{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0001","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-12)=-8，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-12)=-7，右側為 -8，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260925,"parameters":{"form":"x+a=b","a":-12,"b":-8,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-12,\"b\":-8,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0002","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-11)=-7，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-11)=-7，右側為 -7，兩側相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260926,"parameters":{"form":"x+a=b","a":-11,"b":-7,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-11,\"b\":-7,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0003","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-10)=-6，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-10)=-5，右側為 -6，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260927,"parameters":{"form":"x+a=b","a":-10,"b":-6,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-10,\"b\":-6,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0004","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-9)=-5，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-9)=-5，右側為 -5，兩側相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260928,"parameters":{"form":"x+a=b","a":-9,"b":-5,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-9,\"b\":-5,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0005","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-8)=-4，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-8)=-3，右側為 -4，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260929,"parameters":{"form":"x+a=b","a":-8,"b":-4,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-8,\"b\":-4,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0006","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-7)=-3，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-7)=-3，右側為 -3，兩側相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260930,"parameters":{"form":"x+a=b","a":-7,"b":-3,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-7,\"b\":-3,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0007","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-6)=-2，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-6)=-1，右側為 -2，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260931,"parameters":{"form":"x+a=b","a":-6,"b":-2,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-6,\"b\":-2,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0008","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-5)=-1，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-5)=-1，右側為 -1，兩側相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260932,"parameters":{"form":"x+a=b","a":-5,"b":-1,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-5,\"b\":-1,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0009","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-4)=0，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-4)=1，右側為 0，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260933,"parameters":{"form":"x+a=b","a":-4,"b":0,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-4,\"b\":0,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0010","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-3)=1，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-3)=1，右側為 1，兩側相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260934,"parameters":{"form":"x+a=b","a":-3,"b":1,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-3,\"b\":1,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0011","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-2)=2，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(-2)=3，右側為 2，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260935,"parameters":{"form":"x+a=b","a":-2,"b":2,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-2,\"b\":2,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0012","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(-1)=3，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(-1)=3，右側為 3，兩側相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260936,"parameters":{"form":"x+a=b","a":-1,"b":3,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":-1,\"b\":3,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0013","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(0)=4，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(0)=5，右側為 4，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260937,"parameters":{"form":"x+a=b","a":0,"b":4,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":0,\"b\":4,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0014","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(1)=5，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(1)=5，右側為 5，兩側相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260938,"parameters":{"form":"x+a=b","a":1,"b":5,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":1,\"b\":5,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0015","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(2)=6，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(2)=7，右側為 6，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260939,"parameters":{"form":"x+a=b","a":2,"b":6,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":2,\"b\":6,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0016","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(3)=7，候選 x=4。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 4+(3)=7，右側為 7，兩側相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260940,"parameters":{"form":"x+a=b","a":3,"b":7,"candidate":4,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":3,\"b\":7,\"candidate\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0017","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(4)=8，候選 x=5。