{"ok":true,"question":{"id":21641,"question_uuid":"86e23d68-6a1f-4b5b-a235-7030560e6980","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案450.pdf","source_page_start":2,"source_page_end":2,"source_bbox":"[304.69, 143.57, 461.9, 220.43]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"计算：\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{14} \\\\times - \\\\sqrt{(-2)^{2}}\"}, {\"text\": \";\", \"type\": \"text\"}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{−278}\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3}\"}, {\"text\": \"−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{25}+\"}, {\"text\": \"|\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3}\"}, {\"text\": \"− 3| +\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{1−6463}\"}, {\"text\": \".\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)?\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{−278}\"}, {\"text\": \" −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{(−2)^{2}} =\"}, {\"text\": \"−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{2}{3}\"}, {\"text\": \"\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{2}\"}, {\"text\": \"− 2 = −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2\\\\frac{1}{3}\"}, {\"text\": \".?\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{14}\"}, {\"text\": \"(2)? 3 −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{25}+\"}, {\"text\": \"|\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3}\"}, {\"text\": \"− 3| +\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3 \\\\sqrt{1−6463} = \\\\sqrt{3}\"}, {\"text\": \"−+5 3−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3} + \\\\frac{1}{4} =\"}, {\"text\": \"−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{7}{4}\"}, {\"text\": \".?\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [304.69, 143.57, 461.9, 220.43], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案450.pdf\", \"regions\": [{\"bbox\": [304.69, 143.57, 461.9, 220.43], \"page\": 2}], \"section\": \"example\", \"page_end\": 2, \"page_start\": 2, \"section_label\": \"跟我学        常考关键母题各个击破！\", \"answer_regions\": [{\"bbox\": [304.8647766113281, 280.2483215332031, 529.9873046875, 379.1156921386719], \"page\": 2}], \"answer_original\": \"\", \"solution_original\": \"(1)?3 \\\\sqrt{−278}  − \\\\sqrt{(−2)^{2}} = − \\\\frac{2}{3}  \\\\frac{1}{2} − 2 = −2\\\\frac{1}{3}.? \\\\sqrt{14} (2)? 3 − \\\\sqrt{25}+ | \\\\sqrt{3} − 3| + 3 \\\\sqrt{1−6463} = \\\\sqrt{3} −+5 3− \\\\sqrt{3} + \\\\frac{1}{4} = − \\\\frac{7}{4}.?\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"42255f20d6bab75d871f559a110ff3577af4c540d089d1a403ebb402faf975d2\"}","body_html":"<div>计算：\\(\\sqrt{14} \\times - \\sqrt{(-2)^{2}}\\);<br>（1）\\(3 \\sqrt{−278}\\)<br>（2）\\(\\sqrt{3}\\)−\\(\\sqrt{25}+\\)|\\(\\sqrt{3}\\)− 3| +\\(3 \\sqrt{1−6463}\\).</div>","answer_html":"","ways_html":"(1)?\\(3 \\sqrt{−278}\\) −\\(\\sqrt{(−2)^{2}} =\\)−\\(\\frac{2}{3}\\)\\(\\frac{1}{2}\\)− 2 = −\\(2\\frac{1}{3}\\).?\\(\\sqrt{14}\\)(2)? 3 −\\(\\sqrt{25}+\\)|\\(\\sqrt{3}\\)− 3| +\\(3 \\sqrt{1−6463} = \\sqrt{3}\\)−+5 3−\\(\\sqrt{3} + \\frac{1}{4} =\\)−\\(\\frac{7}{4}\\).?","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.883,"error_message":"QA failed: SOLVER,CRITIC,COHERENCE,ANSWER","published_question_id":null,"content_sha256":"42255f20d6bab75d871f559a110ff3577af4c540d089d1a403ebb402faf975d2","created_at":"2026-09-25T02:36:39","updated_at":"2026-09-25T02:52:01","answer_missing":true,"formula_fallback":false,"_number":"2","_section":"example","_section_label":"跟我学        常考关键母题各个击破！"