{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0001","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-12|。","answer":{"kind":"short_text","value":"12","explanation_zh":"-12 <0，所以取相反數；因此 |-12|=12。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260929,"parameters":{"x":-12,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0002","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-11|。","answer":{"kind":"short_text","value":"11","explanation_zh":"-11 <0，所以取相反數；因此 |-11|=11。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260930,"parameters":{"x":-11,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0003","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-10|。","answer":{"kind":"short_text","value":"10","explanation_zh":"-10 <0，所以取相反數；因此 |-10|=10。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260931,"parameters":{"x":-10,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0004","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-9|。","answer":{"kind":"short_text","value":"9","explanation_zh":"-9 <0，所以取相反數；因此 |-9|=9。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260932,"parameters":{"x":-9,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0005","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-8|。","answer":{"kind":"short_text","value":"8","explanation_zh":"-8 <0，所以取相反數；因此 |-8|=8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260933,"parameters":{"x":-8,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0006","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-7|。","answer":{"kind":"short_text","value":"7","explanation_zh":"-7 <0，所以取相反數；因此 |-7|=7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260934,"parameters":{"x":-7,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0007","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-6|。","answer":{"kind":"short_text","value":"6","explanation_zh":"-6 <0，所以取相反數；因此 |-6|=6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260935,"parameters":{"x":-6,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0008","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-5|。","answer":{"kind":"short_text","value":"5","explanation_zh":"-5 <0，所以取相反數；因此 |-5|=5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260936,"parameters":{"x":-5,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0009","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-4|。","answer":{"kind":"short_text","value":"4","explanation_zh":"-4 <0，所以取相反數；因此 |-4|=4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260937,"parameters":{"x":-4,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0010","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-3|。","answer":{"kind":"short_text","value":"3","explanation_zh":"-3 <0，所以取相反數；因此 |-3|=3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260938,"parameters":{"x":-3,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0011","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-2|。","answer":{"kind":"short_text","value":"2","explanation_zh":"-2 <0，所以取相反數；因此 |-2|=2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260939,"parameters":{"x":-2,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0012","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |-1|。","answer":{"kind":"short_text","value":"1","explanation_zh":"-1 <0，所以取相反數；因此 |-1|=1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260940,"parameters":{"x":-1,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0013","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |0|。","answer":{"kind":"short_text","value":"0","explanation_zh":"0 ≥0，所以保留原值；因此 |0|=0。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260941,"parameters":{"x":0,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":0}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0014","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |1|。","answer":{"kind":"short_text","value":"1","explanation_zh":"1 ≥0，所以保留原值；因此 |1|=1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260942,"parameters":{"x":1,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":1}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0015","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |2|。","answer":{"kind":"short_text","value":"2","explanation_zh":"2 ≥0，所以保留原值；因此 |2|=2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260943,"parameters":{"x":2,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":2}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0016","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |3|。","answer":{"kind":"short_text","value":"3","explanation_zh":"3 ≥0，所以保留原值；因此 |3|=3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260944,"parameters":{"x":3,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":3}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0017","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |4|。","answer":{"kind":"short_text","value":"4","explanation_zh":"4 ≥0，所以保留原值；因此 |4|=4。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260945,"parameters":{"x":4,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":4}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0018","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |5|。","answer":{"kind":"short_text","value":"5","explanation_zh":"5 ≥0，所以保留原值；因此 |5|=5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260946,"parameters":{"x":5,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":5}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0019","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |6|。","answer":{"kind":"short_text","value":"6","explanation_zh":"6 ≥0，所以保留原值；因此 |6|=6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260947,"parameters":{"x":6,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":6}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0020","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |7|。","answer":{"kind":"short_text","value":"7","explanation_zh":"7 ≥0，所以保留原值；因此 |7|=7。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260948,"parameters":{"x":7,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":7}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0021","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |8|。","answer":{"kind":"short_text","value":"8","explanation_zh":"8 ≥0，所以保留原值；因此 |8|=8。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260949,"parameters":{"x":8,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":8}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0022","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |9|。","answer":{"kind":"short_text","value":"9","explanation_zh":"9 ≥0，所以保留原值；因此 |9|=9。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260950,"parameters":{"x":9,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":9}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0023","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |10|。","answer":{"kind":"short_text","value":"10","explanation_zh":"10 ≥0，所以保留原值；因此 |10|=10。