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 5+(4)=9，右側為 8，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260941,"parameters":{"form":"x+a=b","a":4,"b":8,"candidate":5,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":4,\"b\":8,\"candidate\":5,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0018","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(5)=-8，候選 x=-13。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 -13+(5)=-8，右側為 -8，兩側相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260942,"parameters":{"form":"x+a=b","a":5,"b":-8,"candidate":-13,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":5,\"b\":-8,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0019","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(6)=-7，候選 x=-12。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 -12+(6)=-6，右側為 -7，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260943,"parameters":{"form":"x+a=b","a":6,"b":-7,"candidate":-12,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":6,\"b\":-7,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0020","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(7)=-6，候選 x=-13。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 -13+(7)=-6，右側為 -6，兩側相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260944,"parameters":{"form":"x+a=b","a":7,"b":-6,"candidate":-13,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":7,\"b\":-6,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0021","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(8)=-5，候選 x=-12。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 -12+(8)=-4，右側為 -5，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260945,"parameters":{"form":"x+a=b","a":8,"b":-5,"candidate":-12,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":8,\"b\":-5,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0022","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(9)=-4，候選 x=-13。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 -13+(9)=-4，右側為 -4，兩側相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260946,"parameters":{"form":"x+a=b","a":9,"b":-4,"candidate":-13,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":9,\"b\":-4,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0023","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(10)=-3，候選 x=-12。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 -12+(10)=-2，右側為 -3，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260947,"parameters":{"form":"x+a=b","a":10,"b":-3,"candidate":-12,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":10,\"b\":-3,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0024","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(11)=-2，候選 x=-13。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"左側 -13+(11)=-2，右側為 -2，兩側相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260948,"parameters":{"form":"x+a=b","a":11,"b":-2,"candidate":-13,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":11,\"b\":-2,\"candidate\":-13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-solution-verification-0025","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"候選解代入驗證","stem_zh":"在整數論域，方程 x+(12)=-1，候選 x=-12。代入原式後，候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"左側 -12+(12)=0，右側為 -1，兩側不相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["代入驗證","等式"]},"variant":{"family_id":"qf-equation-solution-verification","seed":20260949,"parameters":{"form":"x+a=b","a":12,"b":-1,"candidate":-12,"domain":"integers","semantic_template":"qf-equation-solution-verification/{\"a\":12,\"b\":-1,\"candidate\":-12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0001","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-15)=20。","answer":{"kind":"short_text","value":"35","explanation_zh":"x=20−(-15)=35；代回得 35+(-15)=20。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261025,"parameters":{"form":"x+a=b","a":-15,"b":20,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-15,\"b\":20,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0002","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-14)=19。","answer":{"kind":"short_text","value":"33","explanation_zh":"x=19−(-14)=33；代回得 33+(-14)=19。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261026,"parameters":{"form":"x+a=b","a":-14,"b":19,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-14,\"b\":19,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0003","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-13)=18。","answer":{"kind":"short_text","value":"31","explanation_zh":"x=18−(-13)=31；代回得 31+(-13)=18。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261027,"parameters":{"form":"x+a=b","a":-13,"b":18,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-13,\"b\":18,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0004","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-12)=17。","answer":{"kind":"short_text","value":"29","explanation_zh":"x=17−(-12)=29；代回得 29+(-12)=17。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261028,"parameters":{"form":"x+a=b","a":-12,"b":17,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-12,\"b\":17,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0005","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-11)=16。","answer":{"kind":"short_text","value":"27","explanation_zh":"x=16−(-11)=27；代回得 27+(-11)=16。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261029,"parameters":{"form":"x+a=b","a":-11,"b":16,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-11,\"b\":16,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0006","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-10)=15。","answer":{"kind":"short_text","value":"25","explanation_zh":"x=15−(-10)=25；代回得 25+(-10)=15。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261030,"parameters":{"form":"x+a=b","a":-10,"b":15,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-10,\"b\":15,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0007","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-9)=14。","answer":{"kind":"short_text","value":"23","explanation_zh":"x=14−(-9)=23；代回得 23+(-9)=14。