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{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0004","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=9。求代數式 x+4 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":13,"explanation_zh":"代入明示值 x=9，得到 9+4=13；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260937,"parameters":{"number_system":"N","variable":"x","assigned_value":9,"operator":"+","constant":4,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":9,\"constant\":4,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0005","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=12。求代數式 x+5 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":17,"explanation_zh":"代入明示值 x=12，得到 12+5=17；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260938,"parameters":{"number_system":"N","variable":"x","assigned_value":12,"operator":"+","constant":5,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":12,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0006","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=15。求代數式 x+1 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":16,"explanation_zh":"代入明示值 x=15，得到 15+1=16；題目只使用已明示的加法。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260939,"parameters":{"number_system":"N","variable":"x","assigned_value":15,"operator":"+","constant":1,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":15,\"constant\":1,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0008","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=21。求代數式 x+3 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":24,"explanation_zh":"代入明示值 x=21，得到 21+3=24；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260941,"parameters":{"number_system":"N","variable":"x","assigned_value":21,"operator":"+","constant":3,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":21,\"constant\":3,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0009","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=24。求代數式 x+4 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":28,"explanation_zh":"代入明示值 x=24，得到 24+4=28；題目只使用已明示的加法。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260942,"parameters":{"number_system":"N","variable":"x","assigned_value":24,"operator":"+","constant":4,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":24,\"constant\":4,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0010","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=27。求代數式 x+5 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":32,"explanation_zh":"代入明示值 x=27，得到 27+5=32；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260943,"parameters":{"number_system":"N","variable":"x","assigned_value":27,"operator":"+","constant":5,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":27,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0011","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=30。求代數式 x+1 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":31,"explanation_zh":"代入明示值 x=30，得到 30+1=31；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260944,"parameters":{"number_system":"N","variable":"x","assigned_value":30,"operator":"+","constant":1,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":30,\"constant\":1,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0012","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=33。求代數式 x+2 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":35,"explanation_zh":"代入明示值 x=33，得到 33+2=35；題目只使用已明示的加法。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260945,"parameters":{"number_system":"N","variable":"x","assigned_value":33,"operator":"+","constant":2,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":33,\"constant\":2,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0013","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=36。求代數式 x+3 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":39,"explanation_zh":"代入明示值 x=36，得到 36+3=39；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260946,"parameters":{"number_system":"N","variable":"x","assigned_value":36,"operator":"+","constant":3,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":36,\"constant\":3,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0014","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=39。求代數式 x+4 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":43,"explanation_zh":"代入明示值 x=39，得到 39+4=43；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260947,"parameters":{"number_system":"N","variable":"x","assigned_value":39,"operator":"+","constant":4,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":39,\"constant\":4,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0015","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=42。求代數式 x+5 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":47,"explanation_zh":"代入明示值 x=42，得到 42+5=47；題目只使用已明示的加法。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260948,"parameters":{"number_system":"N","variable":"x","assigned_value":42,"operator":"+","constant":5,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":42,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0016","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=45。求代數式 x+1 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":46,"explanation_zh":"代入明示值 x=45，得到 45+1=46；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260949,"parameters":{"number_system":"N","variable":"x","assigned_value":45,"operator":"+","constant":1,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":45,\"constant\":1,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0017","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=48。