{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -12:(1) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-12/1","explanation_zh":"依順序計算前項除以後項，數值比為 -12/(1)，正規化後為 -12/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302001,"parameters":{"operation":"ratio_value","a":-12,"b":1,"semantic_template":"qf-ratio-exact-value/{\"a\":-12,\"b\":1,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -11:(-2) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"11/2","explanation_zh":"依順序計算前項除以後項，數值比為 -11/(-2)，正規化後為 11/2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302002,"parameters":{"operation":"ratio_value","a":-11,"b":-2,"semantic_template":"qf-ratio-exact-value/{\"a\":-11,\"b\":-2,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -10:(3) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-10/3","explanation_zh":"依順序計算前項除以後項，數值比為 -10/(3)，正規化後為 -10/3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302003,"parameters":{"operation":"ratio_value","a":-10,"b":3,"semantic_template":"qf-ratio-exact-value/{\"a\":-10,\"b\":3,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -9:(-4) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"9/4","explanation_zh":"依順序計算前項除以後項，數值比為 -9/(-4)，正規化後為 9/4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302004,"parameters":{"operation":"ratio_value","a":-9,"b":-4,"semantic_template":"qf-ratio-exact-value/{\"a\":-9,\"b\":-4,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -8:(5) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-8/5","explanation_zh":"依順序計算前項除以後項，數值比為 -8/(5)，正規化後為 -8/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302005,"parameters":{"operation":"ratio_value","a":-8,"b":5,"semantic_template":"qf-ratio-exact-value/{\"a\":-8,\"b\":5,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -7:(-6) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"7/6","explanation_zh":"依順序計算前項除以後項，數值比為 -7/(-6)，正規化後為 7/6。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302006,"parameters":{"operation":"ratio_value","a":-7,"b":-6,"semantic_template":"qf-ratio-exact-value/{\"a\":-7,\"b\":-6,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -6:(7) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-6/7","explanation_zh":"依順序計算前項除以後項，數值比為 -6/(7)，正規化後為 -6/7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302007,"parameters":{"operation":"ratio_value","a":-6,"b":7,"semantic_template":"qf-ratio-exact-value/{\"a\":-6,\"b\":7,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -5:(-8) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"5/8","explanation_zh":"依順序計算前項除以後項，數值比為 -5/(-8)，正規化後為 5/8。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302008,"parameters":{"operation":"ratio_value","a":-5,"b":-8,"semantic_template":"qf-ratio-exact-value/{\"a\":-5,\"b\":-8,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -4:(1) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-4/1","explanation_zh":"依順序計算前項除以後項，數值比為 -4/(1)，正規化後為 -4/1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302009,"parameters":{"operation":"ratio_value","a":-4,"b":1,"semantic_template":"qf-ratio-exact-value/{\"a\":-4,\"b\":1,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -3:(-2) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"3/2","explanation_zh":"依順序計算前項除以後項，數值比為 -3/(-2)，正規化後為 3/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302010,"parameters":{"operation":"ratio_value","a":-3,"b":-2,"semantic_template":"qf-ratio-exact-value/{\"a\":-3,\"b\":-2,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -2:(3) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-2/3","explanation_zh":"依順序計算前項除以後項，數值比為 -2/(3)，正規化後為 -2/3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302011,"parameters":{"operation":"ratio_value","a":-2,"b":3,"semantic_template":"qf-ratio-exact-value/{\"a\":-2,\"b\":3,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 -1:(-4) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"1/4","explanation_zh":"依順序計算前項除以後項，數值比為 -1/(-4)，正規化後為 1/4。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302012,"parameters":{"operation":"ratio_value","a":-1,"b":-4,"semantic_template":"qf-ratio-exact-value/{\"a\":-1,\"b\":-4,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 0:(5) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"0/1","explanation_zh":"依順序計算前項除以後項，數值比為 0/(5)，正規化後為 0/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302013,"parameters":{"operation":"ratio_value","a":0,"b":5,"semantic_template":"qf-ratio-exact-value/{\"a\":0,\"b\":5,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 1:(-6) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-1/6","explanation_zh":"依順序計算前項除以後項，數值比為 1/(-6)，正規化後為 -1/6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302014,"parameters":{"operation":"ratio_value","a":1,"b":-6,"semantic_template":"qf-ratio-exact-value/{\"a\":1,\"b\":-6,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 2:(7) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"2/7","explanation_zh":"依順序計算前項除以後項，數值比為 2/(7)，正規化後為 2/7。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302015,"parameters":{"operation":"ratio_value","a":2,"b":7,"semantic_template":"qf-ratio-exact-value/{\"a\":2,\"b\":7,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 3:(-8) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-3/8","explanation_zh":"依順序計算前項除以後項，數值比為 3/(-8)，正規化後為 -3/8。