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261031,"parameters":{"form":"x+a=b","a":-9,"b":14,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-9,\"b\":14,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0008","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-8)=13。","answer":{"kind":"short_text","value":"21","explanation_zh":"x=13−(-8)=21；代回得 21+(-8)=13。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261032,"parameters":{"form":"x+a=b","a":-8,"b":13,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-8,\"b\":13,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0009","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-7)=12。","answer":{"kind":"short_text","value":"19","explanation_zh":"x=12−(-7)=19；代回得 19+(-7)=12。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261033,"parameters":{"form":"x+a=b","a":-7,"b":12,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-7,\"b\":12,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0010","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-6)=11。","answer":{"kind":"short_text","value":"17","explanation_zh":"x=11−(-6)=17；代回得 17+(-6)=11。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261034,"parameters":{"form":"x+a=b","a":-6,"b":11,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-6,\"b\":11,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0011","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-5)=10。","answer":{"kind":"short_text","value":"15","explanation_zh":"x=10−(-5)=15；代回得 15+(-5)=10。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261035,"parameters":{"form":"x+a=b","a":-5,"b":10,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-5,\"b\":10,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0012","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-4)=9。","answer":{"kind":"short_text","value":"13","explanation_zh":"x=9−(-4)=13；代回得 13+(-4)=9。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261036,"parameters":{"form":"x+a=b","a":-4,"b":9,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-4,\"b\":9,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0013","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(-3)=8。","answer":{"kind":"short_text","value":"11","explanation_zh":"x=8−(-3)=11；代回得 11+(-3)=8。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261037,"parameters":{"form":"x+a=b","a":-3,"b":8,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":-3,\"b\":8,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0017","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(1)=4。","answer":{"kind":"short_text","value":"3","explanation_zh":"x=4−(1)=3；代回得 3+(1)=4。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261041,"parameters":{"form":"x+a=b","a":1,"b":4,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":1,\"b\":4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0018","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(2)=3。","answer":{"kind":"short_text","value":"1","explanation_zh":"x=3−(2)=1；代回得 1+(2)=3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261042,"parameters":{"form":"x+a=b","a":2,"b":3,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":2,\"b\":3,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0021","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(5)=0。","answer":{"kind":"short_text","value":"-5","explanation_zh":"x=0−(5)=-5；代回得 -5+(5)=0。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261045,"parameters":{"form":"x+a=b","a":5,"b":0,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":5,\"b\":0,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0022","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(6)=-1。","answer":{"kind":"short_text","value":"-7","explanation_zh":"x=-1−(6)=-7；代回得 -7+(6)=-1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261046,"parameters":{"form":"x+a=b","a":6,"b":-1,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":6,\"b\":-1,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0023","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(7)=-2。","answer":{"kind":"short_text","value":"-9","explanation_zh":"x=-2−(7)=-9；代回得 -9+(7)=-2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261047,"parameters":{"form":"x+a=b","a":7,"b":-2,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":7,\"b\":-2,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0024","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(8)=-3。","answer":{"kind":"short_text","value":"-11","explanation_zh":"x=-3−(8)=-11；代回得 -11+(8)=-3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261048,"parameters":{"form":"x+a=b","a":8,"b":-3,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":8,\"b\":-3,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-additive-solve-0025","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"加法型方程","stem_zh":"在整數論域解 x+(9)=-4。","answer":{"kind":"short_text","value":"-13","explanation_zh":"x=-4−(9)=-13；代回得 -13+(9)=-4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["加法反運算","方程"]},"variant":{"family_id":"qf-equation-additive-solve","seed":20261049,"parameters":{"form":"x+a=b","a":9,"b":-4,"domain":"integers","semantic_template":"qf-equation-additive-solve/{\"a\":9,\"b\":-4,\"domain\":\"integers\",\"form\":\"x+a=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0001","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 1×x=-5；係數 1 已明示非零。","answer":{"kind":"short_text","value":"-5","explanation_zh":"1≠0，x=-5/1=-5；代回 1×-5=-5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261125,"parameters":{"form":"a*x=b","a":1,"b":-5,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":-5,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0002","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 2×x=-8；係數 2 已明示非零。","answer":{"kind":"short_text","value":"-4","explanation_zh":"2≠0，x=-8/2=-4；代回 2×-4=-8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261126,"parameters":{"form":"a*x=b","a":2,"b":-8,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":-8,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0003","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 3×x=-9；係數 3 已明示非零。","answer":{"kind":"short_text","value":"-3","explanation_zh":"3≠0，x=-9/3=-3；代回 3×-3=-9。