{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0001","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 A、A、C；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260926,"parameters":{"vertices":["A","A","C"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"A\",\"A\",\"C\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0002","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 D、E、F；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260927,"parameters":{"vertices":["D","E","F"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"D\",\"E\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0003","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 G、H、I；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260928,"parameters":{"vertices":["G","H","I"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"G\",\"H\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0004","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 J、K、L；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260929,"parameters":{"vertices":["J","K","L"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"J\",\"K\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0005","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 M、M、P；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260930,"parameters":{"vertices":["M","M","P"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"M\",\"M\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0006","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 Q、R、S；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點相異且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260931,"parameters":{"vertices":["Q","R","S"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"Q\",\"R\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0007","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 T、U、V；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260932,"parameters":{"vertices":["T","U","V"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"T\",\"U\",\"V\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0008","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 W、X、Y；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260933,"parameters":{"vertices":["W","X","Y"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"W\",\"X\",\"Y\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0009","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 A、A、D；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260934,"parameters":{"vertices":["A","A","D"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"A\",\"A\",\"D\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0010","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 A、C、E；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260935,"parameters":{"vertices":["A","C","E"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"A\",\"C\",\"E\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0011","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 B、D、F；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點相異且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260936,"parameters":{"vertices":["B","D","F"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"B\",\"D\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0012","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 C、E、G；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260937,"parameters":{"vertices":["C","E","G"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"C\",\"E\",\"G\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0013","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 D、D、H；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260938,"parameters":{"vertices":["D","D","H"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"D\",\"D\",\"H\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0014","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 E、G、I；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260939,"parameters":{"vertices":["E","G","I"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"E\",\"G\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0015","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 F、H、J；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260940,"parameters":{"vertices":["F","H","J"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"F\",\"H\",\"J\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0016","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 G、I、K；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點相異且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260941,"parameters":{"vertices":["G","I","K"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"G\",\"I\",\"K\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0017","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 H、H、L；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260942,"parameters":{"vertices":["H","H","L"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"H\",\"H\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0018","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 I、K、M；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260943,"parameters":{"vertices":["I","K","M"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"I\",\"K\",\"M\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0019","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 J、L、N；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260944,"parameters":{"vertices":["J","L","N"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"J\",\"L\",\"N\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0020","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 K、M、O；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260945,"parameters":{"vertices":["K","M","O"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"K\",\"M\",\"O\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0021","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 L、L、P；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260946,"parameters":{"vertices":["L","L","P"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"L\",\"L\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0022","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 M、O、Q；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260947,"parameters":{"vertices":["M","O","Q"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"M\",\"O\",\"Q\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0023","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 N、P、R；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260948,"parameters":{"vertices":["N","P","R"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"N\",\"P\",\"R\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0024","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 O、Q、S；題幹明示它們不共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"三點相異且不共線，所以形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260949,"parameters":{"vertices":["O","Q","S"],"noncollinear":true,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"O\",\"Q\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-explicit-validity-0025","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"明示條件下的三角形有效性","stem_zh":"三點依序為 P、P、T；題幹明示它們共線。只依相異與不共線條件，是否形成非退化三角形？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"三點有重複且共線，所以不形成本條目的非退化三角形。