# 軌道－穩定子定理基礎 · 脈衝 R01

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-20261110-r01-orbit-stabilizer-theorem-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。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0}。請依 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(2, 0, [0, 1], 2, [0], 1, 2, 是)

Wave6第四層核對=(2, 0, [0, 1], 2, [0], 1, 2, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0001/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 2. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(3, 1, [0, 1, 2], 3, [0], 1, 3, 是)

Wave6第四層核對=(3, 1, [0, 1, 2], 3, [0], 1, 3, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0002/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 3. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(4, 2, [0, 1, 2, 3], 4, [0], 1, 4, 是)

Wave6第四層核對=(4, 2, [0, 1, 2, 3], 4, [0], 1, 4, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0003/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 4. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(5, 3, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)

Wave6第四層核對=(5, 3, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0004/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 5. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(6, 4, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)

Wave6第四層核對=(6, 4, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0005/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 6. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(2, 2, [2], 1, [0, 1], 2, 2, 是)

Wave6第四層核對=(2, 2, [2], 1, [0, 1], 2, 2, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0006/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 7. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(3, 2, [0, 1, 2], 3, [0], 1, 3, 是)

Wave6第四層核對=(3, 2, [0, 1, 2], 3, [0], 1, 3, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0007/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 8. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(4, 2, [0, 1, 2, 3], 4, [0], 1, 4, 是)

Wave6第四層核對=(4, 2, [0, 1, 2, 3], 4, [0], 1, 4, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0008/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 9. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(5, 2, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)

Wave6第四層核對=(5, 2, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0009/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 10. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(6, 2, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)

Wave6第四層核對=(6, 2, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0010/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 11. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(2, 2, [2], 1, [0, 1], 2, 2, 是)

Wave6第四層核對=(2, 2, [2], 1, [0, 1], 2, 2, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0011/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 12. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(3, 1, [0, 1, 2], 3, [0], 1, 3, 是)

Wave6第四層核對=(3, 1, [0, 1, 2], 3, [0], 1, 3, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0012/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 13. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(4, 0, [0, 1, 2, 3], 4, [0], 1, 4, 是)

Wave6第四層核對=(4, 0, [0, 1, 2, 3], 4, [0], 1, 4, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0013/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 14. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(5, 6, [6], 1, [0, 1, 2, 3, 4], 5, 5, 是)

Wave6第四層核對=(5, 6, [6], 1, [0, 1, 2, 3, 4], 5, 5, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0014/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 15. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(6, 6, [6], 1, [0, 1, 2, 3, 4, 5], 6, 6, 是)

Wave6第四層核對=(6, 6, [6], 1, [0, 1, 2, 3, 4, 5], 6, 6, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0015/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 16. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(2, 0, [0, 1], 2, [0], 1, 2, 是)

Wave6第四層核對=(2, 0, [0, 1], 2, [0], 1, 2, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0016/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 17. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(3, 4, [4], 1, [0, 1, 2], 3, 3, 是)

Wave6第四層核對=(3, 4, [4], 1, [0, 1, 2], 3, 3, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0017/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 18. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(4, 3, [0, 1, 2, 3], 4, [0], 1, 4, 是)

Wave6第四層核對=(4, 3, [0, 1, 2, 3], 4, [0], 1, 4, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0018/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 19. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(5, 2, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)

Wave6第四層核對=(5, 2, [0, 1, 2, 3, 4], 5, [0], 1, 5, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0019/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 20. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(6, 1, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)

Wave6第四層核對=(6, 1, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0020/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 21. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(2, 2, [2], 1, [0, 1], 2, 2, 是)

Wave6第四層核對=(2, 2, [2], 1, [0, 1], 2, 2, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0021/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 22. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(3, 0, [0, 1, 2], 3, [0], 1, 3, 是)

Wave6第四層核對=(3, 0, [0, 1, 2], 3, [0], 1, 3, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0022/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 23. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(4, 6, [6], 1, [0, 1, 2, 3], 4, 4, 是)

Wave6第四層核對=(4, 6, [6], 1, [0, 1, 2, 3], 4, 4, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0023/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 24. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(5, 5, [5], 1, [0, 1, 2, 3, 4], 5, 5, 是)

Wave6第四層核對=(5, 5, [5], 1, [0, 1, 2, 3, 4], 5, 5, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0024/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 25. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-counting-identity；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 [group_order, point, orbit, orbit_size, stabilizer, stabilizer_size, product, equal] 欄序回答。

查看答案與解釋(6, 4, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)

Wave6第四層核對=(6, 4, [0, 1, 2, 3, 4, 5], 6, [0], 1, 6, 是)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0025/)

