最佳化密度：有限local/global與證書邊界基礎 · 脈衝 R07
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-20261015-advance-20261119-r07-optimization-problem-foundations · 2026-10-15 · 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
1. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[1,2,3,4]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 1], [B, 2], [C, 3], [D, 4]], [[A, B], [A, C], [B, D], [C, D]], A, 1, [[B, 2], [C, 3]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 1], [B, 2], [C, 3], [D, 4]], [[A, B], [A, C], [B, D], [C, D]], A, 1, [[B, 2], [C, 3]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
2. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[2,4,6,8]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 2], [B, 4], [C, 6], [D, 8]], [[A, B], [A, C], [B, D], [C, D]], A, 2, [[B, 4], [C, 6]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 2], [B, 4], [C, 6], [D, 8]], [[A, B], [A, C], [B, D], [C, D]], A, 2, [[B, 4], [C, 6]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
3. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[3,6,9,12]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 3], [B, 6], [C, 9], [D, 12]], [[A, B], [A, C], [B, D], [C, D]], A, 3, [[B, 6], [C, 9]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 3], [B, 6], [C, 9], [D, 12]], [[A, B], [A, C], [B, D], [C, D]], A, 3, [[B, 6], [C, 9]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
4. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[4,8,12,16]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 4], [B, 8], [C, 12], [D, 16]], [[A, B], [A, C], [B, D], [C, D]], A, 4, [[B, 8], [C, 12]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 4], [B, 8], [C, 12], [D, 16]], [[A, B], [A, C], [B, D], [C, D]], A, 4, [[B, 8], [C, 12]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
5. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[5,10,15,20]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 5], [B, 10], [C, 15], [D, 20]], [[A, B], [A, C], [B, D], [C, D]], A, 5, [[B, 10], [C, 15]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 5], [B, 10], [C, 15], [D, 20]], [[A, B], [A, C], [B, D], [C, D]], A, 5, [[B, 10], [C, 15]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
6. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[6,12,18,24]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 6], [B, 12], [C, 18], [D, 24]], [[A, B], [A, C], [B, D], [C, D]], A, 6, [[B, 12], [C, 18]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 6], [B, 12], [C, 18], [D, 24]], [[A, B], [A, C], [B, D], [C, D]], A, 6, [[B, 12], [C, 18]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
7. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[7,14,21,28]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 7], [B, 14], [C, 21], [D, 28]], [[A, B], [A, C], [B, D], [C, D]], A, 7, [[B, 14], [C, 21]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 7], [B, 14], [C, 21], [D, 28]], [[A, B], [A, C], [B, D], [C, D]], A, 7, [[B, 14], [C, 21]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
8. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[8,16,24,32]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 8], [B, 16], [C, 24], [D, 32]], [[A, B], [A, C], [B, D], [C, D]], A, 8, [[B, 16], [C, 24]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 8], [B, 16], [C, 24], [D, 32]], [[A, B], [A, C], [B, D], [C, D]], A, 8, [[B, 16], [C, 24]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
9. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[9,18,27,36]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 9], [B, 18], [C, 27], [D, 36]], [[A, B], [A, C], [B, D], [C, D]], A, 9, [[B, 18], [C, 27]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 9], [B, 18], [C, 27], [D, 36]], [[A, B], [A, C], [B, D], [C, D]], A, 9, [[B, 18], [C, 27]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
10. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[10,20,30,40]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 10], [B, 20], [C, 30], [D, 40]], [[A, B], [A, C], [B, D], [C, D]], A, 10, [[B, 20], [C, 30]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 10], [B, 20], [C, 30], [D, 40]], [[A, B], [A, C], [B, D], [C, D]], A, 10, [[B, 20], [C, 30]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
11. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[11,22,33,44]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 11], [B, 22], [C, 33], [D, 44]], [[A, B], [A, C], [B, D], [C, D]], A, 11, [[B, 22], [C, 33]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 11], [B, 22], [C, 33], [D, 44]], [[A, B], [A, C], [B, D], [C, D]], A, 11, [[B, 22], [C, 33]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
12. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[12,24,36,48]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 12], [B, 24], [C, 36], [D, 48]], [[A, B], [A, C], [B, D], [C, D]], A, 12, [[B, 24], [C, 36]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 12], [B, 24], [C, 36], [D, 48]], [[A, B], [A, C], [B, D], [C, D]], A, 12, [[B, 24], [C, 36]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
13. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[13,26,39,52]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 13], [B, 26], [C, 39], [D, 52]], [[A, B], [A, C], [B, D], [C, D]], A, 13, [[B, 26], [C, 39]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 13], [B, 26], [C, 39], [D, 52]], [[A, B], [A, C], [B, D], [C, D]], A, 13, [[B, 26], [C, 39]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
14. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[14,28,42,56]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 14], [B, 28], [C, 42], [D, 56]], [[A, B], [A, C], [B, D], [C, D]], A, 14, [[B, 28], [C, 42]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 14], [B, 28], [C, 42], [D, 56]], [[A, B], [A, C], [B, D], [C, D]], A, 14, [[B, 28], [C, 42]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
15. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[15,30,45,60]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 15], [B, 30], [C, 45], [D, 60]], [[A, B], [A, C], [B, D], [C, D]], A, 15, [[B, 30], [C, 45]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 15], [B, 30], [C, 45], [D, 60]], [[A, B], [A, C], [B, D], [C, D]], A, 15, [[B, 30], [C, 45]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
16. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[16,32,48,64]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 16], [B, 32], [C, 48], [D, 64]], [[A, B], [A, C], [B, D], [C, D]], A, 16, [[B, 32], [C, 48]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 16], [B, 32], [C, 48], [D, 64]], [[A, B], [A, C], [B, D], [C, D]], A, 16, [[B, 32], [C, 48]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
17. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[17,34,51,68]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 17], [B, 34], [C, 51], [D, 68]], [[A, B], [A, C], [B, D], [C, D]], A, 17, [[B, 34], [C, 51]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 17], [B, 34], [C, 51], [D, 68]], [[A, B], [A, C], [B, D], [C, D]], A, 17, [[B, 34], [C, 51]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
18. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[18,36,54,72]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 18], [B, 36], [C, 54], [D, 72]], [[A, B], [A, C], [B, D], [C, D]], A, 18, [[B, 36], [C, 54]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 18], [B, 36], [C, 54], [D, 72]], [[A, B], [A, C], [B, D], [C, D]], A, 18, [[B, 36], [C, 54]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
19. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[19,38,57,76]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 19], [B, 38], [C, 57], [D, 76]], [[A, B], [A, C], [B, D], [C, D]], A, 19, [[B, 38], [C, 57]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 19], [B, 38], [C, 57], [D, 76]], [[A, B], [A, C], [B, D], [C, D]], A, 19, [[B, 38], [C, 57]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
20. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[20,40,60,80]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 20], [B, 40], [C, 60], [D, 80]], [[A, B], [A, C], [B, D], [C, D]], A, 20, [[B, 40], [C, 60]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 20], [B, 40], [C, 60], [D, 80]], [[A, B], [A, C], [B, D], [C, D]], A, 20, [[B, 40], [C, 60]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
21. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[21,42,63,84]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 21], [B, 42], [C, 63], [D, 84]], [[A, B], [A, C], [B, D], [C, D]], A, 21, [[B, 42], [C, 63]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 21], [B, 42], [C, 63], [D, 84]], [[A, B], [A, C], [B, D], [C, D]], A, 21, [[B, 42], [C, 63]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
22. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[22,44,66,88]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 22], [B, 44], [C, 66], [D, 88]], [[A, B], [A, C], [B, D], [C, D]], A, 22, [[B, 44], [C, 66]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 22], [B, 44], [C, 66], [D, 88]], [[A, B], [A, C], [B, D], [C, D]], A, 22, [[B, 44], [C, 66]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
23. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[23,46,69,92]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 23], [B, 46], [C, 69], [D, 92]], [[A, B], [A, C], [B, D], [C, D]], A, 23, [[B, 46], [C, 69]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 23], [B, 46], [C, 69], [D, 92]], [[A, B], [A, C], [B, D], [C, D]], A, 23, [[B, 46], [C, 69]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
24. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[24,48,72,96]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 24], [B, 48], [C, 72], [D, 96]], [[A, B], [A, C], [B, D], [C, D]], A, 24, [[B, 48], [C, 72]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 24], [B, 48], [C, 72], [D, 96]], [[A, B], [A, C], [B, D], [C, D]], A, 24, [[B, 48], [C, 72]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
25. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-local-global；明示資料={"candidate":"A","edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"points":["A","B","C","D"],"values":[25,50,75,100]}；請依 [complete_objective_table, undirected_neighborhood_edges, candidate, candidate_value, complete_neighbor_values, neighborhood_local_minimum, global_minimum, all_global_minimizers, comparison_scope] 回答。
local以完整明示graph neighborhood為準，不偷換為未指定連續拓撲的local minimum。global比較完整finite feasible table。
查看答案與解釋
([[A, 25], [B, 50], [C, 75], [D, 100]], [[A, B], [A, C], [B, D], [C, D]], A, 25, [[B, 50], [C, 75]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)
Wave6第十三層核對=([[A, 25], [B, 50], [C, 75], [D, 100]], [[A, B], [A, C], [B, D], [C, D]], A, 25, [[B, 50], [C, 75]], 是, 是, [A], local_uses_complete_declared_neighborhood_global_uses_complete_feasible_domain)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-local-global · candidate
26. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[3,1,4,5]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 3], [B, 1], [C, 4], [D, 5]], A, 3, B, 1, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 3], [B, 1], [C, 4], [D, 5]], A, 3, B, 1, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
27. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[6,2,8,10]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 6], [B, 2], [C, 8], [D, 10]], A, 6, B, 2, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 6], [B, 2], [C, 8], [D, 10]], A, 6, B, 2, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
28. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[9,3,12,15]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 9], [B, 3], [C, 12], [D, 15]], A, 9, B, 3, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 9], [B, 3], [C, 12], [D, 15]], A, 9, B, 3, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
29. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[12,4,16,20]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 12], [B, 4], [C, 16], [D, 20]], A, 12, B, 4, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 12], [B, 4], [C, 16], [D, 20]], A, 12, B, 4, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
30. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[15,5,20,25]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 15], [B, 5], [C, 20], [D, 25]], A, 15, B, 5, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 15], [B, 5], [C, 20], [D, 25]], A, 15, B, 5, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
31. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[18,6,24,30]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 18], [B, 6], [C, 24], [D, 30]], A, 18, B, 6, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 18], [B, 6], [C, 24], [D, 30]], A, 18, B, 6, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
32. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[21,7,28,35]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 21], [B, 7], [C, 28], [D, 35]], A, 21, B, 7, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 21], [B, 7], [C, 28], [D, 35]], A, 21, B, 7, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
33. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[24,8,32,40]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 24], [B, 8], [C, 32], [D, 40]], A, 24, B, 8, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 24], [B, 8], [C, 32], [D, 40]], A, 24, B, 8, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
34. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[27,9,36,45]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 27], [B, 9], [C, 36], [D, 45]], A, 27, B, 9, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 27], [B, 9], [C, 36], [D, 45]], A, 27, B, 9, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
35. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[30,10,40,50]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
36. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[33,11,44,55]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 33], [B, 11], [C, 44], [D, 55]], A, 33, B, 11, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 33], [B, 11], [C, 44], [D, 55]], A, 33, B, 11, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
37. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[36,12,48,60]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 36], [B, 12], [C, 48], [D, 60]], A, 36, B, 12, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 36], [B, 12], [C, 48], [D, 60]], A, 36, B, 12, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
38. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[39,13,52,65]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 39], [B, 13], [C, 52], [D, 65]], A, 39, B, 13, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 39], [B, 13], [C, 52], [D, 65]], A, 39, B, 13, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
39. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[42,14,56,70]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
40. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[45,15,60,75]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
41. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[48,16,64,80]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 48], [B, 16], [C, 64], [D, 80]], A, 48, B, 16, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 48], [B, 16], [C, 64], [D, 80]], A, 48, B, 16, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
42. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[51,17,68,85]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 51], [B, 17], [C, 68], [D, 85]], A, 51, B, 17, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 51], [B, 17], [C, 68], [D, 85]], A, 51, B, 17, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
43. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[54,18,72,90]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 54], [B, 18], [C, 72], [D, 90]], A, 54, B, 18, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 54], [B, 18], [C, 72], [D, 90]], A, 54, B, 18, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
44. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[57,19,76,95]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 57], [B, 19], [C, 76], [D, 95]], A, 57, B, 19, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 57], [B, 19], [C, 76], [D, 95]], A, 57, B, 19, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
45. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[60,20,80,100]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 60], [B, 20], [C, 80], [D, 100]], A, 60, B, 20, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 60], [B, 20], [C, 80], [D, 100]], A, 60, B, 20, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
46. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[63,21,84,105]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 63], [B, 21], [C, 84], [D, 105]], A, 63, B, 21, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 63], [B, 21], [C, 84], [D, 105]], A, 63, B, 21, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
47. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[66,22,88,110]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 66], [B, 22], [C, 88], [D, 110]], A, 66, B, 22, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 66], [B, 22], [C, 88], [D, 110]], A, 66, B, 22, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
48. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[69,23,92,115]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 69], [B, 23], [C, 92], [D, 115]], A, 69, B, 23, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 69], [B, 23], [C, 92], [D, 115]], A, 69, B, 23, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
49. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[72,24,96,120]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 72], [B, 24], [C, 96], [D, 120]], A, 72, B, 24, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 72], [B, 24], [C, 96], [D, 120]], A, 72, B, 24, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
50. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-improvement-witness；明示資料={"candidate":"A","challenger":"B","points":["A","B","C","D"],"values":[75,25,100,125]}；請依 [complete_objective_table, candidate, candidate_value, challenger, challenger_value, strict_feasible_improvement, candidate_global_optimality_claim, refutation_scope] 回答。
查看答案與解釋
([[A, 75], [B, 25], [C, 100], [D, 125]], A, 75, B, 25, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)
Wave6第十三層核對=([[A, 75], [B, 25], [C, 100], [D, 125]], A, 75, B, 25, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-improvement-witness · candidate
51. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":1,"points":["A","B","C","D"],"values":[1,2,3,4]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 1], [B, 2], [C, 3], [D, 4]], 1, A, 1, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 1], [B, 2], [C, 3], [D, 4]], 1, A, 1, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
52. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":2,"points":["A","B","C","D"],"values":[2,4,6,8]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 2], [B, 4], [C, 6], [D, 8]], 2, A, 2, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 2], [B, 4], [C, 6], [D, 8]], 2, A, 2, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
53. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":3,"points":["A","B","C","D"],"values":[3,6,9,12]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 3], [B, 6], [C, 9], [D, 12]], 3, A, 3, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 3], [B, 6], [C, 9], [D, 12]], 3, A, 3, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
54. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":4,"points":["A","B","C","D"],"values":[4,8,12,16]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 4], [B, 8], [C, 12], [D, 16]], 4, A, 4, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 4], [B, 8], [C, 12], [D, 16]], 4, A, 4, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
55. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":5,"points":["A","B","C","D"],"values":[5,10,15,20]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 5], [B, 10], [C, 15], [D, 20]], 5, A, 5, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 5], [B, 10], [C, 15], [D, 20]], 5, A, 5, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
56. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":6,"points":["A","B","C","D"],"values":[6,12,18,24]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 6], [B, 12], [C, 18], [D, 24]], 6, A, 6, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 6], [B, 12], [C, 18], [D, 24]], 6, A, 6, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
57. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":7,"points":["A","B","C","D"],"values":[7,14,21,28]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 7], [B, 14], [C, 21], [D, 28]], 7, A, 7, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 7], [B, 14], [C, 21], [D, 28]], 7, A, 7, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
58. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":8,"points":["A","B","C","D"],"values":[8,16,24,32]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 8], [B, 16], [C, 24], [D, 32]], 8, A, 8, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 8], [B, 16], [C, 24], [D, 32]], 8, A, 8, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
59. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":9,"points":["A","B","C","D"],"values":[9,18,27,36]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 9], [B, 18], [C, 27], [D, 36]], 9, A, 9, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 9], [B, 18], [C, 27], [D, 36]], 9, A, 9, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
60. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":10,"points":["A","B","C","D"],"values":[10,20,30,40]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 10], [B, 20], [C, 30], [D, 40]], 10, A, 10, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 10], [B, 20], [C, 30], [D, 40]], 10, A, 10, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
61. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":11,"points":["A","B","C","D"],"values":[11,22,33,44]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 11], [B, 22], [C, 33], [D, 44]], 11, A, 11, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 11], [B, 22], [C, 33], [D, 44]], 11, A, 11, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
62. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":12,"points":["A","B","C","D"],"values":[12,24,36,48]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 12], [B, 24], [C, 36], [D, 48]], 12, A, 12, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 12], [B, 24], [C, 36], [D, 48]], 12, A, 12, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
63. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":13,"points":["A","B","C","D"],"values":[13,26,39,52]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 13], [B, 26], [C, 39], [D, 52]], 13, A, 13, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 13], [B, 26], [C, 39], [D, 52]], 13, A, 13, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
64. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":14,"points":["A","B","C","D"],"values":[14,28,42,56]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 14], [B, 28], [C, 42], [D, 56]], 14, A, 14, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 14], [B, 28], [C, 42], [D, 56]], 14, A, 14, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
65. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":15,"points":["A","B","C","D"],"values":[15,30,45,60]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 15], [B, 30], [C, 45], [D, 60]], 15, A, 15, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 15], [B, 30], [C, 45], [D, 60]], 15, A, 15, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
66. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":16,"points":["A","B","C","D"],"values":[16,32,48,64]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 16], [B, 32], [C, 48], [D, 64]], 16, A, 16, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 16], [B, 32], [C, 48], [D, 64]], 16, A, 16, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
67. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":17,"points":["A","B","C","D"],"values":[17,34,51,68]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 17], [B, 34], [C, 51], [D, 68]], 17, A, 17, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 17], [B, 34], [C, 51], [D, 68]], 17, A, 17, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
68. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":18,"points":["A","B","C","D"],"values":[18,36,54,72]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 18], [B, 36], [C, 54], [D, 72]], 18, A, 18, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 18], [B, 36], [C, 54], [D, 72]], 18, A, 18, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
69. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":19,"points":["A","B","C","D"],"values":[19,38,57,76]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 19], [B, 38], [C, 57], [D, 76]], 19, A, 19, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 19], [B, 38], [C, 57], [D, 76]], 19, A, 19, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
70. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":20,"points":["A","B","C","D"],"values":[20,40,60,80]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 20], [B, 40], [C, 60], [D, 80]], 20, A, 20, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 20], [B, 40], [C, 60], [D, 80]], 20, A, 20, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
71. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":21,"points":["A","B","C","D"],"values":[21,42,63,84]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 21], [B, 42], [C, 63], [D, 84]], 21, A, 21, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 21], [B, 42], [C, 63], [D, 84]], 21, A, 21, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
72. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":22,"points":["A","B","C","D"],"values":[22,44,66,88]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 22], [B, 44], [C, 66], [D, 88]], 22, A, 22, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 22], [B, 44], [C, 66], [D, 88]], 22, A, 22, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
73. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":23,"points":["A","B","C","D"],"values":[23,46,69,92]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 23], [B, 46], [C, 69], [D, 92]], 23, A, 23, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 23], [B, 46], [C, 69], [D, 92]], 23, A, 23, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
74. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":24,"points":["A","B","C","D"],"values":[24,48,72,96]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 24], [B, 48], [C, 72], [D, 96]], 24, A, 24, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 24], [B, 48], [C, 72], [D, 96]], 24, A, 24, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
75. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-lower-bound-certificate；明示資料={"candidate":"A","lower_bound":25,"points":["A","B","C","D"],"values":[25,50,75,100]}；請依 [complete_objective_table, lower_bound, candidate, candidate_value, all_values_above_bound, bound_attained, global_optimum, unique, all_global_minimizers, certificate_scope] 回答。
查看答案與解釋
([[A, 25], [B, 50], [C, 75], [D, 100]], 25, A, 25, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)
Wave6第十三層核對=([[A, 25], [B, 50], [C, 75], [D, 100]], 25, A, 25, 是, 是, 是, 是, [A], complete_lower_bound_plus_attainment_certifies_global_but_not_automatic_uniqueness)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-lower-bound-certificate · candidate
76. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"empty_feasible","model":{}}；請依 [mode, feasible_set, optimizer_exists_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(empty_feasible, [], 否, empty_feasible_set_has_no_optimizer)
Wave6第十三層核對=(empty_feasible, [], 否, empty_feasible_set_has_no_optimizer)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
77. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[2,4]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 2], [B, 4]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 2], [B, 4]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
78. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[3,3,9]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 3, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 3, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
79. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[8,12,4,16]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 8, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 8, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
80. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[5,10]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 5], [B, 10]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 5], [B, 10]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
81. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[6,6,18]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 6, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 6, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
82. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[14,21,7,28]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 14, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 14, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
83. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[8,16]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 8], [B, 16]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 8], [B, 16]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
84. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[9,9,27]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 9, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 9, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
85. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[20,30,10,40]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 20, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 20, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
86. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[11,22]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 11], [B, 22]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 11], [B, 22]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
87. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[12,12,36]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 12, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 12, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
88. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[26,39,13,52]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 26, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 26, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
89. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[14,28]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 14], [B, 28]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 14], [B, 28]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
90. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[15,15,45]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 15, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 15, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
91. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[32,48,16,64]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 32, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 32, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
92. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[17,34]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 17], [B, 34]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 17], [B, 34]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
93. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[18,18,54]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 18, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 18, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
94. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[38,57,19,76]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 38, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 38, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
95. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[20,40]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 20], [B, 40]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 20], [B, 40]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
96. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[21,21,63]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 21, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 21, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
97. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[44,66,22,88]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 44, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 44, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
98. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[23,46]}}；請依 [mode, listed_objective_rows, global_certificate_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(incomplete_domain, [[A, 23], [B, 46]], 否, an_unverified_partial_list_cannot_support_a_global_claim)
Wave6第十三層核對=(incomplete_domain, [[A, 23], [B, 46]], 否, an_unverified_partial_list_cannot_support_a_global_claim)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
99. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[24,24,72]}}；請依 [mode, minimum_value, all_global_minimizers, global_optimum_exists, unique_claim, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(tie_not_unique, 24, [A, B], 是, 否, global_optimum_need_not_be_unique)
Wave6第十三層核對=(tie_not_unique, 24, [A, B], 是, 否, global_optimum_need_not_be_unique)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
100. 有限最佳化
完整有限feasible domain、明示neighborhood與exact objective table。操作=optdeep-boundary；明示資料={"mode":"local_not_global","model":{"candidate":"A","edges":[["A","B"]],"points":["A","B","C","D"],"values":[50,75,25,100]}}；請依 [mode, candidate, candidate_value, declared_neighbors, neighborhood_local_minimum, global_minimum, boundary] 回答。
四種mode為4/4/6/7欄；不完整清單雖可算listed minimum仍無global certificate。ties保留全部argmin；一個strict improvement只否定候選的global optimality。
查看答案與解釋
(local_not_global, A, 50, [B], 是, 否, local_minimum_does_not_imply_global_minimum)
Wave6第十三層核對=(local_not_global, A, 50, [B], 是, 否, local_minimum_does_not_imply_global_minimum)；依完整明示資料精確重算；local只比較全部neighbors，global比較全部feasible points；lower bound須完整且attained；strict improvement只是否定證書；empty/incomplete domain與ties不得冒充存在、global或unique optimum。
本題逐步詳解（AI 二次覆核）
最佳化問題 · qf-mod50-optdeep-boundary · candidate
原始題目 JSONL · 驗收報告