求代數式 x+2 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":50,"explanation_zh":"代入明示值 x=48，得到 48+2=50；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260950,"parameters":{"number_system":"N","variable":"x","assigned_value":48,"operator":"+","constant":2,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":48,\"constant\":2,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0018","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=51。求代數式 x+3 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":54,"explanation_zh":"代入明示值 x=51，得到 51+3=54；題目只使用已明示的加法。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260951,"parameters":{"number_system":"N","variable":"x","assigned_value":51,"operator":"+","constant":3,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":51,\"constant\":3,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0019","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=54。求代數式 x+4 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":58,"explanation_zh":"代入明示值 x=54，得到 54+4=58；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260952,"parameters":{"number_system":"N","variable":"x","assigned_value":54,"operator":"+","constant":4,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":54,\"constant\":4,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-variable-expression-evaluation-0020","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-variable-expression"],"title_zh":"代數式明示求值","stem_zh":"在數系 N 中，給定 x=57。求代數式 x+5 的值（這是表達式，不是方程式）。","answer":{"kind":"numeric","value":62,"explanation_zh":"代入明示值 x=57，得到 57+5=62；題目只使用已明示的加法。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["代數式","代入求值"]},"variant":{"family_id":"qf-variable-expression-evaluation","seed":20260953,"parameters":{"number_system":"N","variable":"x","assigned_value":57,"operator":"+","constant":5,"expression_form":"x_plus_constant","semantic_template":"qf-variable-expression-evaluation/{\"assigned_value\":57,\"constant\":5,\"expression_form\":\"x_plus_constant\",\"number_system\":\"N\",\"operator\":\"+\",\"variable\":\"x\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0001","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記1、標記2」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記1、標記2}。候選 S={標記1、標記2} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260954,"parameters":{"experiment":"一次讀取明示標記卡 標記1、標記2","observation_scale":"一次明示有限試驗","expected_outcomes":["標記1","標記2"],"listed_outcomes":["標記1","標記2"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記1\",\"標記2\"],\"experiment\":\"一次讀取明示標記卡 標記1、標記2\",\"listed_outcomes\":[\"標記1\",\"標記2\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0002","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記11、標記12、標記13」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記11、標記12、標記13}。候選 S={標記11、標記13} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記12」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260955,"parameters":{"experiment":"一次讀取明示標記卡 標記11、標記12、標記13","observation_scale":"一次明示有限試驗","expected_outcomes":["標記11","標記12","標記13"],"listed_outcomes":["標記11","標記13"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記11\",\"標記12\",\"標記13\"],\"experiment\":\"一次讀取明示標記卡 標記11、標記12、標記13\",\"listed_outcomes\":[\"標記11\",\"標記13\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0003","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記21、標記22、標記23、標記24」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記21、標記22、標記23、標記24}。候選 S={標記21、標記22、標記23、標記24、非此試驗結果3} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果3」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260956,"parameters":{"experiment":"一次讀取明示標記卡 標記21、標記22、標記23、標記24","observation_scale":"一次明示有限試驗","expected_outcomes":["標記21","標記22","標記23","標記24"],"listed_outcomes":["標記21","標記22","標記23","標記24","非此試驗結果3"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記21\",\"標記22\",\"標記23\",\"標記24\"],\"experiment\":\"一次讀取明示標記卡 標記21、標記22、標記23、標記24\",\"listed_outcomes\":[\"標記21\",\"標記22\",\"標記23\",\"標記24\",\"非此試驗結果3\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0004","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記31、標記32、標記33、標記34、標記35」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記31、標記32、標記33、標記34、標記35}。候選 S={標記31、標記32、標記33、標記34、標記35} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260957,"parameters":{"experiment":"一次讀取明示標記卡 標記31、標記32、標記33、標記34、標記35","observation_scale":"一次明示有限試驗","expected_outcomes":["標記31","標記32","標記33","標記34","標記35"],"listed_outcomes":["標記31","標記32","標記33","標記34","標記35"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記31\",\"標記32\",\"標記33\",\"標記34\",\"標記35\"],\"experiment\":\"一次讀取明示標記卡 標記31、標記32、標記33、標記34、標記35\",\"listed_outcomes\":[\"標記31\",\"標記32\",\"標記33\",\"標記34\",\"標記35\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0005","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記41、標記42」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記41、標記42}。候選 S={標記42} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記41」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260958,"parameters":{"experiment":"一次讀取明示標記卡 標記41、標記42","observation_scale":"一次明示有限試驗","expected_outcomes":["標記41","標記42"],"listed_outcomes":["標記42"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記41\",\"標記42\"],\"experiment\":\"一次讀取明示標記卡 標記41、標記42\",\"listed_outcomes\":[\"標記42\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0006","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記51、標記52、標記53」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記51、標記52、標記53}。候選 S={標記51、標記52、標記53、非此試驗結果6} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果6」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260959,"parameters":{"experiment":"一次讀取明示標記卡 標記51、標記52、標記53","observation_scale":"一次明示有限試驗","expected_outcomes":["標記51","標記52","標記53"],"listed_outcomes":["標記51","標記52","標記53","非此試驗結果6"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記51\",\"標記52\",\"標記53\"],\"experiment\":\"一次讀取明示標記卡 標記51、標記52、標記53\",\"listed_outcomes\":[\"標記51\",\"標記52\",\"標記53\",\"非此試驗結果6\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0007","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記61、標記62、標記63、標記64」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記61、標記62、標記63、標記64}。