軌道－穩定子定理 · qf-mod41-orbitstab-counting-identity · candidate





## 26. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0}。請依 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 0], [1, 1]], [[0, [0]], [1, [1]]], 是, [0, 1], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 0], [1, 1]], [[0, [0]], [1, [1]]], 是, [0, 1], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0026/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 27. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 1], [1, 2], [2, 0]], [[0, [2]], [1, [0]], [2, [1]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 1], [1, 2], [2, 0]], [[0, [2]], [1, [0]], [2, [1]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0027/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 28. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 3], [2, 0], [3, 1]], [[0, [2]], [1, [3]], [2, [0]], [3, [1]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 3], [2, 0], [3, 1]], [[0, [2]], [1, [3]], [2, [0]], [3, [1]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0028/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 29. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 3], [1, 4], [2, 0], [3, 1], [4, 2]], [[0, [2]], [1, [3]], [2, [4]], [3, [0]], [4, [1]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 3], [1, 4], [2, 0], [3, 1], [4, 2]], [[0, [2]], [1, [3]], [2, [4]], [3, [0]], [4, [1]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0029/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 30. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 4], [1, 5], [2, 0], [3, 1], [4, 2], [5, 3]], [[0, [2]], [1, [3]], [2, [4]], [3, [5]], [4, [0]], [5, [1]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 4], [1, 5], [2, 0], [3, 1], [4, 2], [5, 3]], [[0, [2]], [1, [3]], [2, [4]], [3, [5]], [4, [0]], [5, [1]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0030/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 31. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0031/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 32. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 0], [2, 1]], [[0, [1]], [1, [2]], [2, [0]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 0], [2, 1]], [[0, [1]], [1, [2]], [2, [0]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0032/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 33. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 3], [2, 0], [3, 1]], [[0, [2]], [1, [3]], [2, [0]], [3, [1]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 3], [2, 0], [3, 1]], [[0, [2]], [1, [3]], [2, [0]], [3, [1]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0033/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 34. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 3], [2, 4], [3, 0], [4, 1]], [[0, [3]], [1, [4]], [2, [0]], [3, [1]], [4, [2]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 3], [2, 4], [3, 0], [4, 1]], [[0, [3]], [1, [4]], [2, [0]], [3, [1]], [4, [2]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0034/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 35. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 3], [2, 4], [3, 5], [4, 0], [5, 1]], [[0, [4]], [1, [5]], [2, [0]], [3, [1]], [4, [2]], [5, [3]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 3], [2, 4], [3, 5], [4, 0], [5, 1]], [[0, [4]], [1, [5]], [2, [0]], [3, [1]], [4, [2]], [5, [3]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0035/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 36. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0036/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 37. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 1], [1, 2], [2, 0]], [[0, [2]], [1, [0]], [2, [1]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 1], [1, 2], [2, 0]], [[0, [2]], [1, [0]], [2, [1]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0037/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 38. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 0], [1, 1], [2, 2], [3, 3]], [[0, [0]], [1, [1]], [2, [2]], [3, [3]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 0], [1, 1], [2, 2], [3, 3]], [[0, [0]], [1, [1]], [2, [2]], [3, [3]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0038/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 39. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 6], [1, 6], [2, 6], [3, 6], [4, 6]], [[6, [0, 1, 2, 3, 4]]], 是, [6], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 6], [1, 6], [2, 6], [3, 6], [4, 6]], [[6, [0, 1, 2, 3, 4]]], 是, [6], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0039/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 40. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6]], [[6, [0, 1, 2, 3, 4, 5]]], 是, [6], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6]], [[6, [0, 1, 2, 3, 4, 5]]], 是, [6], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0040/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 41. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 0], [1, 1]], [[0, [0]], [1, [1]]], 是, [0, 1], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 0], [1, 1]], [[0, [0]], [1, [1]]], 是, [0, 1], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0041/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 42. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 4], [1, 4], [2, 4]], [[4, [0, 1, 2]]], 是, [4], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 4], [1, 4], [2, 4]], [[4, [0, 1, 2]]], 是, [4], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0042/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 43. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 3], [1, 0], [2, 1], [3, 2]], [[0, [1]], [1, [2]], [2, [3]], [3, [0]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 3], [1, 0], [2, 1], [3, 2]], [[0, [1]], [1, [2]], [2, [3]], [3, [0]]], 是, [0, 1, 2, 3], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0043/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 44. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 3], [2, 4], [3, 0], [4, 1]], [[0, [3]], [1, [4]], [2, [0]], [3, [1]], [4, [2]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 3], [2, 4], [3, 0], [4, 1]], [[0, [3]], [1, [4]], [2, [0]], [3, [1]], [4, [2]]], 是, [0, 1, 2, 3, 4], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0044/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 45. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]], [[0, [5]], [1, [0]], [2, [1]], [3, [2]], [4, [3]], [5, [4]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]], [[0, [5]], [1, [0]], [2, [1]], [3, [2]], [4, [3]], [5, [4]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0045/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 46. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 2], [1, 2]], [[2, [0, 1]]], 是, [2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0046/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 47. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 0], [1, 1], [2, 2]], [[0, [0]], [1, [1]], [2, [2]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 0], [1, 1], [2, 2]], [[0, [0]], [1, [1]], [2, [2]]], 是, [0, 1, 2], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0047/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 48. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 6], [1, 6], [2, 6], [3, 6]], [[6, [0, 1, 2, 3]]], 是, [6], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 6], [1, 6], [2, 6], [3, 6]], [[6, [0, 1, 2, 3]]], 是, [6], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0048/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 49. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 5], [1, 5], [2, 5], [3, 5], [4, 5]], [[5, [0, 1, 2, 3, 4]]], 是, [5], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 5], [1, 5], [2, 5], [3, 5], [4, 5]], [[5, [0, 1, 2, 3, 4]]], 是, [5], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0049/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 50. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-action-fibers；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 [action_map, fibers, equal_fiber_sizes, orbit, certificate] 欄序回答。

