{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0001","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[0,1],\"right\":[4,1],\"left_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(0, 4, 1, 1, 否)","explanation_zh":"應用擴展核對=(0, 4, 1, 1, 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215001,"parameters":{"left":[0,1],"right":[4,1],"left_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[0,1],\"left_sign\":1,\"right\":[4,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0002","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[1,1],\"right\":[5,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, -1, 1, 是)","explanation_zh":"應用擴展核對=(1, 5, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215002,"parameters":{"left":[1,1],"right":[5,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[1,1],\"left_sign\":-1,\"right\":[5,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0003","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[2,1],\"right\":[6,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, -1, 1, 是)","explanation_zh":"應用擴展核對=(2, 6, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215003,"parameters":{"left":[2,1],"right":[6,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[2,1],\"left_sign\":-1,\"right\":[6,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0004","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[3,1],\"right\":[7,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, -1, 1, 是)","explanation_zh":"應用擴展核對=(3, 7, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215004,"parameters":{"left":[3,1],"right":[7,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[3,1],\"left_sign\":-1,\"right\":[7,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0005","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[4,1],\"right\":[8,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, -1, 1, 是)","explanation_zh":"應用擴展核對=(4, 8, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215005,"parameters":{"left":[4,1],"right":[8,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[4,1],\"left_sign\":-1,\"right\":[8,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0006","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[5,1],\"right\":[9,1],\"left_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(5, 9, 1, 1, 否)","explanation_zh":"應用擴展核對=(5, 9, 1, 1, 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215006,"parameters":{"left":[5,1],"right":[9,1],"left_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[5,1],\"left_sign\":1,\"right\":[9,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0007","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[6,1],\"right\":[10,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(6, 10, -1, 1, 是)","explanation_zh":"應用擴展核對=(6, 10, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215007,"parameters":{"left":[6,1],"right":[10,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[6,1],\"left_sign\":-1,\"right\":[10,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0008","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[7,1],\"right\":[11,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(7, 11, -1, 1, 是)","explanation_zh":"應用擴展核對=(7, 11, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215008,"parameters":{"left":[7,1],"right":[11,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[7,1],\"left_sign\":-1,\"right\":[11,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0009","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[8,1],\"right\":[12,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(8, 12, -1, 1, 是)","explanation_zh":"應用擴展核對=(8, 12, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215009,"parameters":{"left":[8,1],"right":[12,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[8,1],\"left_sign\":-1,\"right\":[12,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0010","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[9,1],\"right\":[13,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(9, 13, -1, 1, 是)","explanation_zh":"應用擴展核對=(9, 13, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215010,"parameters":{"left":[9,1],"right":[13,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[9,1],\"left_sign\":-1,\"right\":[13,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0011","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[10,1],\"right\":[14,1],\"left_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(10, 14, 1, 1, 否)","explanation_zh":"應用擴展核對=(10, 14, 1, 1, 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215011,"parameters":{"left":[10,1],"right":[14,1],"left_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[10,1],\"left_sign\":1,\"right\":[14,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0012","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[11,1],\"right\":[15,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(11, 15, -1, 1, 是)","explanation_zh":"應用擴展核對=(11, 15, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215012,"parameters":{"left":[11,1],"right":[15,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[11,1],\"left_sign\":-1,\"right\":[15,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0013","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[12,1],\"right\":[16,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(12, 16, -1, 1, 是)","explanation_zh":"應用擴展核對=(12, 16, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215013,"parameters":{"left":[12,1],"right":[16,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[12,1],\"left_sign\":-1,\"right\":[16,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0014","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[13,1],\"right\":[17,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(13, 17, -1, 1, 是)","explanation_zh":"應用擴展核對=(13, 17, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215014,"parameters":{"left":[13,1],"right":[17,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[13,1],\"left_sign\":-1,\"right\":[17,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0015","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[14,1],\"right\":[18,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(14, 18, -1, 1, 是)","explanation_zh":"應用擴展核對=(14, 18, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215015,"parameters":{"left":[14,1],"right":[18,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[14,1],\"left_sign\":-1,\"right\":[18,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0016","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[15,1],\"right\":[19,1],\"left_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(15, 19, 1, 1, 否)","explanation_zh":"應用擴展核對=(15, 19, 1, 1, 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215016,"parameters":{"left":[15,1],"right":[19,1],"left_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[15,1],\"left_sign\":1,\"right\":[19,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0017","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[16,1],\"right\":[20,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(16, 20, -1, 1, 是)","explanation_zh":"應用擴展核對=(16, 20, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215017,"parameters":{"left":[16,1],"right":[20,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[16,1],\"left_sign\":-1,\"right\":[20,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0018","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[17,1],\"right\":[21,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(17, 21, -1, 1, 是)","explanation_zh":"應用擴展核對=(17, 21, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215018,"parameters":{"left":[17,1],"right":[21,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[17,1],\"left_sign\":-1,\"right\":[21,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0019","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[18,1],\"right\":[22,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(18, 22, -1, 1, 是)","explanation_zh":"應用擴展核對=(18, 22, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215019,"parameters":{"left":[18,1],"right":[22,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[18,1],\"left_sign\":-1,\"right\":[22,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0020","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[19,1],\"right\":[23,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(19, 23, -1, 1, 是)","explanation_zh":"應用擴展核對=(19, 23, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215020,"parameters":{"left":[19,1],"right":[23,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[19,1],\"left_sign\":-1,\"right\":[23,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0021","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[20,1],\"right\":[24,1],\"left_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(20, 24, 1, 1, 否)","explanation_zh":"應用擴展核對=(20, 24, 1, 1, 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215021,"parameters":{"left":[20,1],"right":[24,1],"left_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[20,1],\"left_sign\":1,\"right\":[24,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0022","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[21,1],\"right\":[25,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(21, 25, -1, 1, 是)","explanation_zh":"應用擴展核對=(21, 25, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215022,"parameters":{"left":[21,1],"right":[25,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[21,1],\"left_sign\":-1,\"right\":[25,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0023","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[22,1],\"right\":[26,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(22, 26, -1, 1, 是)","explanation_zh":"應用擴展核對=(22, 26, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215023,"parameters":{"left":[22,1],"right":[26,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[22,1],\"left_sign\":-1,\"right\":[26,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0024","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[23,1],\"right\":[27,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(23, 27, -1, 1, 是)","explanation_zh":"應用擴展核對=(23, 27, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215024,"parameters":{"left":[23,1],"right":[27,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[23,1],\"left_sign\":-1,\"right\":[27,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0025","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-bracket-qualification；資料={\"left\":[24,1],\"right\":[28,1],\"left_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,right_sign,declared_sign_bracket] 欄序回答。","answer":{"kind":"expression","value":"(24, 28, -1, 1, 是)","explanation_zh":"應用擴展核對=(24, 28, -1, 1, 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-bracket-qualification","seed":202610215025,"parameters":{"left":[24,1],"right":[28,1],"left_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-bracket-qualification","semantic_template":"qf-app21-bisection-bracket-qualification/{\"left\":[24,1],\"left_sign\":-1,\"right\":[28,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0026","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[0,1],\"right\":[4,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(0, 4, -1, -1, 1, 2, [2, 4, -1, 1])","explanation_zh":"應用擴展核對=(0, 4, -1, -1, 1, 2, [2, 4, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215026,"parameters":{"left":[0,1],"right":[4,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[0,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[4,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0027","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[1,1],\"right\":[5,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, -1, 1, 1, 3, [1, 3, -1, 1])","explanation_zh":"應用擴展核對=(1, 5, -1, 1, 1, 3, [1, 3, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215027,"parameters":{"left":[1,1],"right":[5,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[1,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[5,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0028","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[2,1],\"right\":[6,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, -1, 0, 1, 4, [4, 4, 0, 0])","explanation_zh":"應用擴展核對=(2, 6, -1, 0, 1, 4, [4, 4, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215028,"parameters":{"left":[2,1],"right":[6,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[2,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[6,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0029","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[3,1],\"right\":[7,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, -1, -1, 1, 5, [5, 7, -1, 1])","explanation_zh":"應用擴展核對=(3, 7, -1, -1, 1, 5, [5, 7, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215029,"parameters":{"left":[3,1],"right":[7,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[3,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[7,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0030","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[4,1],\"right\":[8,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, -1, 1, 1, 6, [4, 6, -1, 1])","explanation_zh":"應用擴展核對=(4, 8, -1, 1, 1, 6, [4, 6, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215030,"parameters":{"left":[4,1],"right":[8,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[4,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[8,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0031","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[5,1],\"right\":[9,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(5, 9, -1, 0, 1, 7, [7, 7, 0, 0])","explanation_zh":"應用擴展核對=(5, 9, -1, 0, 1, 7, [7, 7, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215031,"parameters":{"left":[5,1],"right":[9,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[5,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[9,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0032","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[6,1],\"right\":[10,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(6, 10, -1, -1, 1, 8, [8, 10, -1, 1])","explanation_zh":"應用擴展核對=(6, 10, -1, -1, 1, 8, [8, 10, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215032,"parameters":{"left":[6,1],"right":[10,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[6,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[10,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0033","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[7,1],\"right\":[11,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(7, 11, -1, 1, 1, 9, [7, 9, -1, 1])","explanation_zh":"應用擴展核對=(7, 11, -1, 1, 1, 9, [7, 9, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215033,"parameters":{"left":[7,1],"right":[11,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[7,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[11,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0034","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[8,1],\"right\":[12,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(8, 12, -1, 0, 1, 10, [10, 10, 0, 0])","explanation_zh":"應用擴展核對=(8, 12, -1, 0, 1, 10, [10, 10, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215034,"parameters":{"left":[8,1],"right":[12,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[8,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[12,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0035","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[9,1],\"right\":[13,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(9, 13, -1, -1, 1, 11, [11, 13, -1, 1])","explanation_zh":"應用擴展核對=(9, 13, -1, -1, 1, 11, [11, 13, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215035,"parameters":{"left":[9,1],"right":[13,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[9,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[13,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0036","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[10,1],\"right\":[14,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(10, 14, -1, 1, 1, 12, [10, 12, -1, 1])","explanation_zh":"應用擴展核對=(10, 14, -1, 1, 1, 12, [10, 12, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215036,"parameters":{"left":[10,1],"right":[14,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[10,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[14,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0037","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[11,1],\"right\":[15,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(11, 15, -1, 0, 1, 13, [13, 13, 0, 0])","explanation_zh":"應用擴展核對=(11, 15, -1, 0, 1, 13, [13, 13, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215037,"parameters":{"left":[11,1],"right":[15,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[11,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[15,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0038","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[12,1],\"right\":[16,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(12, 16, -1, -1, 1, 14, [14, 16, -1, 1])","explanation_zh":"應用擴展核對=(12, 16, -1, -1, 1, 14, [14, 16, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215038,"parameters":{"left":[12,1],"right":[16,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[12,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[16,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0039","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[13,1],\"right\":[17,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(13, 17, -1, 1, 1, 15, [13, 15, -1, 1])","explanation_zh":"應用擴展核對=(13, 17, -1, 1, 1, 15, [13, 15, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215039,"parameters":{"left":[13,1],"right":[17,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[13,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[17,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0040","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[14,1],\"right\":[18,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(14, 18, -1, 0, 1, 16, [16, 16, 0, 0])","explanation_zh":"應用擴展核對=(14, 18, -1, 0, 1, 16, [16, 16, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215040,"parameters":{"left":[14,1],"right":[18,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[14,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[18,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0041","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[15,1],\"right\":[19,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(15, 19, -1, -1, 1, 17, [17, 19, -1, 1])","explanation_zh":"應用擴展核對=(15, 19, -1, -1, 1, 17, [17, 19, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215041,"parameters":{"left":[15,1],"right":[19,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[15,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[19,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0042","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[16,1],\"right\":[20,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(16, 20, -1, 1, 1, 18, [16, 18, -1, 1])","explanation_zh":"應用擴展核對=(16, 20, -1, 1, 1, 18, [16, 18, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215042,"parameters":{"left":[16,1],"right":[20,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[16,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[20,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0043","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[17,1],\"right\":[21,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(17, 21, -1, 0, 1, 19, [19, 19, 0, 0])","explanation_zh":"應用擴展核對=(17, 21, -1, 0, 1, 19, [19, 19, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215043,"parameters":{"left":[17,1],"right":[21,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[17,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[21,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0044","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[18,1],\"right\":[22,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(18, 22, -1, -1, 1, 20, [20, 22, -1, 1])","explanation_zh":"應用擴展核對=(18, 22, -1, -1, 1, 20, [20, 22, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215044,"parameters":{"left":[18,1],"right":[22,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[18,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[22,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0045","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[19,1],\"right\":[23,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(19, 23, -1, 1, 1, 21, [19, 21, -1, 1])","explanation_zh":"應用擴展核對=(19, 23, -1, 1, 1, 21, [19, 21, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215045,"parameters":{"left":[19,1],"right":[23,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[19,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[23,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0046","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[20,1],\"right\":[24,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(20, 24, -1, 0, 1, 22, [22, 22, 0, 0])","explanation_zh":"應用擴展核對=(20, 24, -1, 0, 1, 22, [22, 22, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215046,"parameters":{"left":[20,1],"right":[24,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[20,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[24,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0047","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[21,1],\"right\":[25,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(21, 25, -1, -1, 1, 23, [23, 25, -1, 1])","explanation_zh":"應用擴展核對=(21, 25, -1, -1, 1, 23, [23, 25, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215047,"parameters":{"left":[21,1],"right":[25,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[21,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[25,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0048","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[22,1],\"right\":[26,1],\"left_sign\":-1,\"mid_sign\":1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(22, 26, -1, 1, 1, 24, [22, 24, -1, 1])","explanation_zh":"應用擴展核對=(22, 26, -1, 1, 1, 24, [22, 24, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215048,"parameters":{"left":[22,1],"right":[26,1],"left_sign":-1,"mid_sign":1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[22,1],\"left_sign\":-1,\"mid_sign\":1,\"right\":[26,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0049","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[23,1],\"right\":[27,1],\"left_sign\":-1,\"mid_sign\":0,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(23, 27, -1, 0, 1, 25, [25, 25, 0, 0])","explanation_zh":"應用擴展核對=(23, 27, -1, 0, 1, 25, [25, 25, 0, 0])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215049,"parameters":{"left":[23,1],"right":[27,1],"left_sign":-1,"mid_sign":0,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[23,1],\"left_sign\":-1,\"mid_sign\":0,\"right\":[27,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0050","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-single-update；資料={\"left\":[24,1],\"right\":[28,1],\"left_sign\":-1,\"mid_sign\":-1,\"right_sign\":1}。請依 [left,right,left_sign,mid_sign,right_sign,midpoint,next_bracket] 欄序回答。","answer":{"kind":"expression","value":"(24, 28, -1, -1, 1, 26, [26, 28, -1, 1])","explanation_zh":"應用擴展核對=(24, 28, -1, -1, 1, 26, [26, 28, -1, 1])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-single-update","seed":202610215050,"parameters":{"left":[24,1],"right":[28,1],"left_sign":-1,"mid_sign":-1,"right_sign":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-single-update","semantic_template":"qf-app21-bisection-single-update/{\"left\":[24,1],\"left_sign\":-1,\"mid_sign\":-1,\"right\":[28,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0051","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[0,1],\"right\":[4,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(0, 4, -1, 1, [1], [[0, 4, 2, 1, 0, 2]], 0, 2)","explanation_zh":"應用擴展核對=(0, 4, -1, 1, [1], [[0, 4, 2, 1, 0, 2]], 0, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215051,"parameters":{"left":[0,1],"right":[4,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[0,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[4,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0052","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[1,1],\"right\":[5,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, -1, 1, [1, 1], [[1, 5, 3, 1, 1, 3], [1, 3, 2, 1, 1, 2]], 1, 2)","explanation_zh":"應用擴展核對=(1, 5, -1, 1, [1, 1], [[1, 5, 3, 1, 1, 3], [1, 3, 2, 1, 1, 2]], 1, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215052,"parameters":{"left":[1,1],"right":[5,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[1,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[5,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0053","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[2,1],\"right\":[6,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, -1, 1, [1, 1, 1], [[2, 6, 4, 1, 2, 4], [2, 4, 3, 1, 2, 3], [2, 3, 5/2, 1, 2, 5/2]], 2, 5/2)","explanation_zh":"應用擴展核對=(2, 6, -1, 1, [1, 1, 1], [[2, 6, 4, 1, 2, 4], [2, 4, 3, 1, 2, 3], [2, 3, 5/2, 1, 2, 5/2]], 2, 5/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215053,"parameters":{"left":[2,1],"right":[6,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[2,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[6,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0054","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[3,1],\"right\":[7,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, -1, 1, [1, 1, 1, -1], [[3, 7, 5, 1, 3, 5], [3, 5, 4, 1, 3, 