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260951,"parameters":{"x":10,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":10}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0024","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |11|。","answer":{"kind":"short_text","value":"11","explanation_zh":"11 ≥0，所以保留原值；因此 |11|=11。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260952,"parameters":{"x":11,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":11}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-exact-evaluation-0025","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值精確計算","stem_zh":"依實數絕對值的分段定義，精確計算 |12|。","answer":{"kind":"short_text","value":"12","explanation_zh":"12 ≥0，所以保留原值；因此 |12|=12。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["分段定義","精確整數計算"]},"variant":{"family_id":"qf-absolute-value-exact-evaluation","seed":20260953,"parameters":{"x":12,"domain":"reals","operation":"exact_absolute_value","semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":12}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0001","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=12，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=12≥0，所以使用 nonnegative 分支，|x|=x=12。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261029,"parameters":{"x":12,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":12}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0002","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=11，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=11≥0，所以使用 nonnegative 分支，|x|=x=11。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261030,"parameters":{"x":11,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":11}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0003","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=10，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=10≥0，所以使用 nonnegative 分支，|x|=x=10。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261031,"parameters":{"x":10,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":10}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0004","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=9，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=9≥0，所以使用 nonnegative 分支，|x|=x=9。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261032,"parameters":{"x":9,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":9}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0005","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=8，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=8≥0，所以使用 nonnegative 分支，|x|=x=8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261033,"parameters":{"x":8,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":8}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0006","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=7，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=7≥0，所以使用 nonnegative 分支，|x|=x=7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261034,"parameters":{"x":7,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":7}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0007","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=6，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=6≥0，所以使用 nonnegative 分支，|x|=x=6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261035,"parameters":{"x":6,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":6}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0009","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=4，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=4≥0，所以使用 nonnegative 分支，|x|=x=4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261037,"parameters":{"x":4,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":4}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0010","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=3，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=3≥0，所以使用 nonnegative 分支，|x|=x=3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261038,"parameters":{"x":3,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":3}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0011","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=2，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=2≥0，所以使用 nonnegative 分支，|x|=x=2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261039,"parameters":{"x":2,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":2}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0012","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=1，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=1≥0，所以使用 nonnegative 分支，|x|=x=1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261040,"parameters":{"x":1,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":1}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0013","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=0，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"非負分支 x","explanation_zh":"x=0≥0，所以使用 nonnegative 分支，|x|=x=0。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261041,"parameters":{"x":0,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":0}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0014","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-1，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-1<0，所以使用 negative 分支，|x|=-x=1。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261042,"parameters":{"x":-1,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0015","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-2，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-2<0，所以使用 negative 分支，|x|=-x=2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261043,"parameters":{"x":-2,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0016","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-3，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-3<0，所以使用 negative 分支，|x|=-x=3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261044,"parameters":{"x":-3,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0017","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-4，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-4<0，所以使用 negative 分支，|x|=-x=4。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261045,"parameters":{"x":-4,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0018","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-5，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-5<0，所以使用 negative 分支，|x|=-x=5。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261046,"parameters":{"x":-5,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-5}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0019","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-6，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-6<0，所以使用 negative 分支，|x|=-x=6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261047,"parameters":{"x":-6,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-6}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0020","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-7，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-7<0，所以使用 negative 分支，|x|=-x=7。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261048,"parameters":{"x":-7,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-7}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0021","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-8，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-8<0，所以使用 negative 分支，|x|=-x=8。