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302016,"parameters":{"operation":"ratio_value","a":3,"b":-8,"semantic_template":"qf-ratio-exact-value/{\"a\":3,\"b\":-8,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 4:(1) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"4/1","explanation_zh":"依順序計算前項除以後項，數值比為 4/(1)，正規化後為 4/1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302017,"parameters":{"operation":"ratio_value","a":4,"b":1,"semantic_template":"qf-ratio-exact-value/{\"a\":4,\"b\":1,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 5:(-2) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-5/2","explanation_zh":"依順序計算前項除以後項，數值比為 5/(-2)，正規化後為 -5/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302018,"parameters":{"operation":"ratio_value","a":5,"b":-2,"semantic_template":"qf-ratio-exact-value/{\"a\":5,\"b\":-2,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 6:(3) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"2/1","explanation_zh":"依順序計算前項除以後項，數值比為 6/(3)，正規化後為 2/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302019,"parameters":{"operation":"ratio_value","a":6,"b":3,"semantic_template":"qf-ratio-exact-value/{\"a\":6,\"b\":3,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 7:(-4) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-7/4","explanation_zh":"依順序計算前項除以後項，數值比為 7/(-4)，正規化後為 -7/4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302020,"parameters":{"operation":"ratio_value","a":7,"b":-4,"semantic_template":"qf-ratio-exact-value/{\"a\":7,\"b\":-4,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 8:(5) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"8/5","explanation_zh":"依順序計算前項除以後項，數值比為 8/(5)，正規化後為 8/5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302021,"parameters":{"operation":"ratio_value","a":8,"b":5,"semantic_template":"qf-ratio-exact-value/{\"a\":8,\"b\":5,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 9:(-6) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-3/2","explanation_zh":"依順序計算前項除以後項，數值比為 9/(-6)，正規化後為 -3/2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302022,"parameters":{"operation":"ratio_value","a":9,"b":-6,"semantic_template":"qf-ratio-exact-value/{\"a\":9,\"b\":-6,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 10:(7) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"10/7","explanation_zh":"依順序計算前項除以後項，數值比為 10/(7)，正規化後為 10/7。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302023,"parameters":{"operation":"ratio_value","a":10,"b":7,"semantic_template":"qf-ratio-exact-value/{\"a\":10,\"b\":7,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 11:(-8) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"-11/8","explanation_zh":"依順序計算前項除以後項，數值比為 11/(-8)，正規化後為 -11/8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302024,"parameters":{"operation":"ratio_value","a":11,"b":-8,"semantic_template":"qf-ratio-exact-value/{\"a\":11,\"b\":-8,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-ratio-exact-value-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"數值比的精確值","stem_zh":"在有理數數值比語境，求 12:(1) 的精確值。後項非零，答案用最簡正分母 p/q。","answer":{"kind":"short_text","value":"12/1","explanation_zh":"依順序計算前項除以後項，數值比為 12/(1)，正規化後為 12/1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比的順序","非零後項"]},"variant":{"family_id":"qf-ratio-exact-value","seed":202609302025,"parameters":{"operation":"ratio_value","a":12,"b":1,"semantic_template":"qf-ratio-exact-value/{\"a\":12,\"b\":1,\"operation\":\"ratio_value\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-12:(-1)=-24:(-2) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 24, 24；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302101,"parameters":{"operation":"proportion_verification","a":-12,"b":-1,"c":-24,"d":-2,"semantic_template":"qf-proportion-verification/{\"a\":-12,\"b\":-1,\"c\":-24,\"d\":-2,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-11:(2)=34:(-6) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 66, 68；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302102,"parameters":{"operation":"proportion_verification","a":-11,"b":2,"c":34,"d":-6,"semantic_template":"qf-proportion-verification/{\"a\":-11,\"b\":2,\"c\":34,\"d\":-6,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-10:(3)=-40:(12) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -120, -120；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302103,"parameters":{"operation":"proportion_verification","a":-10,"b":3,"c":-40,"d":12,"semantic_template":"qf-proportion-verification/{\"a\":-10,\"b\":3,\"c\":-40,\"d\":12,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-9:(-4)=46:(20) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -180, -184；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302104,"parameters":{"operation":"proportion_verification","a":-9,"b":-4,"c":46,"d":20,"semantic_template":"qf-proportion-verification/{\"a\":-9,\"b\":-4,\"c\":46,\"d\":20,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-8:(5)=-48:(30) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -240, -240；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302105,"parameters":{"operation":"proportion_verification","a":-8,"b":5,"c":-48,"d":30,"semantic_template":"qf-proportion-verification/{\"a\":-8,\"b\":5,\"c\":-48,\"d\":30,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-7:(6)=15:(-12) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 84, 90；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302106,"parameters":{"operation":"proportion_verification","a":-7,"b":6,"c":15,"d":-12,"semantic_template":"qf-proportion-verification/{\"a\":-7,\"b\":6,\"c\":15,\"d\":-12,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-6:(-7)=-18:(-21) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 