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["相異頂點","不共線"]},"variant":{"family_id":"qf-triangle-explicit-validity","seed":20260950,"parameters":{"vertices":["P","P","T"],"noncollinear":false,"operation":"validity","semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"P\",\"P\",\"T\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0001","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 ABC；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{A, B, C}","explanation_zh":"由標記取三個頂點並排序，得到 {A, B, C}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261026,"parameters":{"vertices":["A","B","C"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"B\",\"C\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0002","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 DEF；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{D, E, F}","explanation_zh":"由標記取三個頂點並排序，得到 {D, E, F}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261027,"parameters":{"vertices":["D","E","F"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"D\",\"E\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0003","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 GHI；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{G, H, I}","explanation_zh":"由標記取三個頂點並排序，得到 {G, H, I}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261028,"parameters":{"vertices":["G","H","I"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"G\",\"H\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0004","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 JKL；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{J, K, L}","explanation_zh":"由標記取三個頂點並排序，得到 {J, K, L}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261029,"parameters":{"vertices":["J","K","L"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"J\",\"K\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0005","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 MNP；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{M, N, P}","explanation_zh":"由標記取三個頂點並排序，得到 {M, N, P}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261030,"parameters":{"vertices":["M","N","P"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"M\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0006","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 QRS；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{Q, R, S}","explanation_zh":"由標記取三個頂點並排序，得到 {Q, R, S}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261031,"parameters":{"vertices":["Q","R","S"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"Q\",\"R\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0007","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 TUV；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{T, U, V}","explanation_zh":"由標記取三個頂點並排序，得到 {T, U, V}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261032,"parameters":{"vertices":["T","U","V"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"T\",\"U\",\"V\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0008","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 WXY；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{W, X, Y}","explanation_zh":"由標記取三個頂點並排序，得到 {W, X, Y}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261033,"parameters":{"vertices":["W","X","Y"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"W\",\"X\",\"Y\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0009","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 ABD；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{A, B, D}","explanation_zh":"由標記取三個頂點並排序，得到 {A, B, D}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261034,"parameters":{"vertices":["A","B","D"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"B\",\"D\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0010","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 ACE；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{A, C, E}","explanation_zh":"由標記取三個頂點並排序，得到 {A, C, E}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261035,"parameters":{"vertices":["A","C","E"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"C\",\"E\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0011","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 BDF；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{B, D, F}","explanation_zh":"由標記取三個頂點並排序，得到 {B, D, F}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261036,"parameters":{"vertices":["B","D","F"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"B\",\"D\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0012","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 CEG；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{C, E, G}","explanation_zh":"由標記取三個頂點並排序，得到 {C, E, G}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261037,"parameters":{"vertices":["C","E","G"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"C\",\"E\",\"G\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0013","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 DFH；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{D, F, H}","explanation_zh":"由標記取三個頂點並排序，得到 {D, F, H}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261038,"parameters":{"vertices":["D","F","H"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"D\",\"F\",\"H\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0014","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 EGI；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{E, G, I}","explanation_zh":"由標記取三個頂點並排序，得到 {E, G, I}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261039,"parameters":{"vertices":["E","G","I"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"E\",\"G\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0015","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 FHJ；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{F, H, J}","explanation_zh":"由標記取三個頂點並排序，得到 {F, H, J}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261040,"parameters":{"vertices":["F","H","J"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"F\",\"H\",\"J\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0016","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 GIK；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{G, I, K}","explanation_zh":"由標記取三個頂點並排序，得到 {G, I, K}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261041,"parameters":{"vertices":["G","I","K"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"G\",\"I\",\"K\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0017","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 HJL；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{H, J, L}","explanation_zh":"由標記取三個頂點並排序，得到 {H, J, L}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261042,"parameters":{"vertices":["H","J","L"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"H\",\"J\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0018","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 IKM；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{I, K, M}","explanation_zh":"由標記取三個頂點並排序，得到 {I, K, M}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261043,"parameters":{"vertices":["I","K","M"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"I\",\"K\",\"M\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0019","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 JLN；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{J, L, N}","explanation_zh":"由標記取三個頂點並排序，得到 {J, L, N}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261044,"parameters":{"vertices":["J","L","N"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"J\",\"L\",\"N\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0020","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 KMO；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{K, M, O}","explanation_zh":"由標記取三個頂點並排序，得到 {K, M, O}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261045,"parameters":{"vertices":["K","M","O"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"K\",\"M\",\"O\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0021","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 LNP；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{L, N, P}","explanation_zh":"由標記取三個頂點並排序，得到 {L, N, P}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261046,"parameters":{"vertices":["L","N","P"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"L\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0022","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 MOQ；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{M, O, Q}","explanation_zh":"由標記取三個頂點並排序，得到 {M, O, Q}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261047,"parameters":{"vertices":["M","O","Q"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"M\",\"O\",\"Q\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0023","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 NPR；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{N, P, R}","explanation_zh":"由標記取三個頂點並排序，得到 {N, P, R}。