{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0001","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197001,"parameters":{"points":["A","B","C","D"],"values":[1,2,3,4],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[1,1],[2,1],[3,1],[4,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0002","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197002,"parameters":{"points":["A","B","C","D"],"values":[2,4,6,8],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[2,1],[4,1],[6,1],[8,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0003","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197003,"parameters":{"points":["A","B","C","D"],"values":[3,6,9,12],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[3,1],[6,1],[9,1],[12,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0004","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197004,"parameters":{"points":["A","B","C","D"],"values":[4,8,12,16],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[4,1],[8,1],[12,1],[16,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0005","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197005,"parameters":{"points":["A","B","C","D"],"values":[5,10,15,20],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[5,1],[10,1],[15,1],[20,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0006","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197006,"parameters":{"points":["A","B","C","D"],"values":[6,12,18,24],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[6,1],[12,1],[18,1],[24,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0007","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197007,"parameters":{"points":["A","B","C","D"],"values":[7,14,21,28],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[7,1],[14,1],[21,1],[28,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0008","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197008,"parameters":{"points":["A","B","C","D"],"values":[8,16,24,32],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[8,1],[16,1],[24,1],[32,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0009","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197009,"parameters":{"points":["A","B","C","D"],"values":[9,18,27,36],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[9,1],[18,1],[27,1],[36,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0010","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197010,"parameters":{"points":["A","B","C","D"],"values":[10,20,30,40],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[10,1],[20,1],[30,1],[40,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0011","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197011,"parameters":{"points":["A","B","C","D"],"values":[11,22,33,44],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[11,1],[22,1],[33,1],[44,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0012","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197012,"parameters":{"points":["A","B","C","D"],"values":[12,24,36,48],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[12,1],[24,1],[36,1],[48,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0013","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197013,"parameters":{"points":["A","B","C","D"],"values":[13,26,39,52],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[13,1],[26,1],[39,1],[52,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0014","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197014,"parameters":{"points":["A","B","C","D"],"values":[14,28,42,56],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[14,1],[28,1],[42,1],[56,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0015","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197015,"parameters":{"points":["A","B","C","D"],"values":[15,30,45,60],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[15,1],[30,1],[45,1],[60,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0016","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197016,"parameters":{"points":["A","B","C","D"],"values":[16,32,48,64],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[16,1],[32,1],[48,1],[64,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0017","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197017,"parameters":{"points":["A","B","C","D"],"values":[17,34,51,68],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[17,1],[34,1],[51,1],[68,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0018","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197018,"parameters":{"points":["A","B","C","D"],"values":[18,36,54,72],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[18,1],[36,1],[54,1],[72,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0019","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197019,"parameters":{"points":["A","B","C","D"],"values":[19,38,57,76],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[19,1],[38,1],[57,1],[76,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0020","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197020,"parameters":{"points":["A","B","C","D"],"values":[20,40,60,80],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[20,1],[40,1],[60,1],[80,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0021","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197021,"parameters":{"points":["A","B","C","D"],"values":[21,42,63,84],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[21,1],[42,1],[63,1],[84,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0022","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197022,"parameters":{"points":["A","B","C","D"],"values":[22,44,66,88],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[22,1],[44,1],[66,1],[88,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0023","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197023,"parameters":{"points":["A","B","C","D"],"values":[23,46,69,92],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[23,1],[46,1],[69,1],[92,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0024","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197024,"parameters":{"points":["A","B","C","D"],"values":[24,48,72,96],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[24,1],[48,1],[72,1],[96,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0025","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-local-global","seed":202611197025,"parameters":{"points":["A","B","C","D"],"values":[25,50,75,100],"edges":[["A","B"],["A","C"],["B","D"],["C","D"]],"candidate":"A","domain":"Exact_finite_optimization_density","operation":"optdeep-local-global","semantic_template":"optdeep-local-global|{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"],[\"A\",\"C\"],[\"B\",\"D\"],[\"C\",\"D\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[25,1],[50,1],[75,1],[100,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0026","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 3], [B, 1], [C, 4], [D, 5]], A, 3, B, 1, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197026,"parameters":{"points":["A","B","C","D"],"values":[3,1,4,5],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[3,1],[1,1],[4,1],[5,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0027","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 6], [B, 2], [C, 8], [D, 10]], A, 6, B, 2, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197027,"parameters":{"points":["A","B","C","D"],"values":[6,2,8,10],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[6,1],[2,1],[8,1],[10,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0028","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 9], [B, 3], [C, 12], [D, 15]], A, 9, B, 3, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197028,"parameters":{"points":["A","B","C","D"],"values":[9,3,12,15],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[9,1],[3,1],[12,1],[15,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0029","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 12], [B, 4], [C, 16], [D, 20]], A, 12, B, 4, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197029,"parameters":{"points":["A","B","C","D"],"values":[12,4,16,20],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[12,1],[4,1],[16,1],[20,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0030","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 15], [B, 5], [C, 20], [D, 25]], A, 15, B, 5, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197030,"parameters":{"points":["A","B","C","D"],"values":[15,5,20,25],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[15,1],[5,1],[20,1],[25,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0031","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 18], [B, 6], [C, 24], [D, 30]], A, 18, B, 6, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197031,"parameters":{"points":["A","B","C","D"],"values":[18,6,24,30],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[18,1],[6,1],[24,1],[30,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0032","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 21], [B, 7], [C, 28], [D, 35]], A, 21, B, 7, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197032,"parameters":{"points":["A","B","C","D"],"values":[21,7,28,35],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[21,1],[7,1],[28,1],[35,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0033","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 24], [B, 8], [C, 32], [D, 40]], A, 24, B, 8, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197033,"parameters":{"points":["A","B","C","D"],"values":[24,8,32,40],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[24,1],[8,1],[32,1],[40,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0034","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 27], [B, 9], [C, 36], [D, 45]], A, 27, B, 9, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197034,"parameters":{"points":["A","B","C","D"],"values":[27,9,36,45],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[27,1],[9,1],[36,1],[45,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0035","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 30], [B, 10], [C, 40], [D, 50]], A, 30, B, 10, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197035,"parameters":{"points":["A","B","C","D"],"values":[30,10,40,50],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[30,1],[10,1],[40,1],[50,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0036","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 33], [B, 11], [C, 44], [D, 55]], A, 33, B, 11, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197036,"parameters":{"points":["A","B","C","D"],"values":[33,11,44,55],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[33,1],[11,1],[44,1],[55,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0037","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 36], [B, 12], [C, 48], [D, 60]], A, 36, B, 12, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197037,"parameters":{"points":["A","B","C","D"],"values":[36,12,48,60],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[36,1],[12,1],[48,1],[60,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0038","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 39], [B, 13], [C, 52], [D, 65]], A, 39, B, 13, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197038,"parameters":{"points":["A","B","C","D"],"values":[39,13,52,65],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[39,1],[13,1],[52,1],[65,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0039","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 42], [B, 14], [C, 56], [D, 70]], A, 42, B, 14, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197039,"parameters":{"points":["A","B","C","D"],"values":[42,14,56,70],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[42,1],[14,1],[56,1],[70,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0040","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 45], [B, 15], [C, 60], [D, 75]], A, 45, B, 15, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197040,"parameters":{"points":["A","B","C","D"],"values":[45,15,60,75],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[45,1],[15,1],[60,1],[75,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0041","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 48], [B, 16], [C, 64], [D, 80]], A, 48, B, 16, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197041,"parameters":{"points":["A","B","C","D"],"values":[48,16,64,80],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[48,1],[16,1],[64,1],[80,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0042","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 51], [B, 17], [C, 68], [D, 85]], A, 51, B, 17, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197042,"parameters":{"points":["A","B","C","D"],"values":[51,17,68,85],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[51,1],[17,1],[68,1],[85,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0043","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 54], [B, 18], [C, 72], [D, 90]], A, 54, B, 18, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197043,"parameters":{"points":["A","B","C","D"],"values":[54,18,72,90],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[54,1],[18,1],[72,1],[90,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0044","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 57], [B, 19], [C, 76], [D, 95]], A, 57, B, 19, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197044,"parameters":{"points":["A","B","C","D"],"values":[57,19,76,95],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[57,1],[19,1],[76,1],[95,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0045","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 60], [B, 20], [C, 80], [D, 100]], A, 60, B, 20, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197045,"parameters":{"points":["A","B","C","D"],"values":[60,20,80,100],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[60,1],[20,1],[80,1],[100,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0046","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 63], [B, 21], [C, 84], [D, 105]], A, 63, B, 21, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197046,"parameters":{"points":["A","B","C","D"],"values":[63,21,84,105],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[63,1],[21,1],[84,1],[105,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0047","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 66], [B, 22], [C, 88], [D, 110]], A, 66, B, 22, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197047,"parameters":{"points":["A","B","C","D"],"values":[66,22,88,110],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[66,1],[22,1],[88,1],[110,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0048","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 69], [B, 23], [C, 92], [D, 115]], A, 69, B, 23, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197048,"parameters":{"points":["A","B","C","D"],"values":[69,23,92,115],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[69,1],[23,1],[92,1],[115,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0049","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 72], [B, 24], [C, 96], [D, 120]], A, 72, B, 24, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197049,"parameters":{"points":["A","B","C","D"],"values":[72,24,96,120],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[72,1],[24,1],[96,1],[120,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0050","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[A, 75], [B, 25], [C, 100], [D, 125]], A, 75, B, 25, 是, 否, one_strictly_better_feasible_point_refutes_candidate_global_optimality)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-improvement-witness","seed":202611197050,"parameters":{"points":["A","B","C","D"],"values":[75,25,100,125],"candidate":"A","challenger":"B","domain":"Exact_finite_optimization_density","operation":"optdeep-improvement-witness","semantic_template":"optdeep-improvement-witness|{\"candidate\":\"A\",\"challenger\":\"B\",\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[75,1],[25,1],[100,1],[125,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0051","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197051,"parameters":{"points":["A","B","C","D"],"values":[1,2,3,4],"candidate":"A","lower_bound":1,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[1,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[1,1],[2,1],[3,1],[4,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0052","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197052,"parameters":{"points":["A","B","C","D"],"values":[2,4,6,8],"candidate":"A","lower_bound":2,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[2,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[2,1],[4,1],[6,1],[8,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0053","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197053,"parameters":{"points":["A","B","C","D"],"values":[3,6,9,12],"candidate":"A","lower_bound":3,