4], [3, 4, 7/2, 1, 3, 7/2], [3, 7/2, 13/4, -1, 13/4, 7/2]], 13/4, 7/2)","explanation_zh":"應用擴展核對=(3, 7, -1, 1, [1, 1, 1, -1], [[3, 7, 5, 1, 3, 5], [3, 5, 4, 1, 3, 4], [3, 4, 7/2, 1, 3, 7/2], [3, 7/2, 13/4, -1, 13/4, 7/2]], 13/4, 7/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215054,"parameters":{"left":[3,1],"right":[7,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[3,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[7,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0055","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[4,1],\"right\":[8,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, -1, 1, [1], [[4, 8, 6, 1, 4, 6]], 4, 6)","explanation_zh":"應用擴展核對=(4, 8, -1, 1, [1], [[4, 8, 6, 1, 4, 6]], 4, 6)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215055,"parameters":{"left":[4,1],"right":[8,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[4,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[8,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0056","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[5,1],\"right\":[9,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(5, 9, -1, 1, [1, 1], [[5, 9, 7, 1, 5, 7], [5, 7, 6, 1, 5, 6]], 5, 6)","explanation_zh":"應用擴展核對=(5, 9, -1, 1, [1, 1], [[5, 9, 7, 1, 5, 7], [5, 7, 6, 1, 5, 6]], 5, 6)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215056,"parameters":{"left":[5,1],"right":[9,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[5,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[9,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0057","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[6,1],\"right\":[10,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(6, 10, -1, 1, [1, 1, 1], [[6, 10, 8, 1, 6, 8], [6, 8, 7, 1, 6, 7], [6, 7, 13/2, 1, 6, 13/2]], 6, 13/2)","explanation_zh":"應用擴展核對=(6, 10, -1, 1, [1, 1, 1], [[6, 10, 8, 1, 6, 8], [6, 8, 7, 1, 6, 7], [6, 7, 13/2, 1, 6, 13/2]], 6, 13/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215057,"parameters":{"left":[6,1],"right":[10,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[6,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[10,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0058","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[7,1],\"right\":[11,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(7, 11, -1, 1, [1, 1, 1, -1], [[7, 11, 9, 1, 7, 9], [7, 9, 8, 1, 7, 8], [7, 8, 15/2, 1, 7, 15/2], [7, 15/2, 29/4, -1, 29/4, 15/2]], 29/4, 15/2)","explanation_zh":"應用擴展核對=(7, 11, -1, 1, [1, 1, 1, -1], [[7, 11, 9, 1, 7, 9], [7, 9, 8, 1, 7, 8], [7, 8, 15/2, 1, 7, 15/2], [7, 15/2, 29/4, -1, 29/4, 15/2]], 29/4, 15/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215058,"parameters":{"left":[7,1],"right":[11,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[7,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[11,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0059","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[8,1],\"right\":[12,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(8, 12, -1, 1, [1], [[8, 12, 10, 1, 8, 10]], 8, 10)","explanation_zh":"應用擴展核對=(8, 12, -1, 1, [1], [[8, 12, 10, 1, 8, 10]], 8, 10)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215059,"parameters":{"left":[8,1],"right":[12,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[8,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[12,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0060","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[9,1],\"right\":[13,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(9, 13, -1, 1, [1, 1], [[9, 13, 11, 1, 9, 11], [9, 11, 10, 1, 9, 10]], 9, 10)","explanation_zh":"應用擴展核對=(9, 13, -1, 1, [1, 1], [[9, 13, 11, 1, 9, 11], [9, 11, 10, 1, 9, 10]], 9, 10)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215060,"parameters":{"left":[9,1],"right":[13,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[9,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[13,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0061","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[10,1],\"right\":[14,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(10, 14, -1, 1, [1, 1, 1], [[10, 14, 12, 1, 10, 12], [10, 12, 11, 1, 10, 11], [10, 11, 21/2, 1, 10, 21/2]], 10, 21/2)","explanation_zh":"應用擴展核對=(10, 14, -1, 1, [1, 1, 1], [[10, 14, 12, 1, 10, 12], [10, 12, 11, 1, 10, 11], [10, 11, 21/2, 1, 10, 21/2]], 10, 21/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215061,"parameters":{"left":[10,1],"right":[14,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[10,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[14,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0062","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[11,1],\"right\":[15,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(11, 15, -1, 1, [1, 1, 1, -1], [[11, 15, 13, 1, 11, 13], [11, 13, 12, 1, 11, 12], [11, 12, 23/2, 1, 11, 23/2], [11, 23/2, 45/4, -1, 45/4, 23/2]], 45/4, 23/2)","explanation_zh":"應用擴展核對=(11, 15, -1, 1, [1, 1, 1, -1], [[11, 15, 13, 1, 11, 13], [11, 13, 12, 1, 11, 12], [11, 12, 23/2, 1, 11, 23/2], [11, 23/2, 45/4, -1, 45/4, 23/2]], 45/4, 23/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215062,"parameters":{"left":[11,1],"right":[15,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[11,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[15,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0063","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[12,1],\"right\":[16,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(12, 16, -1, 1, [1], [[12, 16, 14, 1, 12, 14]], 12, 14)","explanation_zh":"應用擴展核對=(12, 16, -1, 1, [1], [[12, 16, 14, 1, 12, 14]], 12, 14)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215063,"parameters":{"left":[12,1],"right":[16,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[12,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[16,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0064","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[13,1],\"right\":[17,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(13, 17, -1, 1, [1, 1], [[13, 17, 15, 1, 13, 15], [13, 15, 14, 1, 13, 14]], 13, 14)","explanation_zh":"應用擴展核對=(13, 17, -1, 1, [1, 1], [[13, 17, 15, 1, 13, 15], [13, 15, 14, 1, 13, 14]], 13, 