候選 S={標記61、標記62、標記63、標記64} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260960,"parameters":{"experiment":"一次讀取明示標記卡 標記61、標記62、標記63、標記64","observation_scale":"一次明示有限試驗","expected_outcomes":["標記61","標記62","標記63","標記64"],"listed_outcomes":["標記61","標記62","標記63","標記64"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記61\",\"標記62\",\"標記63\",\"標記64\"],\"experiment\":\"一次讀取明示標記卡 標記61、標記62、標記63、標記64\",\"listed_outcomes\":[\"標記61\",\"標記62\",\"標記63\",\"標記64\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0008","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記71、標記72、標記73、標記74、標記75」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記71、標記72、標記73、標記74、標記75}。候選 S={標記71、標記72、標記74、標記75} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記73」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260961,"parameters":{"experiment":"一次讀取明示標記卡 標記71、標記72、標記73、標記74、標記75","observation_scale":"一次明示有限試驗","expected_outcomes":["標記71","標記72","標記73","標記74","標記75"],"listed_outcomes":["標記71","標記72","標記74","標記75"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記71\",\"標記72\",\"標記73\",\"標記74\",\"標記75\"],\"experiment\":\"一次讀取明示標記卡 標記71、標記72、標記73、標記74、標記75\",\"listed_outcomes\":[\"標記71\",\"標記72\",\"標記74\",\"標記75\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0009","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記81、標記82」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記81、標記82}。候選 S={標記81、標記82、非此試驗結果9} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果9」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260962,"parameters":{"experiment":"一次讀取明示標記卡 標記81、標記82","observation_scale":"一次明示有限試驗","expected_outcomes":["標記81","標記82"],"listed_outcomes":["標記81","標記82","非此試驗結果9"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記81\",\"標記82\"],\"experiment\":\"一次讀取明示標記卡 標記81、標記82\",\"listed_outcomes\":[\"標記81\",\"標記82\",\"非此試驗結果9\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0010","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記91、標記92、標記93」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記91、標記92、標記93}。候選 S={標記91、標記92、標記93} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260963,"parameters":{"experiment":"一次讀取明示標記卡 標記91、標記92、標記93","observation_scale":"一次明示有限試驗","expected_outcomes":["標記91","標記92","標記93"],"listed_outcomes":["標記91","標記92","標記93"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記91\",\"標記92\",\"標記93\"],\"experiment\":\"一次讀取明示標記卡 標記91、標記92、標記93\",\"listed_outcomes\":[\"標記91\",\"標記92\",\"標記93\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0011","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記101、標記102、標記103、標記104」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記101、標記102、標記103、標記104}。候選 S={標記101、標記102、標記104} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記103」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260964,"parameters":{"experiment":"一次讀取明示標記卡 標記101、標記102、標記103、標記104","observation_scale":"一次明示有限試驗","expected_outcomes":["標記101","標記102","標記103","標記104"],"listed_outcomes":["標記101","標記102","標記104"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記101\",\"標記102\",\"標記103\",\"標記104\"],\"experiment\":\"一次讀取明示標記卡 標記101、標記102、標記103、標記104\",\"listed_outcomes\":[\"標記101\",\"標記102\",\"標記104\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0012","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記111、標記112、標記113、標記114、標記115」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記111、標記112、標記113、標記114、標記115}。候選 S={標記111、標記112、標記113、標記114、標記115、非此試驗結果12} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果12」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260965,"parameters":{"experiment":"一次讀取明示標記卡 標記111、標記112、標記113、標記114、標記115","observation_scale":"一次明示有限試驗","expected_outcomes":["標記111","標記112","標記113","標記114","標記115"],"listed_outcomes":["標記111","標記112","標記113","標記114","標記115","非此試驗結果12"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記111\",\"標記112\",\"標記113\",\"標記114\",\"標記115\"],\"experiment\":\"一次讀取明示標記卡 標記111、標記112、標記113、標記114、標記115\",\"listed_outcomes\":[\"標記111\",\"標記112\",\"標記113\",\"標記114\",\"標記115\",\"非此試驗結果12\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0013","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記121、標記122」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記121、標記122}。候選 S={標記121、標記122} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260966,"parameters":{"experiment":"一次讀取明示標記卡 標記121、標記122","observation_scale":"一次明示有限試驗","expected_outcomes":["標記121","標記122"],"listed_outcomes":["標記121","標記122"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記121\",\"標記122\"],\"experiment\":\"一次讀取明示標記卡 標記121、標記122\",\"listed_outcomes\":[\"標記121\",\"標記122\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0014","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記131、標記132、標記133」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記131、標記132、標記133}。候選 S={標記131、標記133} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記132」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260967,"parameters":{"experiment":"一次讀取明示標記卡 標記131、標記132、標記133","observation_scale":"一次明示有限試驗","expected_outcomes":["標記131","標記132","標記133"],"listed_outcomes":["標記131","標記133"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記131\",\"標記132\",\"標記133\"],\"experiment\":\"一次讀取明示標記卡 標記131、標記132、標記133\",\"listed_outcomes\":[\"標記131\",\"標記133\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0015","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記141、標記142、標記143、標記144」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記141、標記142、標記143、標記144}。