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[3,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[3,1],[6,1],[9,1],[12,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0054","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197054,"parameters":{"points":["A","B","C","D"],"values":[4,8,12,16],"candidate":"A","lower_bound":4,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[4,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[4,1],[8,1],[12,1],[16,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0055","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197055,"parameters":{"points":["A","B","C","D"],"values":[5,10,15,20],"candidate":"A","lower_bound":5,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[5,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[5,1],[10,1],[15,1],[20,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0056","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197056,"parameters":{"points":["A","B","C","D"],"values":[6,12,18,24],"candidate":"A","lower_bound":6,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[6,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[6,1],[12,1],[18,1],[24,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0057","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197057,"parameters":{"points":["A","B","C","D"],"values":[7,14,21,28],"candidate":"A","lower_bound":7,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[7,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[7,1],[14,1],[21,1],[28,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0058","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197058,"parameters":{"points":["A","B","C","D"],"values":[8,16,24,32],"candidate":"A","lower_bound":8,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[8,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[8,1],[16,1],[24,1],[32,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0059","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197059,"parameters":{"points":["A","B","C","D"],"values":[9,18,27,36],"candidate":"A","lower_bound":9,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[9,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[9,1],[18,1],[27,1],[36,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0060","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197060,"parameters":{"points":["A","B","C","D"],"values":[10,20,30,40],"candidate":"A","lower_bound":10,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[10,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[10,1],[20,1],[30,1],[40,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0061","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197061,"parameters":{"points":["A","B","C","D"],"values":[11,22,33,44],"candidate":"A","lower_bound":11,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[11,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[11,1],[22,1],[33,1],[44,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0062","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197062,"parameters":{"points":["A","B","C","D"],"values":[12,24,36,48],"candidate":"A","lower_bound":12,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[12,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[12,1],[24,1],[36,1],[48,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0063","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197063,"parameters":{"points":["A","B","C","D"],"values":[13,26,39,52],"candidate":"A","lower_bound":13,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[13,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[13,1],[26,1],[39,1],[52,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0064","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197064,"parameters":{"points":["A","B","C","D"],"values":[14,28,42,56],"candidate":"A","lower_bound":14,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[14,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[14,1],[28,1],[42,1],[56,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0065","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197065,"parameters":{"points":["A","B","C","D"],"values":[15,30,45,60],"candidate":"A","lower_bound":15,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[15,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[15,1],[30,1],[45,1],[60,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0066","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197066,"parameters":{"points":["A","B","C","D"],"values":[16,32,48,64],"candidate":"A","lower_bound":16,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[16,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[16,1],[32,1],[48,1],[64,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0067","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197067,"parameters":{"points":["A","B","C","D"],"values":[17,34,51,68],"candidate":"A","lower_bound":17,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[17,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[17,1],[34,1],[51,1],[68,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0068","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197068,"parameters":{"points":["A","B","C","D"],"values":[18,36,54,72],"candidate":"A","lower_bound":18,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[18,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[18,1],[36,1],[54,1],[72,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0069","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197069,"parameters":{"points":["A","B","C","D"],"values":[19,38,57,76],"candidate":"A","lower_bound":19,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[19,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[19,1],[38,1],[57,1],[76,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0070","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197070,"parameters":{"points":["A","B","C","D"],"values":[20,40,60,80],"candidate":"A","lower_bound":20,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[20,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[20,1],[40,1],[60,1],[80,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0071","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197071,"parameters":{"points":["A","B","C","D"],"values":[21,42,63,84],"candidate":"A","lower_bound":21,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[21,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[21,1],[42,1],[63,1],[84,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0072","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197072,"parameters":{"points":["A","B","C","D"],"values":[22,44,66,88],"candidate":"A","lower_bound":22,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[22,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[22,1],[44,1],[66,1],[88,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0073","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197073,"parameters":{"points":["A","B","C","D"],"values":[23,46,69,92],"candidate":"A","lower_bound":23,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[23,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[23,1],[46,1],[69,1],[92,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0074","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197074,"parameters":{"points":["A","B","C","D"],"values":[24,48,72,96],"candidate":"A","lower_bound":24,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[24,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[24,1],[48,1],[72,1],[96,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0075","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([[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)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-lower-bound-certificate","seed":202611197075,"parameters":{"points":["A","B","C","D"],"values":[25,50,75,100],"candidate":"A","lower_bound":25,"domain":"Exact_finite_optimization_density","operation":"optdeep-lower-bound-certificate","semantic_template":"optdeep-lower-bound-certificate|{\"candidate\":\"A\",\"lower_bound\":[25,1],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[25,1],[50,1],[75,1],[100,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0076","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(empty_feasible, [], 否, empty_feasible_set_has_no_optimizer)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197076,"parameters":{"mode":"empty_feasible","model":{},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"empty_feasible\",\"model\":{}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0077","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 