14)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215064,"parameters":{"left":[13,1],"right":[17,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[13,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[17,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0065","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[14,1],\"right\":[18,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(14, 18, -1, 1, [1, 1, 1], [[14, 18, 16, 1, 14, 16], [14, 16, 15, 1, 14, 15], [14, 15, 29/2, 1, 14, 29/2]], 14, 29/2)","explanation_zh":"應用擴展核對=(14, 18, -1, 1, [1, 1, 1], [[14, 18, 16, 1, 14, 16], [14, 16, 15, 1, 14, 15], [14, 15, 29/2, 1, 14, 29/2]], 14, 29/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215065,"parameters":{"left":[14,1],"right":[18,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[14,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[18,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0066","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[15,1],\"right\":[19,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(15, 19, -1, 1, [1, 1, 1, -1], [[15, 19, 17, 1, 15, 17], [15, 17, 16, 1, 15, 16], [15, 16, 31/2, 1, 15, 31/2], [15, 31/2, 61/4, -1, 61/4, 31/2]], 61/4, 31/2)","explanation_zh":"應用擴展核對=(15, 19, -1, 1, [1, 1, 1, -1], [[15, 19, 17, 1, 15, 17], [15, 17, 16, 1, 15, 16], [15, 16, 31/2, 1, 15, 31/2], [15, 31/2, 61/4, -1, 61/4, 31/2]], 61/4, 31/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215066,"parameters":{"left":[15,1],"right":[19,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[15,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[19,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0067","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[16,1],\"right\":[20,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(16, 20, -1, 1, [1], [[16, 20, 18, 1, 16, 18]], 16, 18)","explanation_zh":"應用擴展核對=(16, 20, -1, 1, [1], [[16, 20, 18, 1, 16, 18]], 16, 18)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215067,"parameters":{"left":[16,1],"right":[20,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[16,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[20,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0068","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[17,1],\"right\":[21,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(17, 21, -1, 1, [1, 1], [[17, 21, 19, 1, 17, 19], [17, 19, 18, 1, 17, 18]], 17, 18)","explanation_zh":"應用擴展核對=(17, 21, -1, 1, [1, 1], [[17, 21, 19, 1, 17, 19], [17, 19, 18, 1, 17, 18]], 17, 18)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215068,"parameters":{"left":[17,1],"right":[21,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[17,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[21,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0069","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[18,1],\"right\":[22,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(18, 22, -1, 1, [1, 1, 1], [[18, 22, 20, 1, 18, 20], [18, 20, 19, 1, 18, 19], [18, 19, 37/2, 1, 18, 37/2]], 18, 37/2)","explanation_zh":"應用擴展核對=(18, 22, -1, 1, [1, 1, 1], [[18, 22, 20, 1, 18, 20], [18, 20, 19, 1, 18, 19], [18, 19, 37/2, 1, 18, 37/2]], 18, 37/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215069,"parameters":{"left":[18,1],"right":[22,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[18,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[22,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0070","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[19,1],\"right\":[23,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(19, 23, -1, 1, [1, 1, 1, -1], [[19, 23, 21, 1, 19, 21], [19, 21, 20, 1, 19, 20], [19, 20, 39/2, 1, 19, 39/2], [19, 39/2, 77/4, -1, 77/4, 39/2]], 77/4, 39/2)","explanation_zh":"應用擴展核對=(19, 23, -1, 1, [1, 1, 1, -1], [[19, 23, 21, 1, 19, 21], [19, 21, 20, 1, 19, 20], [19, 20, 39/2, 1, 19, 39/2], [19, 39/2, 77/4, -1, 77/4, 39/2]], 77/4, 39/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215070,"parameters":{"left":[19,1],"right":[23,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[19,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[23,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0071","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[20,1],\"right\":[24,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(20, 24, -1, 1, [1], [[20, 24, 22, 1, 20, 22]], 20, 22)","explanation_zh":"應用擴展核對=(20, 24, -1, 1, [1], [[20, 24, 22, 1, 20, 22]], 20, 22)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215071,"parameters":{"left":[20,1],"right":[24,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[20,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[24,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0072","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[21,1],\"right\":[25,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(21, 25, -1, 1, [1, 1], [[21, 25, 23, 1, 21, 23], [21, 23, 22, 1, 21, 22]], 21, 22)","explanation_zh":"應用擴展核對=(21, 25, -1, 1, [1, 1], [[21, 25, 23, 1, 21, 23], [21, 23, 22, 1, 21, 22]], 21, 22)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215072,"parameters":{"left":[21,1],"right":[25,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[21,1],\"left_sign\":-1,\"mid_signs\":[1,1],\"right\":[25,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0073","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[22,1],\"right\":[26,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(22, 26, -1, 1, [1, 1, 1], [[22, 26, 24, 1, 22, 24], [22, 24, 23, 1, 22, 23], [22, 23, 45/2, 1, 22, 45/2]], 22, 45/2)","explanation_zh":"應用擴展核對=(22, 26, -1, 1, [1, 1, 1], [[22, 26, 24, 1, 22, 24], [22, 24, 23, 1, 22, 23], [22, 23, 45/2, 1, 22, 45/2]], 22, 45/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215073,"parameters":{"left":[22,1],"right":[26,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[22,1],\"left_sign\":-1,\"mid_signs\":[1,1,1],\"right\":[26,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0074","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[23,1],\"right\":[27,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1,1,1,-1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(23, 27, -1, 1, [1, 1, 1, -1], [[23, 27, 25, 1, 23, 25], [23, 25, 24, 1, 23, 24], [23, 24, 47/2, 1, 23, 47/2], [23, 47/2, 93/4, -1, 93/4, 47/2]], 93/4, 47/2)","explanation_zh":"應用擴展核對=(23, 27, -1, 1, [1, 1, 1, -1], [[23, 27, 25, 1, 23, 25], [23, 25, 24, 1, 23, 24], [23, 24, 47/2, 1, 23, 47/2], [23, 47/2, 93/4, -1, 93/4, 47/2]], 93/4, 47/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215074,"parameters":{"left":[23,1],"right":[27,1],"left_sign":-1,"right_sign":1,"mid_signs":[1,1,1,-1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[23,1],\"left_sign\":-1,\"mid_signs\":[1,1,1,-1],\"right\":[27,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0075","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-finite-trace；資料={\"left\":[24,1],\"right\":[28,1],\"left_sign\":-1,\"right_sign\":1,\"mid_signs\":[1]}。