126, 126；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302107,"parameters":{"operation":"proportion_verification","a":-6,"b":-7,"c":-18,"d":-21,"semantic_template":"qf-proportion-verification/{\"a\":-6,\"b\":-7,\"c\":-18,\"d\":-21,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-5:(8)=21:(-32) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 160, 168；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302108,"parameters":{"operation":"proportion_verification","a":-5,"b":8,"c":21,"d":-32,"semantic_template":"qf-proportion-verification/{\"a\":-5,\"b\":8,\"c\":21,\"d\":-32,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-4:(1)=-20:(5) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -20, -20；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302109,"parameters":{"operation":"proportion_verification","a":-4,"b":1,"c":-20,"d":5,"semantic_template":"qf-proportion-verification/{\"a\":-4,\"b\":1,\"c\":-20,\"d\":5,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-3:(-2)=19:(12) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -36, -38；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302110,"parameters":{"operation":"proportion_verification","a":-3,"b":-2,"c":19,"d":12,"semantic_template":"qf-proportion-verification/{\"a\":-3,\"b\":-2,\"c\":19,\"d\":12,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-2:(3)=-4:(6) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -12, -12；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302111,"parameters":{"operation":"proportion_verification","a":-2,"b":3,"c":-4,"d":6,"semantic_template":"qf-proportion-verification/{\"a\":-2,\"b\":3,\"c\":-4,\"d\":6,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，-1:(4)=4:(-12) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 12, 16；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302112,"parameters":{"operation":"proportion_verification","a":-1,"b":4,"c":4,"d":-12,"semantic_template":"qf-proportion-verification/{\"a\":-1,\"b\":4,\"c\":4,\"d\":-12,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，0:(-5)=0:(-20) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 0, 0；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302113,"parameters":{"operation":"proportion_verification","a":0,"b":-5,"c":0,"d":-20,"semantic_template":"qf-proportion-verification/{\"a\":0,\"b\":-5,\"c\":0,\"d\":-20,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，1:(6)=-4:(-30) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -30, -24；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302114,"parameters":{"operation":"proportion_verification","a":1,"b":6,"c":-4,"d":-30,"semantic_template":"qf-proportion-verification/{\"a\":1,\"b\":6,\"c\":-4,\"d\":-30,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，2:(7)=12:(42) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 84, 84；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302115,"parameters":{"operation":"proportion_verification","a":2,"b":7,"c":12,"d":42,"semantic_template":"qf-proportion-verification/{\"a\":2,\"b\":7,\"c\":12,\"d\":42,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，3:(-8)=-5:(16) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 48, 40；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302116,"parameters":{"operation":"proportion_verification","a":3,"b":-8,"c":-5,"d":16,"semantic_template":"qf-proportion-verification/{\"a\":3,\"b\":-8,\"c\":-5,\"d\":16,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，4:(1)=12:(3) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 12, 12；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302117,"parameters":{"operation":"proportion_verification","a":4,"b":1,"c":12,"d":3,"semantic_template":"qf-proportion-verification/{\"a\":4,\"b\":1,\"c\":12,\"d\":3,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，5:(2)=-19:(-8) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -40, -38；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302118,"parameters":{"operation":"proportion_verification","a":5,"b":2,"c":-19,"d":-8,"semantic_template":"qf-proportion-verification/{\"a\":5,\"b\":2,\"c\":-19,\"d\":-8,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，6:(-3)=30:(-15) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -90, -90；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302119,"parameters":{"operation":"proportion_verification","a":6,"b":-3,"c":30,"d":-15,"semantic_template":"qf-proportion-verification/{\"a\":6,\"b\":-3,\"c\":30,\"d\":-15,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，7:(4)=-41:(-24) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -168, -164；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302120,"parameters":{"operation":"proportion_verification","a":7,"b":4,"c":-41,"d":-24,"semantic_template":"qf-proportion-verification/{\"a\":7,\"b\":4,\"c\":-41,\"d\":-24,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，8:(5)=16:(10) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 80, 80；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302121,"parameters":{"operation":"proportion_verification","a":8,"b":5,"c":16,"d":10,"semantic_template":"qf-proportion-verification/{\"a\":8,\"b\":5,\"c\":16,\"d\":10,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，9:(-6)=-26:(18) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 162, 156；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302122,"parameters":{"operation":"proportion_verification","a":9,"b":-6,"c":-26,"d":18,"semantic_template":"qf-proportion-verification/{\"a\":9,\"b\":-6,\"c\":-26,\"d\":18,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，10:(7)=40:(28) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 280, 280；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302123,"parameters":{"operation":"proportion_verification","a":10,"b":7,"c":40,"d":28,"semantic_template":"qf-proportion-verification/{\"a\":10,\"b\":7,\"c\":40,\"d\":28,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，11:(8)=-54:(-40) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"否","explanation_zh":"合法分母下的兩個交叉乘積為 -440, -432；兩者不相等，所以答案為否。