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261127,"parameters":{"form":"a*x=b","a":3,"b":-9,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":-9,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0004","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 4×x=-8；係數 4 已明示非零。","answer":{"kind":"short_text","value":"-2","explanation_zh":"4≠0，x=-8/4=-2；代回 4×-2=-8。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261128,"parameters":{"form":"a*x=b","a":4,"b":-8,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":-8,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0005","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 5×x=-5；係數 5 已明示非零。","answer":{"kind":"short_text","value":"-1","explanation_zh":"5≠0，x=-5/5=-1；代回 5×-1=-5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261129,"parameters":{"form":"a*x=b","a":5,"b":-5,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-5,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0006","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 6×x=0；係數 6 已明示非零。","answer":{"kind":"short_text","value":"0","explanation_zh":"6≠0，x=0/6=0；代回 6×0=0。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261130,"parameters":{"form":"a*x=b","a":6,"b":0,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":0,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0007","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 7×x=7；係數 7 已明示非零。","answer":{"kind":"short_text","value":"1","explanation_zh":"7≠0，x=7/7=1；代回 7×1=7。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261131,"parameters":{"form":"a*x=b","a":7,"b":7,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":7,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0008","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 8×x=16；係數 8 已明示非零。","answer":{"kind":"short_text","value":"2","explanation_zh":"8≠0，x=16/8=2；代回 8×2=16。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261132,"parameters":{"form":"a*x=b","a":8,"b":16,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":8,\"b\":16,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0009","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 9×x=27；係數 9 已明示非零。","answer":{"kind":"short_text","value":"3","explanation_zh":"9≠0，x=27/9=3；代回 9×3=27。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261133,"parameters":{"form":"a*x=b","a":9,"b":27,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":9,\"b\":27,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0010","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 1×x=4；係數 1 已明示非零。","answer":{"kind":"short_text","value":"4","explanation_zh":"1≠0，x=4/1=4；代回 1×4=4。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261134,"parameters":{"form":"a*x=b","a":1,"b":4,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":4,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0011","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 2×x=10；係數 2 已明示非零。","answer":{"kind":"short_text","value":"5","explanation_zh":"2≠0，x=10/2=5；代回 2×5=10。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261135,"parameters":{"form":"a*x=b","a":2,"b":10,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":10,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0012","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 3×x=-15；係數 3 已明示非零。","answer":{"kind":"short_text","value":"-5","explanation_zh":"3≠0，x=-15/3=-5；代回 3×-5=-15。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261136,"parameters":{"form":"a*x=b","a":3,"b":-15,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":-15,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0013","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 4×x=-16；係數 4 已明示非零。","answer":{"kind":"short_text","value":"-4","explanation_zh":"4≠0，x=-16/4=-4；代回 4×-4=-16。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261137,"parameters":{"form":"a*x=b","a":4,"b":-16,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":-16,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0014","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 5×x=-15；係數 5 已明示非零。","answer":{"kind":"short_text","value":"-3","explanation_zh":"5≠0，x=-15/5=-3；代回 5×-3=-15。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261138,"parameters":{"form":"a*x=b","a":5,"b":-15,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-15,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0015","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 6×x=-12；係數 6 已明示非零。","answer":{"kind":"short_text","value":"-2","explanation_zh":"6≠0，x=-12/6=-2；代回 6×-2=-12。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261139,"parameters":{"form":"a*x=b","a":6,"b":-12,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":-12,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0016","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 7×x=-7；係數 7 已明示非零。","answer":{"kind":"short_text","value":"-1","explanation_zh":"7≠0，x=-7/7=-1；代回 7×-1=-7。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261140,"parameters":{"form":"a*x=b","a":7,"b":-7,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":-7,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0017","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 8×x=0；係數 8 已明示非零。","answer":{"kind":"short_text","value":"0","explanation_zh":"8≠0，x=0/8=0；代回 8×0=0。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261141,"parameters":{"form":"a*x=b","a":8,"b":0,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":8,\"b\":0,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0018","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 9×x=9；係數 9 已明示非零。","answer":{"kind":"short_text","value":"1","explanation_zh":"9≠0，x=9/9=1；代回 9×1=9。