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261048,"parameters":{"vertices":["N","P","R"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"N\",\"P\",\"R\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0024","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 OQS；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{O, Q, S}","explanation_zh":"由標記取三個頂點並排序，得到 {O, Q, S}。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261049,"parameters":{"vertices":["O","Q","S"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"O\",\"Q\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-vertex-set-0025","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的頂點集合","stem_zh":"三角形標記為 PRT；三頂點相異且不共線已明示。以 canonical 排序寫出頂點集合。","answer":{"kind":"short_text","value":"{P, R, T}","explanation_zh":"由標記取三個頂點並排序，得到 {P, R, T}。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點集合","canonical 排序"]},"variant":{"family_id":"qf-triangle-vertex-set","seed":20261050,"parameters":{"vertices":["P","R","T"],"noncollinear":true,"operation":"vertex_set","semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"P\",\"R\",\"T\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0001","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 ABC；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"AB, AC, BC","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 AB, AC, BC。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261126,"parameters":{"vertices":["A","B","C"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"B\",\"C\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0002","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 DEF；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"DE, DF, EF","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 DE, DF, EF。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261127,"parameters":{"vertices":["D","E","F"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"D\",\"E\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0003","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 GHI；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"GH, GI, HI","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 GH, GI, HI。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261128,"parameters":{"vertices":["G","H","I"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"G\",\"H\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0004","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 JKL；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"JK, JL, KL","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 JK, JL, KL。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261129,"parameters":{"vertices":["J","K","L"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"J\",\"K\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0005","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 MNP；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"MN, MP, NP","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 MN, MP, NP。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261130,"parameters":{"vertices":["M","N","P"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"M\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0006","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 QRS；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"QR, QS, RS","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 QR, QS, RS。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261131,"parameters":{"vertices":["Q","R","S"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"Q\",\"R\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0007","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 TUV；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"TU, TV, UV","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 TU, TV, UV。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261132,"parameters":{"vertices":["T","U","V"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"T\",\"U\",\"V\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0008","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 WXY；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"WX, WY, XY","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 WX, WY, XY。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261133,"parameters":{"vertices":["W","X","Y"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"W\",\"X\",\"Y\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0009","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 ABD；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"AB, AD, BD","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 AB, AD, BD。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261134,"parameters":{"vertices":["A","B","D"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"B\",\"D\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0010","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 ACE；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"AC, AE, CE","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 AC, AE, CE。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261135,"parameters":{"vertices":["A","C","E"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"C\",\"E\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0011","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 BDF；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"BD, BF, DF","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 BD, BF, DF。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261136,"parameters":{"vertices":["B","D","F"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"B\",\"D\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0012","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 CEG；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"CE, CG, EG","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 CE, CG, EG。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261137,"parameters":{"vertices":["C","E","G"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"C\",\"E\",\"G\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0013","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 DFH；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"DF, DH, FH","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 DF, DH, FH。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261138,"parameters":{"vertices":["D","F","H"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"D\",\"F\",\"H\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0014","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 EGI；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"EG, EI, GI","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 EG, EI, GI。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261139,"parameters":{"vertices":["E","G","I"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"E\",\"G\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0015","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 FHJ；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"FH, FJ, HJ","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 FH, FJ, HJ。