候選 S={標記141、標記142、標記143、標記144、非此試驗結果15} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果15」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260968,"parameters":{"experiment":"一次讀取明示標記卡 標記141、標記142、標記143、標記144","observation_scale":"一次明示有限試驗","expected_outcomes":["標記141","標記142","標記143","標記144"],"listed_outcomes":["標記141","標記142","標記143","標記144","非此試驗結果15"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記141\",\"標記142\",\"標記143\",\"標記144\"],\"experiment\":\"一次讀取明示標記卡 標記141、標記142、標記143、標記144\",\"listed_outcomes\":[\"標記141\",\"標記142\",\"標記143\",\"標記144\",\"非此試驗結果15\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0016","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記151、標記152、標記153、標記154、標記155」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記151、標記152、標記153、標記154、標記155}。候選 S={標記151、標記152、標記153、標記154、標記155} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260969,"parameters":{"experiment":"一次讀取明示標記卡 標記151、標記152、標記153、標記154、標記155","observation_scale":"一次明示有限試驗","expected_outcomes":["標記151","標記152","標記153","標記154","標記155"],"listed_outcomes":["標記151","標記152","標記153","標記154","標記155"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記151\",\"標記152\",\"標記153\",\"標記154\",\"標記155\"],\"experiment\":\"一次讀取明示標記卡 標記151、標記152、標記153、標記154、標記155\",\"listed_outcomes\":[\"標記151\",\"標記152\",\"標記153\",\"標記154\",\"標記155\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0017","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記161、標記162」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記161、標記162}。候選 S={標記162} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記161」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260970,"parameters":{"experiment":"一次讀取明示標記卡 標記161、標記162","observation_scale":"一次明示有限試驗","expected_outcomes":["標記161","標記162"],"listed_outcomes":["標記162"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記161\",\"標記162\"],\"experiment\":\"一次讀取明示標記卡 標記161、標記162\",\"listed_outcomes\":[\"標記162\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0018","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記171、標記172、標記173」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記171、標記172、標記173}。候選 S={標記171、標記172、標記173、非此試驗結果18} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"列入「非此試驗結果18」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260971,"parameters":{"experiment":"一次讀取明示標記卡 標記171、標記172、標記173","observation_scale":"一次明示有限試驗","expected_outcomes":["標記171","標記172","標記173"],"listed_outcomes":["標記171","標記172","標記173","非此試驗結果18"],"mode":"extra_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記171\",\"標記172\",\"標記173\"],\"experiment\":\"一次讀取明示標記卡 標記171、標記172、標記173\",\"listed_outcomes\":[\"標記171\",\"標記172\",\"標記173\",\"非此試驗結果18\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0019","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記181、標記182、標記183、標記184」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記181、標記182、標記183、標記184}。候選 S={標記181、標記182、標記183、標記184} 是否完整？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"列舉與本題明示的所有基本結果完全一致；本結論只談完整性，不指派機率或等可能性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260972,"parameters":{"experiment":"一次讀取明示標記卡 標記181、標記182、標記183、標記184","observation_scale":"一次明示有限試驗","expected_outcomes":["標記181","標記182","標記183","標記184"],"listed_outcomes":["標記181","標記182","標記183","標記184"],"mode":"complete","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記181\",\"標記182\",\"標記183\",\"標記184\"],\"experiment\":\"一次讀取明示標記卡 標記181、標記182、標記183、標記184\",\"listed_outcomes\":[\"標記181\",\"標記182\",\"標記183\",\"標記184\"],\"mode\":\"complete\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-finite-sample-space-completeness-0020","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-sample-space"],"title_zh":"有限樣本空間完整性","stem_zh":"試驗為「一次讀取明示標記卡 標記191、標記192、標記193、標記194、標記195」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記191、標記192、標記193、標記194、標記195}。候選 S={標記191、標記192、標記193、標記194} 是否完整？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"缺少明示可能結果「標記195」，因此列舉不完整；本題不從樣本空間推論機率。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["樣本空間","有限列舉"]},"variant":{"family_id":"qf-finite-sample-space-completeness","seed":20260973,"parameters":{"experiment":"一次讀取明示標記卡 標記191、標記192、標記193、標記194、標記195","observation_scale":"一次明示有限試驗","expected_outcomes":["標記191","標記192","標記193","標記194","標記195"],"listed_outcomes":["標記191","標記192","標記193","標記194"],"mode":"missing_outcome","semantic_template":"qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記191\",\"標記192\",\"標記193\",\"標記194\",\"標記195\"],\"experiment\":\"一次讀取明示標記卡 標記191、標記192、標記193、標記194、標記195\",\"listed_outcomes\":[\"標記191\",\"標記192\",\"標記193\",\"標記194\"],\"mode\":\"missing_outcome\",\"observation_scale\":\"一次明示有限試驗\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0001","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：令 n 為任意自然數並暫設 P(n)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(1) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「證明 P(0)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260974,"parameters":{"mode":"missing_role","target_role":"base_case","provided_roles":["induction_hypothesis","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":1,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":1,\"mode\":\"missing_role\",\"provided_roles\":[\"induction_hypothesis\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0002","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「證明 P(0)」。草稿另列出 P(0) 到 P(2) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「證明 P(0)」在此草稿中扮演 base_case；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260975,"parameters":{"mode":"identify_role","target_role":"base_case","provided_roles":["base_case"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":2,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":2,\"mode\":\"identify_role\",\"provided_roles\":[\"base_case\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0003","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(3) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「令 n 為任意自然數並暫設 P(n)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260976,"parameters":{"mode":"missing_role","target_role":"induction_hypothesis","provided_roles":["base_case","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":3,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":3,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0004","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「令 n 為任意自然數並暫設 P(n)」。