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261049,"parameters":{"x":-8,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-8}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0022","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-9，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-9<0，所以使用 negative 分支，|x|=-x=9。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261050,"parameters":{"x":-9,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-9}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0023","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-10，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-10<0，所以使用 negative 分支，|x|=-x=10。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261051,"parameters":{"x":-10,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-10}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0024","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-11，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-11<0，所以使用 negative 分支，|x|=-x=11。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261052,"parameters":{"x":-11,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-11}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-piecewise-branch-0025","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值分段判定","stem_zh":"對實數 x=-12，應使用 |x| 分段定義中的哪個分支？請回答「非負分支 x」或「負分支 -x」。","answer":{"kind":"short_text","value":"負分支 -x","explanation_zh":"x=-12<0，所以使用 negative 分支，|x|=-x=12。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["零的邊界","分段函數"]},"variant":{"family_id":"qf-absolute-value-piecewise-branch","seed":20261053,"parameters":{"x":-12,"domain":"reals","operation":"piecewise_branch","semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-12}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0001","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-12、b=-15。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"3","explanation_zh":"|a-b|=|-12-(-15)|=|3|=3；交換端點得到 |b-a| 仍為 3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261129,"parameters":{"a":-12,"b":-15,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-12,\"b\":-15,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0002","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-11、b=-8。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"3","explanation_zh":"|a-b|=|-11-(-8)|=|-3|=3；交換端點得到 |b-a| 仍為 3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261130,"parameters":{"a":-11,"b":-8,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-11,\"b\":-8,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0003","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-10、b=-1。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"9","explanation_zh":"|a-b|=|-10-(-1)|=|-9|=9；交換端點得到 |b-a| 仍為 9。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261131,"parameters":{"a":-10,"b":-1,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-10,\"b\":-1,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0004","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-9、b=6。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"15","explanation_zh":"|a-b|=|-9-(6)|=|-15|=15；交換端點得到 |b-a| 仍為 15。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261132,"parameters":{"a":-9,"b":6,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-9,\"b\":6,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0005","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-8、b=13。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"21","explanation_zh":"|a-b|=|-8-(13)|=|-21|=21；交換端點得到 |b-a| 仍為 21。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261133,"parameters":{"a":-8,"b":13,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-8,\"b\":13,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0006","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-7、b=-11。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"4","explanation_zh":"|a-b|=|-7-(-11)|=|4|=4；交換端點得到 |b-a| 仍為 4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261134,"parameters":{"a":-7,"b":-11,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-7,\"b\":-11,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0007","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-6、b=-4。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"2","explanation_zh":"|a-b|=|-6-(-4)|=|-2|=2；交換端點得到 |b-a| 仍為 2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261135,"parameters":{"a":-6,"b":-4,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-6,\"b\":-4,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0008","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-5、b=3。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"8","explanation_zh":"|a-b|=|-5-(3)|=|-8|=8；交換端點得到 |b-a| 仍為 8。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261136,"parameters":{"a":-5,"b":3,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-5,\"b\":3,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0009","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-4、b=10。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"14","explanation_zh":"|a-b|=|-4-(10)|=|-14|=14；交換端點得到 |b-a| 仍為 14。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261137,"parameters":{"a":-4,"b":10,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-4,\"b\":10,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0010","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-3、b=-14。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"11","explanation_zh":"|a-b|=|-3-(-14)|=|11|=11；交換端點得到 |b-a| 仍為 11。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261138,"parameters":{"a":-3,"b":-14,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-3,\"b\":-14,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0011","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-2、b=-7。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"5","explanation_zh":"|a-b|=|-2-(-7)|=|5|=5；交換端點得到 |b-a| 仍為 5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261139,"parameters":{"a":-2,"b":-7,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-2,\"b\":-7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0012","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=-1、b=0。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"1","explanation_zh":"|a-b|=|-1-(0)|=|-1|=1；交換端點得到 |b-a| 仍為 1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261140,"parameters":{"a":-1,"b":0,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":-1,\"b\":0,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0013","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=0、b=7。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"7","explanation_zh":"|a-b|=|0-(7)|=|-7|=7；交換端點得到 |b-a| 仍為 7。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261141,"parameters":{"a":0,"b":7,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":0,\"b\":7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0014","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=1、b=14。