [], 否, [2], [3], 是)
Wave6第二層核對=(2, 3, [], 否, [2], [3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]],"x":1,"y":2}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(1, 2, [1], 是, [0, 1, 2], [0, 1, 2], 是)
Wave6第二層核對=(1, 2, [1], 是, [0, 1, 2], [0, 1, 2], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]],"x":0,"y":1}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(0, 1, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)
Wave6第二層核對=(0, 1, [1], 是, [0, 1, 2, 3], [0, 1, 2, 3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]],"x":6,"y":0}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(6, 0, [], 否, [6], [0, 1, 2, 3, 4], 是)
Wave6第二層核對=(6, 0, [], 否, [6], [0, 1, 2, 3, 4], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]],"x":6,"y":7}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(6, 7, [], 否, [6], [7], 是)
Wave6第二層核對=(6, 7, [], 否, [6], [7], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]],"x":0,"y":1}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(0, 1, [1], 是, [0, 1], [0, 1], 是)
Wave6第二層核對=(0, 1, [1], 是, [0, 1], [0, 1], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]],"x":4,"y":5}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(4, 5, [], 否, [4], [5], 是)
Wave6第二層核對=(4, 5, [], 否, [4], [5], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]],"x":3,"y":4}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(3, 4, [], 否, [0, 1, 2, 3], [4], 是)
Wave6第二層核對=(3, 4, [], 否, [0, 1, 2, 3], [4], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)
Wave6第二層核對=(2, 3, [1], 是, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]],"x":1,"y":2}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(1, 2, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)
Wave6第二層核對=(1, 2, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]],"x":2,"y":3}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(2, 3, [], 否, [2], [3], 是)
Wave6第二層核對=(2, 3, [], 否, [2], [3], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]],"x":0,"y":1}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(0, 1, [1], 是, [0, 1, 2], [0, 1, 2], 是)
Wave6第二層核對=(0, 1, [1], 是, [0, 1, 2], [0, 1, 2], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]],"x":6,"y":7}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(6, 7, [], 否, [6], [7], 是)
Wave6第二層核對=(6, 7, [], 否, [6], [7], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]],"x":5,"y":6}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(5, 6, [], 否, [5], [6], 是)
Wave6第二層核對=(5, 6, [], 否, [5], [6], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-equivalence-audit；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]],"x":4,"y":5}。請依 [x, y, sending_elements, same_orbit_relation, orbit_x, orbit_y, relation_iff_orbit_equality] 欄序回答。
(4, 5, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)
Wave6第二層核對=(4, 5, [1], 是, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-equivalence-audit · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 0, 0, [0, 1], 2, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 0, 0, [0, 1], 2, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,2,0],[2,0,1]],"point":1,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 1, 2, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 1, 2, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"point":2,"group_element":2}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(2, 2, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(2, 2, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"point":3,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 3, 1, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 3, 1, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"point":4,"group_element":4}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(4, 4, 2, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(4, 4, 2, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,2,0,3],[2,0,1,3]],"point":2,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 2, 2, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 2, 2, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,3,0,4],[2,3,0,1,4],[3,0,1,2,4]],"point":2,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 2, 1, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 2, 1, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,4,0,5],[2,3,4,0,1,5],[3,4,0,1,2,5],[4,0,1,2,3,5]],"point":2,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 2, 0, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 2, 0, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,5,0,6],[2,3,4,5,0,1,6],[3,4,5,0,1,2,6],[4,5,0,1,2,3,6],[5,0,1,2,3,4,6]],"point":2,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 2, 5, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 2, 5, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":4,"action_table":[[0,1,2,3],[1,0,2,3]],"point":2,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,2,0,3,4],[2,0,1,3,4]],"point":1,"group_element":2}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(2, 1, 0, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(2, 1, 0, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,3,0,4,5],[2,3,0,1,4,5],[3,0,1,2,4,5]],"point":0,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 0, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 0, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,4,0,5,6],[2,3,4,0,1,5,6],[3,4,0,1,2,5,6],[4,0,1,2,3,5,6]],"point":6,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,0,6,7],[2,3,4,5,0,1,6,7],[3,4,5,0,1,2,6,7],[4,5,0,1,2,3,6,7],[5,0,1,2,3,4,6,7]],"point":6,"group_element":2}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(2, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(2, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":5,"action_table":[[0,1,2,3,4],[1,0,2,3,4]],"point":0,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 0, 1, [0, 1], 2, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 0, 1, [0, 1], 2, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,2,0,3,4,5],[2,0,1,3,4,5]],"point":4,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 4, 4, [4], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 4, 4, [4], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,3,0,4,5,6],[2,3,0,1,4,5,6],[3,0,1,2,4,5,6]],"point":3,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 3, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 3, 0, [0, 1, 2, 3], 4, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,0,5,6,7],[2,3,4,0,1,5,6,7],[3,4,0,1,2,5,6,7],[4,0,1,2,3,5,6,7]],"point":2,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 2, 0, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 2, 0, [0, 1, 2, 3, 4], 5, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,5,0,6,7,8],[2,3,4,5,0,1,6,7,8],[3,4,5,0,1,2,6,7,8],[4,5,0,1,2,3,6,7,8],[5,0,1,2,3,4,6,7,8]],"point":1,"group_element":1}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(1, 1, 2, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(1, 1, 2, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":6,"action_table":[[0,1,2,3,4,5],[1,0,2,3,4,5]],"point":2,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 2, 2, [2], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2],[1,2,0],[2,0,1]],"identity":0,"point_count":7,"action_table":[[0,1,2,3,4,5,6],[1,2,0,3,4,5,6],[2,0,1,3,4,5,6]],"point":0,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 0, 0, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 0, 0, [0, 1, 2], 3, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3],[1,2,3,0],[2,3,0,1],[3,0,1,2]],"identity":0,"point_count":8,"action_table":[[0,1,2,3,4,5,6,7],[1,2,3,0,4,5,6,7],[2,3,0,1,4,5,6,7],[3,0,1,2,4,5,6,7]],"point":6,"group_element":2}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(2, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(2, 6, 6, [6], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"identity":0,"point_count":9,"action_table":[[0,1,2,3,4,5,6,7,8],[1,2,3,4,0,5,6,7,8],[2,3,4,0,1,5,6,7,8],[3,4,0,1,2,5,6,7,8],[4,0,1,2,3,5,6,7,8]],"point":5,"group_element":3}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(3, 5, 5, [5], 1, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(3, 5, 5, [5], 1, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate
完整已認證有限群作用與全部群元素。操作=orbit-single-step-boundary；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"point_count":10,"action_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,0,6,7,8,9],[2,3,4,5,0,1,6,7,8,9],[3,4,5,0,1,2,6,7,8,9],[4,5,0,1,2,3,6,7,8,9],[5,0,1,2,3,4,6,7,8,9]],"point":4,"group_element":0}。請依 [group_element, point, image, orbit, orbit_size, single_image_alone_claim, boundary] 欄序回答。
最後的否是不由單次作用像提供整個orbit的證書；不否認全表算出的orbit可能只有一點。
(0, 4, 4, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)
Wave6第二層核對=(0, 4, 4, [0, 1, 2, 3, 4, 5], 6, 否, single_action_image_not_the_whole_orbit)；依完整明示資料獨立重算；orbit為全部g作用像且x約y iff存在g送x到y；單一步不是orbit；orbits相等或不交並分割carrier；不混同stabilizer、時間軌道或單generator reachability。
有限群作用的軌道 · qf-mod39-orbit-single-step-boundary · candidate