草稿另列出 P(0) 到 P(4) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「令 n 為任意自然數並暫設 P(n)」在此草稿中扮演 induction_hypothesis；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260977,"parameters":{"mode":"identify_role","target_role":"induction_hypothesis","provided_roles":["induction_hypothesis"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":4,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":4,\"mode\":\"identify_role\",\"provided_roles\":[\"induction_hypothesis\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0005","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；令 n 為任意自然數並暫設 P(n)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(5) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"induction_step","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「在歸納假設下證明 P(n+1)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260978,"parameters":{"mode":"missing_role","target_role":"induction_step","provided_roles":["base_case","induction_hypothesis","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":5,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":5,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_hypothesis\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_step\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0006","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「在歸納假設下證明 P(n+1)」。草稿另列出 P(0) 到 P(6) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"induction_step","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「在歸納假設下證明 P(n+1)」在此草稿中扮演 induction_step；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260979,"parameters":{"mode":"identify_role","target_role":"induction_step","provided_roles":["induction_step"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":6,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":6,\"mode\":\"identify_role\",\"provided_roles\":[\"induction_step\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_step\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0007","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；令 n 為任意自然數並暫設 P(n)；在歸納假設下證明 P(n+1)。草稿另列出 P(0) 到 P(7) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"conclusion","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「據此斷言所有 n∈N 的 P(n)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260980,"parameters":{"mode":"missing_role","target_role":"conclusion","provided_roles":["base_case","induction_hypothesis","induction_step"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":7,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":7,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_hypothesis\",\"induction_step\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"conclusion\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0008","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「據此斷言所有 n∈N 的 P(n)」。草稿另列出 P(0) 到 P(8) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"conclusion","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「據此斷言所有 n∈N 的 P(n)」在此草稿中扮演 conclusion；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260981,"parameters":{"mode":"identify_role","target_role":"conclusion","provided_roles":["conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":8,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":8,\"mode\":\"identify_role\",\"provided_roles\":[\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"conclusion\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0009","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：令 n 為任意自然數並暫設 P(n)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(9) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「證明 P(0)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260982,"parameters":{"mode":"missing_role","target_role":"base_case","provided_roles":["induction_hypothesis","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":9,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":9,\"mode\":\"missing_role\",\"provided_roles\":[\"induction_hypothesis\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0010","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「證明 P(0)」。草稿另列出 P(0) 到 P(10) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「證明 P(0)」在此草稿中扮演 base_case；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260983,"parameters":{"mode":"identify_role","target_role":"base_case","provided_roles":["base_case"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":10,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":10,\"mode\":\"identify_role\",\"provided_roles\":[\"base_case\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0011","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(11) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「令 n 為任意自然數並暫設 P(n)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260984,"parameters":{"mode":"missing_role","target_role":"induction_hypothesis","provided_roles":["base_case","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":11,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":11,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0012","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「令 n 為任意自然數並暫設 P(n)」。