查看答案與解釋([[0, 4], [1, 5], [2, 0], [3, 1], [4, 2], [5, 3]], [[0, [2]], [1, [3]], [2, [4]], [3, [5]], [4, [0]], [5, [1]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)

Wave6第四層核對=([[0, 4], [1, 5], [2, 0], [3, 1], [4, 2], [5, 3]], [[0, [2]], [1, [3]], [2, [4]], [3, [5]], [4, [0]], [5, [1]]], 是, [0, 1, 2, 3, 4, 5], action_map_surjective_onto_orbit)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0050/)

軌道－穩定子定理 · qf-mod41-orbitstab-action-fibers · candidate





## 51. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0051/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 52. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":0}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(0, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(0, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0052/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 53. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 3, [3], [3], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 3, [3], [3], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0053/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 54. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":2}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(2, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(2, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0054/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 55. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":3}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(3, 5, [5], [5], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(3, 5, [5], [5], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0055/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 56. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2,"orbit_point":2}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0056/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 57. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":0}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(0, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(0, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0057/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 58. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":2}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(2, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(2, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0058/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 59. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0059/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 60. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":0}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(0, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(0, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0060/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 61. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":2}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0061/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 62. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0062/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 63. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0063/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 64. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":6}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(6, 0, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(6, 0, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0064/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 65. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":6}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(6, 0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(6, 0, [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0065/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 66. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":0}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(0, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(0, 0, [0], [0], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0066/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 67. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":4}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(4, 0, [0, 1, 2], [0, 1, 2], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(4, 0, [0, 1, 2], [0, 1, 2], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0067/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 68. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0068/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 69. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 4, [4], [4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0069/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 70. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":3}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(3, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(3, 2, [2], [2], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0070/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 71. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":2}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(2, 0, [0, 1], [0, 1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0071/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 72. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":1}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(1, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0072/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 73. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":6}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(6, 0, [0, 1, 2, 3], [0, 1, 2, 3], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(6, 0, [0, 1, 2, 3], [0, 1, 2, 3], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0073/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 74. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":5}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(5, 0, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(5, 0, [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0074/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 75. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-coset-fiber-bijection；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,"orbit_point":5}。請依 [orbit_point, representative, fiber, left_coset, equal, certificate] 欄序回答。

查看答案與解釋(5, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)

Wave6第四層核對=(5, 1, [1], [1], 是, fiber_equals_left_coset_of_same_point_stabilizer)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0075/)