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261142,"parameters":{"form":"a*x=b","a":9,"b":9,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":9,\"b\":9,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0019","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 1×x=2；係數 1 已明示非零。","answer":{"kind":"short_text","value":"2","explanation_zh":"1≠0，x=2/1=2；代回 1×2=2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261143,"parameters":{"form":"a*x=b","a":1,"b":2,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":1,\"b\":2,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0020","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 2×x=6；係數 2 已明示非零。","answer":{"kind":"short_text","value":"3","explanation_zh":"2≠0，x=6/2=3；代回 2×3=6。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261144,"parameters":{"form":"a*x=b","a":2,"b":6,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":2,\"b\":6,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0021","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 3×x=12；係數 3 已明示非零。","answer":{"kind":"short_text","value":"4","explanation_zh":"3≠0，x=12/3=4；代回 3×4=12。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261145,"parameters":{"form":"a*x=b","a":3,"b":12,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":3,\"b\":12,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0022","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 4×x=20；係數 4 已明示非零。","answer":{"kind":"short_text","value":"5","explanation_zh":"4≠0，x=20/4=5；代回 4×5=20。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261146,"parameters":{"form":"a*x=b","a":4,"b":20,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":4,\"b\":20,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0023","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 5×x=-25；係數 5 已明示非零。","answer":{"kind":"short_text","value":"-5","explanation_zh":"5≠0，x=-25/5=-5；代回 5×-5=-25。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261147,"parameters":{"form":"a*x=b","a":5,"b":-25,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":5,\"b\":-25,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0024","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 6×x=-24；係數 6 已明示非零。","answer":{"kind":"short_text","value":"-4","explanation_zh":"6≠0，x=-24/6=-4；代回 6×-4=-24。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261148,"parameters":{"form":"a*x=b","a":6,"b":-24,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":6,\"b\":-24,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-multiplicative-solve-0025","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"乘法型方程","stem_zh":"在整數論域解 7×x=-21；係數 7 已明示非零。","answer":{"kind":"short_text","value":"-3","explanation_zh":"7≠0，x=-21/7=-3；代回 7×-3=-21。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["非零係數","乘法反運算"]},"variant":{"family_id":"qf-equation-multiplicative-solve","seed":20261149,"parameters":{"form":"a*x=b","a":7,"b":-21,"domain":"integers","semantic_template":"qf-equation-multiplicative-solve/{\"a\":7,\"b\":-21,\"domain\":\"integers\",\"form\":\"a*x=b\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-linear-solution-class-0007","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"一般一次方程的解分類","stem_zh":"在有理數論域分類 8x+(6)=11x+(0) 的解集。","answer":{"kind":"short_text","value":"唯一解 x=2","explanation_zh":"(8−11)x=-6，故 唯一解 x=2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["一次方程","解分類"]},"variant":{"family_id":"qf-equation-linear-solution-class","seed":20261231,"parameters":{"form":"a*x+b=c*x+d","a":8,"b":6,"c":11,"d":0,"domain":"rationals","semantic_template":"qf-equation-linear-solution-class/{\"a\":8,\"b\":6,\"c\":11,\"d\":0,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-linear-solution-class-0008","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"一般一次方程的解分類","stem_zh":"在有理數論域分類 8x+(3)=8x+(3) 的解集。","answer":{"kind":"short_text","value":"所有有理數皆為解","explanation_zh":"兩側係數與常數皆相同，所以所有有理數皆為解。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["一次方程","解分類"]},"variant":{"family_id":"qf-equation-linear-solution-class","seed":20261232,"parameters":{"form":"a*x+b=c*x+d","a":8,"b":3,"c":8,"d":3,"domain":"rationals","semantic_template":"qf-equation-linear-solution-class/{\"a\":8,\"b\":3,\"c\":8,\"d\":3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-linear-solution-class-0009","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"一般一次方程的解分類","stem_zh":"在有理數論域分類 9x+(8)=9x+(9) 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"x 係數相同但常數不同，所以無解。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["一次方程","解分類"]},"variant":{"family_id":"qf-equation-linear-solution-class","seed":20261233,"parameters":{"form":"a*x+b=c*x+d","a":9,"b":8,"c":9,"d":9,"domain":"rationals","semantic_template":"qf-equation-linear-solution-class/{\"a\":9,\"b\":8,\"c\":9,\"d\":9,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260924-equation-linear-solution-class-0010","batch_id":"batch-20260924-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-equation"],"title_zh":"一般一次方程的解分類","stem_zh":"在有理數論域分類 11x+(9)=14x+(3) 的解集。","answer":{"kind":"short_text","value":"唯一解 x=2","explanation_zh":"(11−14)x=-6，故 唯一解 x=2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["一次方程","解分類"]},"variant":{"family_id":"qf-equation-linear-solution-class","seed":20261234,"parameters":{"form":"a*x+b=c*x+d","a":11,"b":9,"c":14,"d":3,"domain":"rationals","semantic_template":"qf-equation-linear-solution-class/{\"a\":11,\"b\":9,\"c\":14,\"d\":3,\"domain\":\"rationals\",\"form\":\"a*x+b=c*x+d\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate 練習；有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-24","contract_version":"ocme-question-factory-v0.1"}}
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