草稿另列出 P(0) 到 P(12) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「令 n 為任意自然數並暫設 P(n)」在此草稿中扮演 induction_hypothesis；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260985,"parameters":{"mode":"identify_role","target_role":"induction_hypothesis","provided_roles":["induction_hypothesis"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":12,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":12,\"mode\":\"identify_role\",\"provided_roles\":[\"induction_hypothesis\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0013","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；令 n 為任意自然數並暫設 P(n)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(13) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"induction_step","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「在歸納假設下證明 P(n+1)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260986,"parameters":{"mode":"missing_role","target_role":"induction_step","provided_roles":["base_case","induction_hypothesis","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":13,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":13,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_hypothesis\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_step\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0014","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「在歸納假設下證明 P(n+1)」。草稿另列出 P(0) 到 P(14) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"induction_step","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「在歸納假設下證明 P(n+1)」在此草稿中扮演 induction_step；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260987,"parameters":{"mode":"identify_role","target_role":"induction_step","provided_roles":["induction_step"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":14,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":14,\"mode\":\"identify_role\",\"provided_roles\":[\"induction_step\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_step\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0015","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；令 n 為任意自然數並暫設 P(n)；在歸納假設下證明 P(n+1)。草稿另列出 P(0) 到 P(15) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"conclusion","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「據此斷言所有 n∈N 的 P(n)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260988,"parameters":{"mode":"missing_role","target_role":"conclusion","provided_roles":["base_case","induction_hypothesis","induction_step"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":15,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":15,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_hypothesis\",\"induction_step\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"conclusion\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0016","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「據此斷言所有 n∈N 的 P(n)」。草稿另列出 P(0) 到 P(16) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"conclusion","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「據此斷言所有 n∈N 的 P(n)」在此草稿中扮演 conclusion；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260989,"parameters":{"mode":"identify_role","target_role":"conclusion","provided_roles":["conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":16,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":16,\"mode\":\"identify_role\",\"provided_roles\":[\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"conclusion\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0017","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：令 n 為任意自然數並暫設 P(n)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(17) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「證明 P(0)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260990,"parameters":{"mode":"missing_role","target_role":"base_case","provided_roles":["induction_hypothesis","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":17,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":17,\"mode\":\"missing_role\",\"provided_roles\":[\"induction_hypothesis\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0018","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「證明 P(0)」。草稿另列出 P(0) 到 P(18) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"base_case","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「證明 P(0)」在此草稿中扮演 base_case；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260991,"parameters":{"mode":"identify_role","target_role":"base_case","provided_roles":["base_case"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":18,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":18,\"mode\":\"identify_role\",\"provided_roles\":[\"base_case\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"base_case\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0019","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿已明示：證明 P(0)；在歸納假設下證明 P(n+1)；據此斷言所有 n∈N 的 P(n)。草稿另列出 P(0) 到 P(19) 的有限例子；這本身不構成普遍證明。下列哪個歸納角色缺漏？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"草稿缺少「令 n 為任意自然數並暫設 P(n)」這個角色；列出有限例子不能補足歸納證明義務。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260992,"parameters":{"mode":"missing_role","target_role":"induction_hypothesis","provided_roles":["base_case","induction_step","conclusion"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":19,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":19,\"mode\":\"missing_role\",\"provided_roles\":[\"base_case\",\"induction_step\",\"conclusion\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-induction-proof-obligation-0020","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-induction"],"title_zh":"歸納證明義務辨識","stem_zh":"對從 0 起的命題族 P(n)，草稿中的步驟是「令 n 為任意自然數並暫設 P(n)」。草稿另列出 P(0) 到 P(20) 的有限例子；這本身不構成普遍證明。