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"13","explanation_zh":"|a-b|=|1-(14)|=|-13|=13；交換端點得到 |b-a| 仍為 13。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261142,"parameters":{"a":1,"b":14,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":1,\"b\":14,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0015","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=2、b=-10。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"12","explanation_zh":"|a-b|=|2-(-10)|=|12|=12；交換端點得到 |b-a| 仍為 12。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261143,"parameters":{"a":2,"b":-10,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":2,\"b\":-10,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0016","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=3、b=-3。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"6","explanation_zh":"|a-b|=|3-(-3)|=|6|=6；交換端點得到 |b-a| 仍為 6。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261144,"parameters":{"a":3,"b":-3,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":3,\"b\":-3,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0017","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=4、b=4。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"0","explanation_zh":"|a-b|=|4-(4)|=|0|=0；交換端點得到 |b-a| 仍為 0。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261145,"parameters":{"a":4,"b":4,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":4,\"b\":4,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0018","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=5、b=11。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"6","explanation_zh":"|a-b|=|5-(11)|=|-6|=6；交換端點得到 |b-a| 仍為 6。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261146,"parameters":{"a":5,"b":11,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":5,\"b\":11,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0019","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=6、b=-13。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"19","explanation_zh":"|a-b|=|6-(-13)|=|19|=19；交換端點得到 |b-a| 仍為 19。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261147,"parameters":{"a":6,"b":-13,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":6,\"b\":-13,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0020","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=7、b=-6。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"13","explanation_zh":"|a-b|=|7-(-6)|=|13|=13；交換端點得到 |b-a| 仍為 13。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261148,"parameters":{"a":7,"b":-6,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":7,\"b\":-6,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0021","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=8、b=1。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"7","explanation_zh":"|a-b|=|8-(1)|=|7|=7；交換端點得到 |b-a| 仍為 7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261149,"parameters":{"a":8,"b":1,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":8,\"b\":1,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0022","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=9、b=8。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"1","explanation_zh":"|a-b|=|9-(8)|=|1|=1；交換端點得到 |b-a| 仍為 1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261150,"parameters":{"a":9,"b":8,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":9,\"b\":8,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0023","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=10、b=15。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"5","explanation_zh":"|a-b|=|10-(15)|=|-5|=5；交換端點得到 |b-a| 仍為 5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261151,"parameters":{"a":10,"b":15,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":10,\"b\":15,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0024","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=11、b=-9。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"20","explanation_zh":"|a-b|=|11-(-9)|=|20|=20；交換端點得到 |b-a| 仍為 20。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261152,"parameters":{"a":11,"b":-9,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":11,\"b\":-9,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-distance-0025","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"數線上的兩點距離","stem_zh":"實數線上兩點 a=12、b=-2。用 |a-b| 精確計算兩點距離。","answer":{"kind":"short_text","value":"14","explanation_zh":"|a-b|=|12-(-2)|=|14|=14；交換端點得到 |b-a| 仍為 14。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["數線距離","差的絕對值"]},"variant":{"family_id":"qf-absolute-value-distance","seed":20261153,"parameters":{"a":12,"b":-2,"domain":"reals","operation":"number_line_distance","semantic_template":"qf-absolute-value-distance/{\"a\":12,\"b\":-2,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0001","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=-4 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"絕對值永遠非負，不可能等於 -4，所以無解。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261229,"parameters":{"c":-4,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":-4,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0002","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=-3 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"絕對值永遠非負，不可能等於 -3，所以無解。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261230,"parameters":{"c":-3,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":-3,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0003","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=-2 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"絕對值永遠非負，不可能等於 -2，所以無解。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261231,"parameters":{"c":-2,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":-2,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0004","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=-1 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"絕對值永遠非負，不可能等於 -1，所以無解。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261232,"parameters":{"c":-1,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":-1,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0005","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=0","explanation_zh":"|x|=0 只在 x=0 時成立。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261233,"parameters":{"c":0,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":0,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0006","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=1 的解集。","answer":{"kind":"short_text","value":"兩解 x=-1, 1","explanation_zh":"到 0 的距離為 1 的實數位於兩側，因此 x=-1 或 x=1。