請依 [initial_left,initial_right,left_sign,right_sign,mid_signs,rows,final_left,final_right] 欄序回答。","answer":{"kind":"expression","value":"(24, 28, -1, 1, [1], [[24, 28, 26, 1, 24, 26]], 24, 26)","explanation_zh":"應用擴展核對=(24, 28, -1, 1, [1], [[24, 28, 26, 1, 24, 26]], 24, 26)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-finite-trace","seed":202610215075,"parameters":{"left":[24,1],"right":[28,1],"left_sign":-1,"right_sign":1,"mid_signs":[1],"domain":"Declared_sign_bracket_updates","operation":"bisection-finite-trace","semantic_template":"qf-app21-bisection-finite-trace/{\"left\":[24,1],\"left_sign\":-1,\"mid_signs\":[1],\"right\":[28,1],\"right_sign\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0076","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[-3,1],\"right\":[5,1],\"steps\":0}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(-3, 5, 0, 8)","explanation_zh":"應用擴展核對=(-3, 5, 0, 8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215076,"parameters":{"left":[-3,1],"right":[5,1],"steps":0,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[-3,1],\"right\":[5,1],\"steps\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0077","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[-2,1],\"right\":[6,1],\"steps\":1}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(-2, 6, 1, 4)","explanation_zh":"應用擴展核對=(-2, 6, 1, 4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215077,"parameters":{"left":[-2,1],"right":[6,1],"steps":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[-2,1],\"right\":[6,1],\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0078","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[-1,1],\"right\":[7,1],\"steps\":2}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(-1, 7, 2, 2)","explanation_zh":"應用擴展核對=(-1, 7, 2, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215078,"parameters":{"left":[-1,1],"right":[7,1],"steps":2,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[-1,1],\"right\":[7,1],\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0079","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[0,1],\"right\":[8,1],\"steps\":3}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(0, 8, 3, 1)","explanation_zh":"應用擴展核對=(0, 8, 3, 1)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215079,"parameters":{"left":[0,1],"right":[8,1],"steps":3,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[0,1],\"right\":[8,1],\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0080","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[1,1],\"right\":[9,1],\"steps\":4}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(1, 9, 4, 1/2)","explanation_zh":"應用擴展核對=(1, 9, 4, 1/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215080,"parameters":{"left":[1,1],"right":[9,1],"steps":4,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[1,1],\"right\":[9,1],\"steps\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0081","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[2,1],\"right\":[10,1],\"steps\":5}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(2, 10, 5, 1/4)","explanation_zh":"應用擴展核對=(2, 10, 5, 1/4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215081,"parameters":{"left":[2,1],"right":[10,1],"steps":5,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[2,1],\"right\":[10,1],\"steps\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0082","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[3,1],\"right\":[11,1],\"steps\":6}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(3, 11, 6, 1/8)","explanation_zh":"應用擴展核對=(3, 11, 6, 1/8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215082,"parameters":{"left":[3,1],"right":[11,1],"steps":6,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[3,1],\"right\":[11,1],\"steps\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0083","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[4,1],\"right\":[12,1],\"steps\":0}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(4, 12, 0, 8)","explanation_zh":"應用擴展核對=(4, 12, 0, 8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215083,"parameters":{"left":[4,1],"right":[12,1],"steps":0,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[4,1],\"right\":[12,1],\"steps\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0084","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[5,1],\"right\":[13,1],\"steps\":1}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(5, 13, 1, 4)","explanation_zh":"應用擴展核對=(5, 13, 1, 4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215084,"parameters":{"left":[5,1],"right":[13,1],"steps":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[5,1],\"right\":[13,1],\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0085","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[6,1],\"right\":[14,1],\"steps\":2}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(6, 14, 2, 2)","explanation_zh":"應用擴展核對=(6, 14, 2, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215085,"parameters":{"left":[6,1],"right":[14,1],"steps":2,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[6,1],\"right\":[14,1],\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0086","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[7,1],\"right\":[15,1],\"steps\":3}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(7, 15, 3, 1)","explanation_zh":"應用擴展核對=(7, 15, 3, 1)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215086,"parameters":{"left":[7,1],"right":[15,1],"steps":3,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[7,1],\"right\":[15,1],\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0087","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[8,1],\"right\":[16,1],\"steps\":4}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(8, 16, 4, 1/2)","explanation_zh":"應用擴展核對=(8, 16, 4, 1/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215087,"parameters":{"left":[8,1],"right":[16,1],"steps":4,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[8,1],\"right\":[16,1],\"steps\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0088","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[9,1],\"right\":[17,1],\"steps\":5}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(9, 