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302124,"parameters":{"operation":"proportion_verification","a":11,"b":8,"c":-54,"d":-40,"semantic_template":"qf-proportion-verification/{\"a\":11,\"b\":8,\"c\":-54,\"d\":-40,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-verification-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例精確判定","stem_zh":"在有理數數值比語境，12:(-1)=72:(-6) 是比例嗎？兩個後項均非零。","answer":{"kind":"short_text","value":"是","explanation_zh":"合法分母下的兩個交叉乘積為 -72, -72；兩者相等，所以答案為是。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零後項","交叉乘積"]},"variant":{"family_id":"qf-proportion-verification","seed":202609302125,"parameters":{"operation":"proportion_verification","a":12,"b":-1,"c":72,"d":-6,"semantic_template":"qf-proportion-verification/{\"a\":12,\"b\":-1,\"c\":72,\"d\":-6,\"operation\":\"proportion_verification\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -12/(1)=x/(-2)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"24/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=24/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302201,"parameters":{"operation":"missing_term","a":-12,"b":1,"d":-2,"semantic_template":"qf-proportion-missing-term/{\"a\":-12,\"b\":1,\"d\":-2,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -11/(-2)=x/(3)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"33/2","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=33/2。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302202,"parameters":{"operation":"missing_term","a":-11,"b":-2,"d":3,"semantic_template":"qf-proportion-missing-term/{\"a\":-11,\"b\":-2,\"d\":3,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -10/(3)=x/(4)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-40/3","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-40/3。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302203,"parameters":{"operation":"missing_term","a":-10,"b":3,"d":4,"semantic_template":"qf-proportion-missing-term/{\"a\":-10,\"b\":3,\"d\":4,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -9/(-4)=x/(-5)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-45/4","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-45/4。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302204,"parameters":{"operation":"missing_term","a":-9,"b":-4,"d":-5,"semantic_template":"qf-proportion-missing-term/{\"a\":-9,\"b\":-4,\"d\":-5,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -8/(5)=x/(6)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-48/5","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-48/5。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302205,"parameters":{"operation":"missing_term","a":-8,"b":5,"d":6,"semantic_template":"qf-proportion-missing-term/{\"a\":-8,\"b\":5,\"d\":6,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -7/(-6)=x/(2)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"7/3","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=7/3。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302206,"parameters":{"operation":"missing_term","a":-7,"b":-6,"d":2,"semantic_template":"qf-proportion-missing-term/{\"a\":-7,\"b\":-6,\"d\":2,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -6/(7)=x/(-3)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"18/7","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=18/7。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302207,"parameters":{"operation":"missing_term","a":-6,"b":7,"d":-3,"semantic_template":"qf-proportion-missing-term/{\"a\":-6,\"b\":7,\"d\":-3,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -5/(-1)=x/(4)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"20/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=20/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302208,"parameters":{"operation":"missing_term","a":-5,"b":-1,"d":4,"semantic_template":"qf-proportion-missing-term/{\"a\":-5,\"b\":-1,\"d\":4,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -4/(2)=x/(5)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-10/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-10/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302209,"parameters":{"operation":"missing_term","a":-4,"b":2,"d":5,"semantic_template":"qf-proportion-missing-term/{\"a\":-4,\"b\":2,\"d\":5,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -3/(-3)=x/(-6)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-6/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-6/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302210,"parameters":{"operation":"missing_term","a":-3,"b":-3,"d":-6,"semantic_template":"qf-proportion-missing-term/{\"a\":-3,\"b\":-3,\"d\":-6,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -2/(4)=x/(2)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-1/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-1/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302211,"parameters":{"operation":"missing_term","a":-2,"b":4,"d":2,"semantic_template":"qf-proportion-missing-term/{\"a\":-2,\"b\":4,\"d\":2,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 -1/(-5)=x/(3)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"3/5","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=3/5。