它扮演哪個歸納角色？","answer":{"kind":"choice","value":"induction_hypothesis","choices":["base_case","induction_hypothesis","induction_step","conclusion"],"explanation_zh":"「令 n 為任意自然數並暫設 P(n)」在此草稿中扮演 induction_hypothesis；這只是角色辨識，並不表示命題已被證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學歸納法","證明義務"]},"variant":{"family_id":"qf-induction-proof-obligation","seed":20260993,"parameters":{"mode":"identify_role","target_role":"induction_hypothesis","provided_roles":["induction_hypothesis"],"base_index":0,"step_relation":"P(n)_implies_P(n+1)","finite_examples_checked":20,"semantic_template":"qf-induction-proof-obligation/{\"base_index\":0,\"finite_examples_checked\":20,\"mode\":\"identify_role\",\"provided_roles\":[\"induction_hypothesis\"],\"step_relation\":\"P(n)_implies_P(n+1)\",\"target_role\":\"induction_hypothesis\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0001","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一件工作可由兩個明示互斥分支完成，分支數分別為 2 與 3。總數是多少？","answer":{"kind":"numeric","value":5,"explanation_zh":"分支已明示互斥，所以 2+3=5。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260994,"parameters":{"mode":"addition_disjoint","branch_counts":[2,3],"stages":[2,3],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[2,3],\"mode\":\"addition_disjoint\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0002","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一個流程有兩個連續階段；第一階段有 3 種選擇，且每一種之後第二階段固定有 5 種選擇。總組合數是多少？","answer":{"kind":"numeric","value":15,"explanation_zh":"每一個第一階段選擇後都有固定 5 種後續選擇，所以 3×5=15。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260995,"parameters":{"mode":"multiplication_fixed","branch_counts":[3,4],"stages":[3,5],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"mode\":\"multiplication_fixed\",\"stages\":[3,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0003","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"兩個選擇分支各報稱有 4 與 5 種結果，但都包含「共用結果3」。是否可無條件直接相加？","answer":{"kind":"choice","value":"不可無條件相加","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"「共用結果3」同時屬於兩分支，直接相加會重複計數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260996,"parameters":{"mode":"addition_overlap","branch_counts":[4,5],"stages":[4,7],"overlap_witness":"共用結果3","conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[4,5],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果3\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0004","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"流程第一階段有 5 種選擇；第二階段的選項數會隨第一步而為 4 或 5。是否可無條件套用固定乘法？","answer":{"kind":"choice","value":"不可無條件相乘","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"第二階段選項數為 4 或 5，依前一步改變，不能無條件使用單一乘積。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260997,"parameters":{"mode":"multiplication_conditional","branch_counts":[5,6],"stages":[5,4],"overlap_witness":null,"conditional_stage_witness":[4,5],"semantic_template":"qf-basic-counting-principle/{\"conditional_stage_witness\":[4,5],\"mode\":\"multiplication_conditional\",\"stages\":[5,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0005","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一件工作可由兩個明示互斥分支完成，分支數分別為 6 與 7。總數是多少？","answer":{"kind":"numeric","value":13,"explanation_zh":"分支已明示互斥，所以 6+7=13。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260998,"parameters":{"mode":"addition_disjoint","branch_counts":[6,7],"stages":[2,6],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[6,7],\"mode\":\"addition_disjoint\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0006","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一個流程有兩個連續階段；第一階段有 3 種選擇，且每一種之後第二階段固定有 3 種選擇。總組合數是多少？","answer":{"kind":"numeric","value":9,"explanation_zh":"每一個第一階段選擇後都有固定 3 種後續選擇，所以 3×3=9。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20260999,"parameters":{"mode":"multiplication_fixed","branch_counts":[7,8],"stages":[3,3],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"mode\":\"multiplication_fixed\",\"stages\":[3,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0007","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"兩個選擇分支各報稱有 8 與 3 種結果，但都包含「共用結果7」。是否可無條件直接相加？","answer":{"kind":"choice","value":"不可無條件相加","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"「共用結果7」同時屬於兩分支，直接相加會重複計數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261000,"parameters":{"mode":"addition_overlap","branch_counts":[8,3],"stages":[4,5],"overlap_witness":"共用結果7","conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[8,3],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果7\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0008","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"流程第一階段有 5 種選擇；第二階段的選項數會隨第一步而為 7 或 8。是否可無條件套用固定乘法？","answer":{"kind":"choice","value":"不可無條件相乘","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"第二階段選項數為 7 或 8，依前一步改變，不能無條件使用單一乘積。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261001,"parameters":{"mode":"multiplication_conditional","branch_counts":[9,4],"stages":[5,7],"overlap_witness":null,"conditional_stage_witness":[7,8],"semantic_template":"qf-basic-counting-principle/{\"conditional_stage_witness\":[7,8],\"mode\":\"multiplication_conditional\",\"stages\":[5,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0009","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一件工作可由兩個明示互斥分支完成，分支數分別為 10 與 5。總數是多少？","answer":{"kind":"numeric","value":15,"explanation_zh":"分支已明示互斥，所以 10+5=15。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261002,"parameters":{"mode":"addition_disjoint","branch_counts":[10,5],"stages":[2,4],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[10,5],\"mode\":\"addition_disjoint\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0010","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一個流程有兩個連續階段；第一階段有 3 種選擇，且每一種之後第二階段固定有 6 種選擇。總組合數是多少？","answer":{"kind":"numeric","value":18,"explanation_zh":"每一個第一階段選擇後都有固定 6 種後續選擇，所以 3×6=18。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261003,"parameters":{"mode":"multiplication_fixed","branch_counts":[11,6],"stages":[3,6],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"mode\":\"multiplication_fixed\",\"stages\":[3,6]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0011","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"兩個選擇分支各報稱有 12 與 7 種結果，但都包含「共用結果11」。