2], [B, 4]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197077,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[2,4]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[2,1],[4,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0078","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 3, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197078,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[3,3,9]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[3,1],[3,1],[9,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0079","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 8, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197079,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[8,12,4,16],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[8,1],[12,1],[4,1],[16,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0080","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 5], [B, 10]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197080,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[5,10]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[5,1],[10,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0081","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 6, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197081,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[6,6,18]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[6,1],[6,1],[18,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0082","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 14, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197082,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[14,21,7,28],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[14,1],[21,1],[7,1],[28,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0083","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 8], [B, 16]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197083,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[8,16]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[8,1],[16,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0084","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 9, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197084,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[9,9,27]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[9,1],[9,1],[27,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0085","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 20, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197085,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[20,30,10,40],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[20,1],[30,1],[10,1],[40,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0086","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 11], [B, 22]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197086,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[11,22]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[11,1],[22,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0087","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 12, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197087,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[12,12,36]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[12,1],[12,1],[36,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0088","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 26, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197088,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[26,39,13,52],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[26,1],[39,1],[13,1],[52,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0089","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 14], [B, 28]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197089,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[14,28]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[14,1],[28,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0090","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 15, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197090,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[15,15,45]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[15,1],[15,1],[45,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0091","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 32, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197091,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[32,48,16,64],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[32,1],[48,1],[16,1],[64,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0092","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 17], [B, 34]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197092,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[17,34]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[17,1],[34,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0093","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 18, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197093,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[18,18,54]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[18,1],[18,1],[54,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0094","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 38, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197094,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[38,57,19,76],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[38,1],[57,1],[19,1],[76,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0095","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 20], [B, 40]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197095,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[20,40]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[20,1],[40,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0096","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 21, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197096,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[21,21,63]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[21,1],[21,1],[63,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0097","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 44, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197097,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[44,66,22,88],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[44,1],[66,1],[22,1],[88,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0098","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(incomplete_domain, [[A, 23], [B, 46]], 否, an_unverified_partial_list_cannot_support_a_global_claim)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197098,"parameters":{"mode":"incomplete_domain","model":{"listed_points":["A","B"],"values":[23,46]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"incomplete_domain\",\"model\":{\"listed_points\":[\"A\",\"B\"],\"values\":[[23,1],[46,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0099","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(tie_not_unique, 24, [A, B], 是, 否, global_optimum_need_not_be_unique)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197099,"parameters":{"mode":"tie_not_unique","model":{"points":["A","B","C"],"values":[24,24,72]},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"tie_not_unique\",\"model\":{\"points\":[\"A\",\"B\",\"C\"],\"values\":[[24,1],[24,1],[72,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r07-0100","batch_id":"batch-20261015-advance-20261119-r07-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限最佳化","stem_zh":"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 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(local_not_global, A, 50, [B], 是, 否, local_minimum_does_not_imply_global_minimum)","explanation_zh":"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。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限最佳化"]},"variant":{"family_id":"qf-mod50-optdeep-boundary","seed":202611197100,"parameters":{"mode":"local_not_global","model":{"points":["A","B","C","D"],"values":[50,75,25,100],"edges":[["A","B"]],"candidate":"A"},"domain":"Exact_finite_optimization_density","operation":"optdeep-boundary","semantic_template":"optdeep-boundary|{\"mode\":\"local_not_global\",\"model\":{\"candidate\":\"A\",\"edges\":[[\"A\",\"B\"]],\"points\":[\"A\",\"B\",\"C\",\"D\"],\"values\":[[50,1],[75,1],[25,1],[100,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}