17, 5, 1/4)","explanation_zh":"應用擴展核對=(9, 17, 5, 1/4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215088,"parameters":{"left":[9,1],"right":[17,1],"steps":5,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[9,1],\"right\":[17,1],\"steps\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0089","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[10,1],\"right\":[18,1],\"steps\":6}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(10, 18, 6, 1/8)","explanation_zh":"應用擴展核對=(10, 18, 6, 1/8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215089,"parameters":{"left":[10,1],"right":[18,1],"steps":6,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[10,1],\"right\":[18,1],\"steps\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0090","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[11,1],\"right\":[19,1],\"steps\":0}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(11, 19, 0, 8)","explanation_zh":"應用擴展核對=(11, 19, 0, 8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215090,"parameters":{"left":[11,1],"right":[19,1],"steps":0,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[11,1],\"right\":[19,1],\"steps\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0091","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[12,1],\"right\":[20,1],\"steps\":1}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(12, 20, 1, 4)","explanation_zh":"應用擴展核對=(12, 20, 1, 4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215091,"parameters":{"left":[12,1],"right":[20,1],"steps":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[12,1],\"right\":[20,1],\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0092","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[13,1],\"right\":[21,1],\"steps\":2}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(13, 21, 2, 2)","explanation_zh":"應用擴展核對=(13, 21, 2, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215092,"parameters":{"left":[13,1],"right":[21,1],"steps":2,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[13,1],\"right\":[21,1],\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0093","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[14,1],\"right\":[22,1],\"steps\":3}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(14, 22, 3, 1)","explanation_zh":"應用擴展核對=(14, 22, 3, 1)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215093,"parameters":{"left":[14,1],"right":[22,1],"steps":3,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[14,1],\"right\":[22,1],\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0094","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[15,1],\"right\":[23,1],\"steps\":4}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(15, 23, 4, 1/2)","explanation_zh":"應用擴展核對=(15, 23, 4, 1/2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215094,"parameters":{"left":[15,1],"right":[23,1],"steps":4,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[15,1],\"right\":[23,1],\"steps\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0095","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[16,1],\"right\":[24,1],\"steps\":5}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(16, 24, 5, 1/4)","explanation_zh":"應用擴展核對=(16, 24, 5, 1/4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215095,"parameters":{"left":[16,1],"right":[24,1],"steps":5,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[16,1],\"right\":[24,1],\"steps\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0096","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[17,1],\"right\":[25,1],\"steps\":6}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(17, 25, 6, 1/8)","explanation_zh":"應用擴展核對=(17, 25, 6, 1/8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215096,"parameters":{"left":[17,1],"right":[25,1],"steps":6,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[17,1],\"right\":[25,1],\"steps\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0097","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[18,1],\"right\":[26,1],\"steps\":0}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(18, 26, 0, 8)","explanation_zh":"應用擴展核對=(18, 26, 0, 8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215097,"parameters":{"left":[18,1],"right":[26,1],"steps":0,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[18,1],\"right\":[26,1],\"steps\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0098","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[19,1],\"right\":[27,1],\"steps\":1}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(19, 27, 1, 4)","explanation_zh":"應用擴展核對=(19, 27, 1, 4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215098,"parameters":{"left":[19,1],"right":[27,1],"steps":1,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[19,1],\"right\":[27,1],\"steps\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0099","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[20,1],\"right\":[28,1],\"steps\":2}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(20, 28, 2, 2)","explanation_zh":"應用擴展核對=(20, 28, 2, 2)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215099,"parameters":{"left":[20,1],"right":[28,1],"steps":2,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[20,1],\"right\":[28,1],\"steps\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r05-bisection-method-0100","batch_id":"batch-20261013-advance-20261021-r05-bisection-method-foundations","language":"zh-Hant","source_mko_ids":["mko-bisection-method"],"title_zh":"有限二分bracket","stem_zh":"已提供的符號 bracket 資料。操作=bisection-width-after-steps；資料={\"left\":[21,1],\"right\":[29,1],\"steps\":3}。請依 [left,right,steps,width] 欄序回答。","answer":{"kind":"expression","value":"(21, 29, 3, 1)","explanation_zh":"應用擴展核對=(21, 29, 3, 1)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由異號自行推出根存在；只核對有限更新與寬度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限二分bracket"]},"variant":{"family_id":"qf-app21-bisection-width-after-steps","seed":202610215100,"parameters":{"left":[21,1],"right":[29,1],"steps":3,"domain":"Declared_sign_bracket_updates","operation":"bisection-width-after-steps","semantic_template":"qf-app21-bisection-width-after-steps/{\"left\":[21,1],\"right\":[29,1],\"steps\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}