是否可無條件直接相加？","answer":{"kind":"choice","value":"不可無條件相加","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"「共用結果11」同時屬於兩分支，直接相加會重複計數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261004,"parameters":{"mode":"addition_overlap","branch_counts":[12,7],"stages":[4,3],"overlap_witness":"共用結果11","conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[12,7],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果11\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0012","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"流程第一階段有 5 種選擇；第二階段的選項數會隨第一步而為 5 或 6。是否可無條件套用固定乘法？","answer":{"kind":"choice","value":"不可無條件相乘","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"第二階段選項數為 5 或 6，依前一步改變，不能無條件使用單一乘積。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261005,"parameters":{"mode":"multiplication_conditional","branch_counts":[13,8],"stages":[5,5],"overlap_witness":null,"conditional_stage_witness":[5,6],"semantic_template":"qf-basic-counting-principle/{\"conditional_stage_witness\":[5,6],\"mode\":\"multiplication_conditional\",\"stages\":[5,5]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0013","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一件工作可由兩個明示互斥分支完成，分支數分別為 14 與 3。總數是多少？","answer":{"kind":"numeric","value":17,"explanation_zh":"分支已明示互斥，所以 14+3=17。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261006,"parameters":{"mode":"addition_disjoint","branch_counts":[14,3],"stages":[2,7],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[14,3],\"mode\":\"addition_disjoint\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0014","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一個流程有兩個連續階段；第一階段有 3 種選擇，且每一種之後第二階段固定有 4 種選擇。總組合數是多少？","answer":{"kind":"numeric","value":12,"explanation_zh":"每一個第一階段選擇後都有固定 4 種後續選擇，所以 3×4=12。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261007,"parameters":{"mode":"multiplication_fixed","branch_counts":[15,4],"stages":[3,4],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"mode\":\"multiplication_fixed\",\"stages\":[3,4]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0015","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"兩個選擇分支各報稱有 16 與 5 種結果，但都包含「共用結果15」。是否可無條件直接相加？","answer":{"kind":"choice","value":"不可無條件相加","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"「共用結果15」同時屬於兩分支，直接相加會重複計數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261008,"parameters":{"mode":"addition_overlap","branch_counts":[16,5],"stages":[4,6],"overlap_witness":"共用結果15","conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[16,5],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果15\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0016","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"流程第一階段有 5 種選擇；第二階段的選項數會隨第一步而為 3 或 4。是否可無條件套用固定乘法？","answer":{"kind":"choice","value":"不可無條件相乘","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"第二階段選項數為 3 或 4，依前一步改變，不能無條件使用單一乘積。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261009,"parameters":{"mode":"multiplication_conditional","branch_counts":[17,6],"stages":[5,3],"overlap_witness":null,"conditional_stage_witness":[3,4],"semantic_template":"qf-basic-counting-principle/{\"conditional_stage_witness\":[3,4],\"mode\":\"multiplication_conditional\",\"stages\":[5,3]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0017","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一件工作可由兩個明示互斥分支完成，分支數分別為 18 與 7。總數是多少？","answer":{"kind":"numeric","value":25,"explanation_zh":"分支已明示互斥，所以 18+7=25。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261010,"parameters":{"mode":"addition_disjoint","branch_counts":[18,7],"stages":[2,5],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[18,7],\"mode\":\"addition_disjoint\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0018","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"一個流程有兩個連續階段；第一階段有 3 種選擇，且每一種之後第二階段固定有 7 種選擇。總組合數是多少？","answer":{"kind":"numeric","value":21,"explanation_zh":"每一個第一階段選擇後都有固定 7 種後續選擇，所以 3×7=21。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261011,"parameters":{"mode":"multiplication_fixed","branch_counts":[19,8],"stages":[3,7],"overlap_witness":null,"conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"mode\":\"multiplication_fixed\",\"stages\":[3,7]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0019","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"兩個選擇分支各報稱有 20 與 3 種結果，但都包含「共用結果19」。是否可無條件直接相加？","answer":{"kind":"choice","value":"不可無條件相加","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"「共用結果19」同時屬於兩分支，直接相加會重複計數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261012,"parameters":{"mode":"addition_overlap","branch_counts":[20,3],"stages":[4,4],"overlap_witness":"共用結果19","conditional_stage_witness":null,"semantic_template":"qf-basic-counting-principle/{\"branch_counts\":[20,3],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果19\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260914-basic-counting-principle-0020","batch_id":"batch-20260914-domain-foundations","language":"zh-Hant","source_mko_ids":["mko-counting-principle"],"title_zh":"基本計數原理邊界","stem_zh":"流程第一階段有 5 種選擇；第二階段的選項數會隨第一步而為 6 或 7。是否可無條件套用固定乘法？","answer":{"kind":"choice","value":"不可無條件相乘","choices":["不可無條件相加","不可無條件相乘"],"explanation_zh":"第二階段選項數為 6 或 7，依前一步改變，不能無條件使用單一乘積。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["基本計數原理","條件辨識"]},"variant":{"family_id":"qf-basic-counting-principle","seed":20261013,"parameters":{"mode":"multiplication_conditional","branch_counts":[21,4],"stages":[5,6],"overlap_witness":null,"conditional_stage_witness":[6,7],"semantic_template":"qf-basic-counting-principle/{\"conditional_stage_witness\":[6,7],\"mode\":\"multiplication_conditional\",\"stages\":[5,6]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-14","contract_version":"ocme-question-factory-v0.1"}}