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302212,"parameters":{"operation":"missing_term","a":-1,"b":-5,"d":3,"semantic_template":"qf-proportion-missing-term/{\"a\":-1,\"b\":-5,\"d\":3,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 0/(6)=x/(-4)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"0/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=0/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302213,"parameters":{"operation":"missing_term","a":0,"b":6,"d":-4,"semantic_template":"qf-proportion-missing-term/{\"a\":0,\"b\":6,\"d\":-4,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 1/(-7)=x/(5)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-5/7","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-5/7。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302214,"parameters":{"operation":"missing_term","a":1,"b":-7,"d":5,"semantic_template":"qf-proportion-missing-term/{\"a\":1,\"b\":-7,\"d\":5,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 2/(1)=x/(6)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"12/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=12/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302215,"parameters":{"operation":"missing_term","a":2,"b":1,"d":6,"semantic_template":"qf-proportion-missing-term/{\"a\":2,\"b\":1,\"d\":6,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 3/(-2)=x/(-2)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"3/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=3/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302216,"parameters":{"operation":"missing_term","a":3,"b":-2,"d":-2,"semantic_template":"qf-proportion-missing-term/{\"a\":3,\"b\":-2,\"d\":-2,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 4/(3)=x/(3)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"4/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=4/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302217,"parameters":{"operation":"missing_term","a":4,"b":3,"d":3,"semantic_template":"qf-proportion-missing-term/{\"a\":4,\"b\":3,\"d\":3,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 5/(-4)=x/(4)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-5/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-5/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302218,"parameters":{"operation":"missing_term","a":5,"b":-4,"d":4,"semantic_template":"qf-proportion-missing-term/{\"a\":5,\"b\":-4,\"d\":4,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 6/(5)=x/(-5)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-6/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-6/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302219,"parameters":{"operation":"missing_term","a":6,"b":5,"d":-5,"semantic_template":"qf-proportion-missing-term/{\"a\":6,\"b\":5,\"d\":-5,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 7/(-6)=x/(6)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-7/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-7/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302220,"parameters":{"operation":"missing_term","a":7,"b":-6,"d":6,"semantic_template":"qf-proportion-missing-term/{\"a\":7,\"b\":-6,\"d\":6,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 8/(7)=x/(2)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"16/7","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=16/7。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302221,"parameters":{"operation":"missing_term","a":8,"b":7,"d":2,"semantic_template":"qf-proportion-missing-term/{\"a\":8,\"b\":7,\"d\":2,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 9/(-1)=x/(-3)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"27/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=27/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302222,"parameters":{"operation":"missing_term","a":9,"b":-1,"d":-3,"semantic_template":"qf-proportion-missing-term/{\"a\":9,\"b\":-1,\"d\":-3,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 10/(2)=x/(4)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"20/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=20/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302223,"parameters":{"operation":"missing_term","a":10,"b":2,"d":4,"semantic_template":"qf-proportion-missing-term/{\"a\":10,\"b\":2,\"d\":4,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 11/(-3)=x/(5)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-55/3","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-55/3。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302224,"parameters":{"operation":"missing_term","a":11,"b":-3,"d":5,"semantic_template":"qf-proportion-missing-term/{\"a\":11,\"b\":-3,\"d\":5,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-missing-term-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"比例未知前項","stem_zh":"在有理數語境解比例 12/(4)=x/(-6)；已知兩個分母非零，求 x 的最簡正分母 p/q 值。","answer":{"kind":"short_text","value":"-18/1","explanation_zh":"由 bx=ad 得 x=ad/b；精確代入並約分後 x=-18/1。非零 b 保證此有理解唯一。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["比例求解","精確有理數"]},"variant":{"family_id":"qf-proportion-missing-term","seed":202609302225,"parameters":{"operation":"missing_term","a":12,"b":4,"d":-6,"semantic_template":"qf-proportion-missing-term/{\"a\":12,\"b\":4,\"d\":-6,\"operation\":\"missing_term\"}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0001","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-12。