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261140,"parameters":{"vertices":["F","H","J"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"F\",\"H\",\"J\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0016","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 GIK；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"GI, GK, IK","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 GI, GK, IK。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261141,"parameters":{"vertices":["G","I","K"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"G\",\"I\",\"K\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0017","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 HJL；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"HJ, HL, JL","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 HJ, HL, JL。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261142,"parameters":{"vertices":["H","J","L"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"H\",\"J\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0018","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 IKM；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"IK, IM, KM","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 IK, IM, KM。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261143,"parameters":{"vertices":["I","K","M"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"I\",\"K\",\"M\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0019","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 JLN；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"JL, JN, LN","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 JL, JN, LN。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261144,"parameters":{"vertices":["J","L","N"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"J\",\"L\",\"N\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0020","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 KMO；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"KM, KO, MO","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 KM, KO, MO。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261145,"parameters":{"vertices":["K","M","O"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"K\",\"M\",\"O\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0021","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 LNP；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"LN, LP, NP","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 LN, LP, NP。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261146,"parameters":{"vertices":["L","N","P"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"L\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0022","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 MOQ；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"MO, MQ, OQ","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 MO, MQ, OQ。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261147,"parameters":{"vertices":["M","O","Q"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"M\",\"O\",\"Q\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0023","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 NPR；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"NP, NR, PR","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 NP, NR, PR。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261148,"parameters":{"vertices":["N","P","R"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"N\",\"P\",\"R\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0024","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 OQS；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"OQ, OS, QS","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 OQ, OS, QS。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261149,"parameters":{"vertices":["O","Q","S"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"O\",\"Q\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-side-set-0025","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"三角形的無向邊集合","stem_zh":"三角形標記為 PRT；三頂點相異且不共線已明示。以 canonical 排序列出三條無向邊。","answer":{"kind":"short_text","value":"PR, PT, RT","explanation_zh":"由三頂點兩兩連接並把無向邊 canonical 排序，得到 PR, PT, RT。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["無向邊","canonical 排序"]},"variant":{"family_id":"qf-triangle-side-set","seed":20261150,"parameters":{"vertices":["P","R","T"],"noncollinear":true,"operation":"side_set","semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"P\",\"R\",\"T\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0001","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 ABC；三頂點相異且不共線已明示。頂點 A 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"BC","explanation_zh":"移除頂點 A 後，另外兩頂點形成無向邊 BC。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261226,"parameters":{"vertices":["A","B","C"],"noncollinear":true,"vertex":"A","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"A\",\"vertices\":[\"A\",\"B\",\"C\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0002","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 DEF；三頂點相異且不共線已明示。頂點 E 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"DF","explanation_zh":"移除頂點 E 後，另外兩頂點形成無向邊 DF。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261227,"parameters":{"vertices":["D","E","F"],"noncollinear":true,"vertex":"E","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"E\",\"vertices\":[\"D\",\"E\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0003","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 GHI；三頂點相異且不共線已明示。頂點 I 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"GH","explanation_zh":"移除頂點 I 後，另外兩頂點形成無向邊 GH。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261228,"parameters":{"vertices":["G","H","I"],"noncollinear":true,"vertex":"I","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"I\",\"vertices\":[\"G\",\"H\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0004","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 JKL；三頂點相異且不共線已明示。頂點 J 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"KL","explanation_zh":"移除頂點 J 後，另外兩頂點形成無向邊 KL。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261229,"parameters":{"vertices":["J","K","L"],"noncollinear":true,"vertex":"J","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"J\",\"K\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0005","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 MNP；三頂點相異且不共線已明示。頂點 N 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"MP","explanation_zh":"移除頂點 N 後，另外兩頂點形成無向邊 MP。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261230,"parameters":{"vertices":["M","N","P"],"noncollinear":true,"vertex":"N","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"N\",\"vertices\":[\"M\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0006","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 QRS；三頂點相異且不共線已明示。頂點 S 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"QR","explanation_zh":"移除頂點 S 後，另外兩頂點形成無向邊 QR。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261231,"parameters":{"vertices":["Q","R","S"],"noncollinear":true,"vertex":"S","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"S\",\"vertices\":[\"Q\",\"R\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0007","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 TUV；三頂點相異且不共線已明示。頂點 T 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"UV","explanation_zh":"移除頂點 T 後，另外兩頂點形成無向邊 UV。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261232,"parameters":{"vertices":["T","U","V"],"noncollinear":true,"vertex":"T","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"T\",\"vertices\":[\"T\",\"U\",\"V\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0008","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 WXY；三頂點相異且不共線已明示。頂點 X 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"WY","explanation_zh":"移除頂點 X 後，另外兩頂點形成無向邊 WY。