軌道－穩定子定理 · qf-mod41-orbitstab-coset-fiber-bijection · candidate





## 76. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":2,"action_table":[[0,1],[1,0]],"point":0,"other_point":1,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [0], [0, 1], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [0], [0, 1], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0076/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 77. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":2,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [1, 2], [0, 1, 2], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [1, 2], [0, 1, 2], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0077/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 78. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0,1,2]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2], [0, 2, 3], [0, 1, 2, 3], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2], [0, 2, 3], [0, 1, 2, 3], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0078/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 79. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":4,"sampled_elements":[0,1,2,3]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3], [0, 1, 3, 4], [0, 1, 2, 3, 4], [0], 4, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3], [0, 1, 3, 4], [0, 1, 2, 3, 4], [0], 4, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0079/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 80. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":5,"sampled_elements":[0,1,2,3,4]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3, 4], [0, 1, 2, 4, 5], [0, 1, 2, 3, 4, 5], [0], 5, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3, 4], [0, 1, 2, 4, 5], [0, 1, 2, 3, 4, 5], [0], 5, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0080/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 81. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-boundary；資料={"group_table":[[0,1],[1,0]],"identity":0,"point_count":3,"action_table":[[0,1,2],[1,0,2]],"point":2,"other_point":0,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [2], [2], [0, 1], 0, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [2], [2], [0, 1], 0, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0081/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 82. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [2], [0, 1, 2], [0], 3, [0, 1, 2], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [2], [0, 1, 2], [0], 3, [0, 1, 2], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0082/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 83. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [2, 3], [0, 1, 2, 3], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [2, 3], [0, 1, 2, 3], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0083/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 84. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [2], [0, 1, 2, 3, 4], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [2], [0, 1, 2, 3, 4], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0084/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 85. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0,1,2,3,4]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3, 4], [0, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3, 4], [0, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0085/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 86. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [2], [2], [0, 1], 3, [0, 1], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [2], [2], [0, 1], 3, [0, 1], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0086/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 87. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":2,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [1, 2], [0, 1, 2], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [1, 2], [0, 1, 2], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0087/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 88. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":1,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [0], [0, 1, 2, 3], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [0], [0, 1, 2, 3], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0088/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 89. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":0,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [6], [6], [0, 1, 2, 3, 4], 0, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [6], [6], [0, 1, 2, 3, 4], 0, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0089/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 90. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":7,"sampled_elements":[0,1,2,3,4]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3, 4], [6], [6], [0, 1, 2, 3, 4, 5], 7, [0, 1, 2, 3, 4, 5], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3, 4], [6], [6], [0, 1, 2, 3, 4, 5], 7, [0, 1, 2, 3, 4, 5], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0090/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 91. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":1,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [0], [0, 1], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [0], [0, 1], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0091/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 92. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":5,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [4], [4], [0, 1, 2], 5, [0, 1, 2], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [4], [4], [0, 1, 2], 5, [0, 1, 2], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0092/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 93. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":4,"sampled_elements":[0,1,2]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2], [0, 1, 3], [0, 1, 2, 3], [0], 4, [0, 1, 2, 3], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2], [0, 1, 3], [0, 1, 2, 3], [0], 4, [0, 1, 2, 3], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0093/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 94. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0,1,2]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2], [2, 3, 4], [0, 1, 2, 3, 4], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2], [2, 3, 4], [0, 1, 2, 3, 4], [0], 3, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0094/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 95. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":2,"sampled_elements":[0,1,2,3,4]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3, 4], [1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3, 4], [1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5], [0], 2, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0095/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 96. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":3,"sampled_elements":[0]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0], [2], [2], [0, 1], 3, [0, 1], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0], [2], [2], [0, 1], 3, [0, 1], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0096/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 97. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":1,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [0, 1], [0, 1, 2], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [0, 1], [0, 1, 2], [0], 1, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0097/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 98. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":7,"sampled_elements":[0,1]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1], [6], [6], [0, 1, 2, 3], 7, [0, 1, 2, 3], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1], [6], [6], [0, 1, 2, 3], 7, [0, 1, 2, 3], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0098/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 99. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":6,"sampled_elements":[0,1,2,3]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3], [5], [5], [0, 1, 2, 3, 4], 6, [0, 1, 2, 3, 4], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3], [5], [5], [0, 1, 2, 3, 4], 6, [0, 1, 2, 3, 4], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0099/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate





## 100. 軌道－穩定子定理

同一完整已認證有限群作用與同一指定point。操作=orbitstab-binding-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,"other_point":5,"sampled_elements":[0,1,2,3,4]}。請依 [sampled_elements, sample_image, full_orbit, point_stabilizer, other_point, other_stabilizer, sample_or_mixed_binding_certificate, boundary] 欄序回答。

固定的否是不由proper sample或混用point綁定提供定理證書；不否認sample image可能已等於完整orbit，或兩點的stabilizer碰巧相同。

查看答案與解釋([0, 1, 2, 3, 4], [0, 1, 2, 4, 5], [0, 1, 2, 3, 4, 5], [0], 5, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)

Wave6第四層核對=([0, 1, 2, 3, 4], [0, 1, 2, 4, 5], [0, 1, 2, 3, 4, 5], [0], 5, [0], 否, proper_sample_or_other_point_binding_cannot_certify_orbit_stabilizer_identity)；依完整明示資料獨立重算；action map對orbit滿射且每個fiber須核對為同一point stabilizer的左陪集；不要求free、faithful或transitive；proper sample、不同point或只有數值乘積皆不足。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r01-orbit-stabilizer-theorem-0100/)

軌道－穩定子定理 · qf-mod41-orbitstab-binding-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r01-orbit-stabilizer-theorem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r01-orbit-stabilizer-theorem-foundations/validation-report.json)