明示資料點 (x,y)=(-3,36) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 36, 36；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302301,"parameters":{"operation":"fixed_factor","k":-12,"x":-3,"y":36,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-12,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":36}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0002","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-11。明示資料點 (x,y)=(-2,23) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 22, 23；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302302,"parameters":{"operation":"fixed_factor","k":-11,"x":-2,"y":23,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-11,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":23}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0003","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-10。明示資料點 (x,y)=(-1,10) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 10, 10；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302303,"parameters":{"operation":"fixed_factor","k":-10,"x":-1,"y":10,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-10,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0004","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-9。明示資料點 (x,y)=(0,1) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 0, 1；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302304,"parameters":{"operation":"fixed_factor","k":-9,"x":0,"y":1,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-9,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0005","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-8。明示資料點 (x,y)=(1,-8) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 -8, -8；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302305,"parameters":{"operation":"fixed_factor","k":-8,"x":1,"y":-8,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-8,\"operation\":\"fixed_factor\",\"x\":1,\"y\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0006","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-7。明示資料點 (x,y)=(2,-13) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 -14, -13；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302306,"parameters":{"operation":"fixed_factor","k":-7,"x":2,"y":-13,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-7,\"operation\":\"fixed_factor\",\"x\":2,\"y\":-13}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0007","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-6。明示資料點 (x,y)=(3,-18) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 -18, -18；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302307,"parameters":{"operation":"fixed_factor","k":-6,"x":3,"y":-18,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-6,\"operation\":\"fixed_factor\",\"x\":3,\"y\":-18}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0008","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-5。明示資料點 (x,y)=(-3,16) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 15, 16；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302308,"parameters":{"operation":"fixed_factor","k":-5,"x":-3,"y":16,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-5,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":16}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0009","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-4。明示資料點 (x,y)=(-2,8) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 8, 8；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302309,"parameters":{"operation":"fixed_factor","k":-4,"x":-2,"y":8,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-4,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":8}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0010","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-3。明示資料點 (x,y)=(-1,4) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 3, 4；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302310,"parameters":{"operation":"fixed_factor","k":-3,"x":-1,"y":4,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-3,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0011","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-2。明示資料點 (x,y)=(0,0) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 0, 0；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302311,"parameters":{"operation":"fixed_factor","k":-2,"x":0,"y":0,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-2,\"operation\":\"fixed_factor\",\"x\":0,\"y\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0012","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=-1。明示資料點 (x,y)=(1,0) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 -1, 0；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302312,"parameters":{"operation":"fixed_factor","k":-1,"x":1,"y":0,"semantic_template":"qf-proportion-fixed-factor/{\"k\":-1,\"operation\":\"fixed_factor\",\"x\":1,\"y\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0013","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=0。明示資料點 (x,y)=(2,0) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 0, 0；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302313,"parameters":{"operation":"fixed_factor","k":0,"x":2,"y":0,"semantic_template":"qf-proportion-fixed-factor/{\"k\":0,\"operation\":\"fixed_factor\",\"x\":2,\"y\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0014","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=1。