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261233,"parameters":{"vertices":["W","X","Y"],"noncollinear":true,"vertex":"X","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"X\",\"vertices\":[\"W\",\"X\",\"Y\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0009","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 ABD；三頂點相異且不共線已明示。頂點 D 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"AB","explanation_zh":"移除頂點 D 後，另外兩頂點形成無向邊 AB。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261234,"parameters":{"vertices":["A","B","D"],"noncollinear":true,"vertex":"D","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"A\",\"B\",\"D\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0010","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 ACE；三頂點相異且不共線已明示。頂點 A 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"CE","explanation_zh":"移除頂點 A 後，另外兩頂點形成無向邊 CE。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261235,"parameters":{"vertices":["A","C","E"],"noncollinear":true,"vertex":"A","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"A\",\"vertices\":[\"A\",\"C\",\"E\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0011","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 BDF；三頂點相異且不共線已明示。頂點 D 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"BF","explanation_zh":"移除頂點 D 後，另外兩頂點形成無向邊 BF。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261236,"parameters":{"vertices":["B","D","F"],"noncollinear":true,"vertex":"D","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"B\",\"D\",\"F\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0012","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 CEG；三頂點相異且不共線已明示。頂點 G 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"CE","explanation_zh":"移除頂點 G 後，另外兩頂點形成無向邊 CE。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261237,"parameters":{"vertices":["C","E","G"],"noncollinear":true,"vertex":"G","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"C\",\"E\",\"G\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0013","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 DFH；三頂點相異且不共線已明示。頂點 D 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"FH","explanation_zh":"移除頂點 D 後，另外兩頂點形成無向邊 FH。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261238,"parameters":{"vertices":["D","F","H"],"noncollinear":true,"vertex":"D","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"D\",\"F\",\"H\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0014","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 EGI；三頂點相異且不共線已明示。頂點 G 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"EI","explanation_zh":"移除頂點 G 後，另外兩頂點形成無向邊 EI。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261239,"parameters":{"vertices":["E","G","I"],"noncollinear":true,"vertex":"G","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"E\",\"G\",\"I\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0015","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 FHJ；三頂點相異且不共線已明示。頂點 J 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"FH","explanation_zh":"移除頂點 J 後，另外兩頂點形成無向邊 FH。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261240,"parameters":{"vertices":["F","H","J"],"noncollinear":true,"vertex":"J","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"F\",\"H\",\"J\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0016","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 GIK；三頂點相異且不共線已明示。頂點 G 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"IK","explanation_zh":"移除頂點 G 後，另外兩頂點形成無向邊 IK。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261241,"parameters":{"vertices":["G","I","K"],"noncollinear":true,"vertex":"G","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"G\",\"I\",\"K\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0017","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 HJL；三頂點相異且不共線已明示。頂點 J 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"HL","explanation_zh":"移除頂點 J 後，另外兩頂點形成無向邊 HL。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261242,"parameters":{"vertices":["H","J","L"],"noncollinear":true,"vertex":"J","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"H\",\"J\",\"L\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0018","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 IKM；三頂點相異且不共線已明示。頂點 M 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"IK","explanation_zh":"移除頂點 M 後，另外兩頂點形成無向邊 IK。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261243,"parameters":{"vertices":["I","K","M"],"noncollinear":true,"vertex":"M","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"I\",\"K\",\"M\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0019","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 JLN；三頂點相異且不共線已明示。頂點 J 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"LN","explanation_zh":"移除頂點 J 後，另外兩頂點形成無向邊 LN。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261244,"parameters":{"vertices":["J","L","N"],"noncollinear":true,"vertex":"J","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"J\",\"L\",\"N\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0020","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 KMO；三頂點相異且不共線已明示。頂點 M 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"KO","explanation_zh":"移除頂點 M 後，另外兩頂點形成無向邊 KO。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261245,"parameters":{"vertices":["K","M","O"],"noncollinear":true,"vertex":"M","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"K\",\"M\",\"O\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0021","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 LNP；三頂點相異且不共線已明示。頂點 P 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"LN","explanation_zh":"移除頂點 P 後，另外兩頂點形成無向邊 LN。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261246,"parameters":{"vertices":["L","N","P"],"noncollinear":true,"vertex":"P","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"L\",\"N\",\"P\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0022","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 MOQ；三頂點相異且不共線已明示。頂點 M 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"OQ","explanation_zh":"移除頂點 M 後，另外兩頂點形成無向邊 OQ。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261247,"parameters":{"vertices":["M","O","Q"],"noncollinear":true,"vertex":"M","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"M\",\"O\",\"Q\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0023","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 NPR；三頂點相異且不共線已明示。頂點 P 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"NR","explanation_zh":"移除頂點 P 後，另外兩頂點形成無向邊 NR。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261248,"parameters":{"vertices":["N","P","R"],"noncollinear":true,"vertex":"P","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"N\",\"P\",\"R\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0024","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 OQS；三頂點相異且不共線已明示。頂點 S 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"OQ","explanation_zh":"移除頂點 S 後，另外兩頂點形成無向邊 OQ。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261249,"parameters":{"vertices":["O","Q","S"],"noncollinear":true,"vertex":"S","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"S\",\"vertices\":[\"O\",\"Q\",\"S\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260925-triangle-opposite-side-0025","batch_id":"batch-20260925-triangle-object-language","language":"zh-Hant","source_mko_ids":["mko-triangle"],"title_zh":"頂點的對邊","stem_zh":"三角形標記為 PRT；三頂點相異且不共線已明示。頂點 P 的對邊是哪一條無向邊？","answer":{"kind":"short_text","value":"RT","explanation_zh":"移除頂點 P 後，另外兩頂點形成無向邊 RT。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["頂點","對邊"]},"variant":{"family_id":"qf-triangle-opposite-side","seed":20261250,"parameters":{"vertices":["P","R","T"],"noncollinear":true,"vertex":"P","operation":"opposite_side","semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"P\",\"R\",\"T\"]}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-25","contract_version":"ocme-question-factory-v0.1"}}