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261234,"parameters":{"c":1,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":1,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0007","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=2 的解集。","answer":{"kind":"short_text","value":"兩解 x=-2, 2","explanation_zh":"到 0 的距離為 2 的實數位於兩側，因此 x=-2 或 x=2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261235,"parameters":{"c":2,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":2,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0008","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=3 的解集。","answer":{"kind":"short_text","value":"兩解 x=-3, 3","explanation_zh":"到 0 的距離為 3 的實數位於兩側，因此 x=-3 或 x=3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261236,"parameters":{"c":3,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":3,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0009","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=4 的解集。","answer":{"kind":"short_text","value":"兩解 x=-4, 4","explanation_zh":"到 0 的距離為 4 的實數位於兩側，因此 x=-4 或 x=4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261237,"parameters":{"c":4,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":4,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0010","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=5 的解集。","answer":{"kind":"short_text","value":"兩解 x=-5, 5","explanation_zh":"到 0 的距離為 5 的實數位於兩側，因此 x=-5 或 x=5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261238,"parameters":{"c":5,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":5,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0011","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=6 的解集。","answer":{"kind":"short_text","value":"兩解 x=-6, 6","explanation_zh":"到 0 的距離為 6 的實數位於兩側，因此 x=-6 或 x=6。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261239,"parameters":{"c":6,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":6,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0012","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=7 的解集。","answer":{"kind":"short_text","value":"兩解 x=-7, 7","explanation_zh":"到 0 的距離為 7 的實數位於兩側，因此 x=-7 或 x=7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261240,"parameters":{"c":7,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":7,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0013","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=8 的解集。","answer":{"kind":"short_text","value":"兩解 x=-8, 8","explanation_zh":"到 0 的距離為 8 的實數位於兩側，因此 x=-8 或 x=8。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261241,"parameters":{"c":8,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":8,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0014","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=9 的解集。","answer":{"kind":"short_text","value":"兩解 x=-9, 9","explanation_zh":"到 0 的距離為 9 的實數位於兩側，因此 x=-9 或 x=9。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261242,"parameters":{"c":9,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":9,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0015","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=10 的解集。","answer":{"kind":"short_text","value":"兩解 x=-10, 10","explanation_zh":"到 0 的距離為 10 的實數位於兩側，因此 x=-10 或 x=10。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261243,"parameters":{"c":10,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":10,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0016","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=11 的解集。","answer":{"kind":"short_text","value":"兩解 x=-11, 11","explanation_zh":"到 0 的距離為 11 的實數位於兩側，因此 x=-11 或 x=11。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261244,"parameters":{"c":11,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":11,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0017","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=12 的解集。","answer":{"kind":"short_text","value":"兩解 x=-12, 12","explanation_zh":"到 0 的距離為 12 的實數位於兩側，因此 x=-12 或 x=12。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261245,"parameters":{"c":12,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":12,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0018","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=13 的解集。","answer":{"kind":"short_text","value":"兩解 x=-13, 13","explanation_zh":"到 0 的距離為 13 的實數位於兩側，因此 x=-13 或 x=13。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261246,"parameters":{"c":13,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":13,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0019","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=14 的解集。","answer":{"kind":"short_text","value":"兩解 x=-14, 14","explanation_zh":"到 0 的距離為 14 的實數位於兩側，因此 x=-14 或 x=14。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261247,"parameters":{"c":14,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":14,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0020","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=15 的解集。","answer":{"kind":"short_text","value":"兩解 x=-15, 15","explanation_zh":"到 0 的距離為 15 的實數位於兩側，因此 x=-15 或 x=15。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261248,"parameters":{"c":15,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":15,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0021","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=16 的解集。","answer":{"kind":"short_text","value":"兩解 x=-16, 16","explanation_zh":"到 0 的距離為 16 的實數位於兩側，因此 x=-16 或 x=16。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261249,"parameters":{"c":16,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":16,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0022","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=17 的解集。","answer":{"kind":"short_text","value":"兩解 x=-17, 17","explanation_zh":"到 0 的距離為 17 的實數位於兩側，因此 x=-17 或 x=17。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261250,"parameters":{"c":17,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":17,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0023","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=18 的解集。","answer":{"kind":"short_text","value":"兩解 x=-18, 18","explanation_zh":"到 0 的距離為 18 的實數位於兩側，因此 x=-18 或 x=18。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261251,"parameters":{"c":18,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":18,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0024","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=19 的解集。","answer":{"kind":"short_text","value":"兩解 x=-19, 19","explanation_zh":"到 0 的距離為 19 的實數位於兩側，因此 x=-19 或 x=19。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261252,"parameters":{"c":19,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":19,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260928-absolute-value-equation-class-0025","batch_id":"batch-20260928-absolute-value-foundations","language":"zh-Hant","source_mko_ids":["mko-absolute-value"],"title_zh":"絕對值方程的解分類","stem_zh":"在實數論域，分類方程 |x|=20 的解集。","answer":{"kind":"short_text","value":"兩解 x=-20, 20","explanation_zh":"到 0 的距離為 20 的實數位於兩側，因此 x=-20 或 x=20。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["絕對值方程","解集合分類"]},"variant":{"family_id":"qf-absolute-value-equation-class","seed":20261253,"parameters":{"c":20,"domain":"reals","operation":"absolute_equation_solution_class","semantic_template":"qf-absolute-value-equation-class/{\"c\":20,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"}},"verification":{"status":"candidate","checks":["json_schema","independent_answer_recomputation"],"warning_zh":"本題為 candidate；有限整數案例的精確重算不是全部實數性質的形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex GPT-5 (single-context degraded run)","generated_at":"2026-09-28","contract_version":"ocme-question-factory-v0.1"}}