明示資料點 (x,y)=(3,4) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 3, 4；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302314,"parameters":{"operation":"fixed_factor","k":1,"x":3,"y":4,"semantic_template":"qf-proportion-fixed-factor/{\"k\":1,\"operation\":\"fixed_factor\",\"x\":3,\"y\":4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0015","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=2。明示資料點 (x,y)=(-3,-6) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 -6, -6；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302315,"parameters":{"operation":"fixed_factor","k":2,"x":-3,"y":-6,"semantic_template":"qf-proportion-fixed-factor/{\"k\":2,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0016","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=3。明示資料點 (x,y)=(-2,-5) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 -6, -5；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302316,"parameters":{"operation":"fixed_factor","k":3,"x":-2,"y":-5,"semantic_template":"qf-proportion-fixed-factor/{\"k\":3,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0017","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=4。明示資料點 (x,y)=(-1,-4) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 -4, -4；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302317,"parameters":{"operation":"fixed_factor","k":4,"x":-1,"y":-4,"semantic_template":"qf-proportion-fixed-factor/{\"k\":4,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0018","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=5。明示資料點 (x,y)=(0,1) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 0, 1；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302318,"parameters":{"operation":"fixed_factor","k":5,"x":0,"y":1,"semantic_template":"qf-proportion-fixed-factor/{\"k\":5,\"operation\":\"fixed_factor\",\"x\":0,\"y\":1}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0019","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=6。明示資料點 (x,y)=(1,6) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 6, 6；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302319,"parameters":{"operation":"fixed_factor","k":6,"x":1,"y":6,"semantic_template":"qf-proportion-fixed-factor/{\"k\":6,\"operation\":\"fixed_factor\",\"x\":1,\"y\":6}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0020","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=7。明示資料點 (x,y)=(2,15) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 14, 15；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302320,"parameters":{"operation":"fixed_factor","k":7,"x":2,"y":15,"semantic_template":"qf-proportion-fixed-factor/{\"k\":7,\"operation\":\"fixed_factor\",\"x\":2,\"y\":15}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0021","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=8。明示資料點 (x,y)=(3,24) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 24, 24；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302321,"parameters":{"operation":"fixed_factor","k":8,"x":3,"y":24,"semantic_template":"qf-proportion-fixed-factor/{\"k\":8,\"operation\":\"fixed_factor\",\"x\":3,\"y\":24}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0022","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=9。明示資料點 (x,y)=(-3,-26) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 -27, -26；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302322,"parameters":{"operation":"fixed_factor","k":9,"x":-3,"y":-26,"semantic_template":"qf-proportion-fixed-factor/{\"k\":9,\"operation\":\"fixed_factor\",\"x\":-3,\"y\":-26}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0023","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=10。明示資料點 (x,y)=(-2,-20) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 -20, -20；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302323,"parameters":{"operation":"fixed_factor","k":10,"x":-2,"y":-20,"semantic_template":"qf-proportion-fixed-factor/{\"k\":10,\"operation\":\"fixed_factor\",\"x\":-2,\"y\":-20}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0024","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=11。明示資料點 (x,y)=(-1,-10) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"否","explanation_zh":"kx 與給定 y 的精確值分別是 -11, -10；比較後答案為否，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302324,"parameters":{"operation":"fixed_factor","k":11,"x":-1,"y":-10,"semantic_template":"qf-proportion-fixed-factor/{\"k\":11,\"operation\":\"fixed_factor\",\"x\":-1,\"y\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260930-r02-proportion-fixed-factor-0025","batch_id":"batch-20260930-r02-ratio-proportion-foundations","language":"zh-Hant","source_mko_ids":["mko-ratio-proportion"],"title_zh":"固定比例因子檢查","stem_zh":"在有理數語境，固定因子 k=12。明示資料點 (x,y)=(0,0) 是否滿足 y=kx？只判定此點。","answer":{"kind":"short_text","value":"是","explanation_zh":"kx 與給定 y 的精確值分別是 0, 0；比較後答案為是，不由此點推論其他輸入。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["固定因子","逐點驗證"]},"variant":{"family_id":"qf-proportion-fixed-factor","seed":202609302325,"parameters":{"operation":"fixed_factor","k":12,"x":0,"y":0,"semantic_template":"qf-proportion-fixed-factor/{\"k\":12,\"operation\":\"fixed_factor\",\"x\":0,\"y\":0}"}},"verification":{"status":"candidate","checks":["json_schema","producer_local_answer_invariants","explanation_witness_accuracy"],"warning_zh":"本題保持 candidate；有限精確計算與產生者自檢不構成人工審查、形式證明或主架構者驗收。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-6 question producer","generated_at":"2026-09-30","contract_version":"ocme-question-factory-v0.1"}}