},"assets":[],"knowledge":[],"audits":[{"id":427481,"import_question_id":21641,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"计算： \\sqrt{14} \\times - \\sqrt{(-2)^{2}} ; (1) 3 \\sqrt{−278} (2) \\sqrt{3} − \\sqrt{25}+ | \\sqrt{3} − 3| + 3 \\sqrt{1−6463} .","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T02:46:32"},{"id":427482,"import_question_id":21641,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\sqrt{14} \\times - \\sqrt{(-2)^{2}}; 3 \\sqrt{−278}; \\sqrt{3}; \\sqrt{25}+; \\sqrt{3}","result_json":"{\"risky\": 17, \"issues\": [], \"checked\": 17, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T02:46:32"},{"id":427483,"import_question_id":21641,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"计算： \\sqrt{14} \\times - \\sqrt{(-2)^{2}} ; (1) 3 \\sqrt{−278} (2) \\sqrt{3} − \\sqrt{25}+ | \\sqrt{3} − 3| + 3 \\sqrt{1−6463} .","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T02:46:32"},{"id":427485,"import_question_id":21641,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.8,"input_snapshot":"题干：\n计算：\\(\\sqrt{14} \\times - \\sqrt{(-2)^{2}}\\); （1）\\(3 \\sqrt{−278}\\) （2）\\(\\sqrt{3}\\)−\\(\\sqrt{25}+\\)|\\(\\sqrt{3}\\)− 3| +\\(3 \\sqrt{1−6463}\\).\n答案：\n\n解析：\n(1)?\\(3 \\sqrt{−278}\\) −\\(\\sqrt{(−2)^{2}} =\\)−\\(\\frac{2}{3}\\)\\(\\frac{1}{2}\\)− 2 = −\\(2\\frac{1}{3}\\).?\\(\\sqrt{14}\\)(2)? 3 −\\(\\sqrt{25}+\\)|\\(\\sqrt{3}\\)− 3| +\\(3 \\sqrt{1−6463} = \\sqrt{3}\\)−+5 3−\\(\\sqrt{3} + \\frac{1}{4} =\\)−\\(\\frac{7}{4}\\).?","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.8, \"suggestions\": [\"建议补充完整题干和答案的清晰排版，避免公式碎片化\"]}","created_at":"2026-09-25T02:46:47"},{"id":427541,"import_question_id":21641,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"WARN","score":0.4,"input_snapshot":"计算： \\sqrt{14} \\times - \\sqrt{(-2)^{2}} ; (1) 3 \\sqrt{−278} (2) \\sqrt{3} − \\sqrt{25}+ | \\sqrt{3} − 3| + 3 \\sqrt{1−6463} .","result_json":"{\"note\": \"盲解+评判合并调用未返回\"}","created_at":"2026-09-25T02:51:37"},{"id":427542,"import_question_id":21641,"audit_type":"CRITIC","auditor_name":"critic","status":"WARN","score":0.5,"input_snapshot":"计算： \\sqrt{14} \\times - \\sqrt{(-2)^{2}} ; (1) 3 \\sqrt{−278} (2) \\sqrt{3} − \\sqrt{25}+ | \\sqrt{3} − 3| + 3 \\sqrt{1−6463} .","result_json":"{\"note\": \"Critic 未返回结果\"}","created_at":"2026-09-25T02:51:37"},{"id":427543,"import_question_id":21641,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-25T02:51:37"},{"id":427544,"import_question_id":21641,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案: || 解析:(1)?\\(3 \\sqrt{−278}\\) −\\(\\sqrt{(−2)^{2}} =\\)−\\(\\frac{2}{3}\\)\\(\\frac{1}{2}\\)− 2 = −\\(2\\frac{1}{3}\\).?\\(\\sqrt{14}\\)(2)? 3 −\\(\\sqrt{25}+\\)|\\(\\sqrt{3}\\)− 3| +\\(3 \\sqrt{1−6463} = \\sqrt{3}\\)−+5 3−\\(\\sqrt{","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中两个计算均存在数值或定义域错误\", \"√((-2)^2) 被误算为 1/2\", \"3√(-278) 和 3√(1-6463) 在实数范围内无意义，但解析强行计算\", \"3√(-278) × -√((-2)^2) = -2/3 × 1/2 - 2 = -2 1/3: √((-2)^2) = √4 = 2，不是 1/2；且 3√(-278) 在实数范围内无意义（负数开偶次方），原题可能为 3√(-27) 或类似，但解析中直接用了 -2/3，推导错误。\", \"√3 - √25 + |√3 - 3| + 3√(1-6463) = √3 - 5 + 3 - √3 + 1/4 = -7/4: √25 = 5 正确；|√3 - 3| = 3 - √3 正确；但 3√(1-6463) = 3√(-6462) 在实数范围内无意义，解析却算成 1/4，错误。\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": false, \"reason\": \"√((-2)^2) = √4 = 2，不是 1/2；且 3√(-278) 在实数范围内无意义（负数开偶次方），原题可能为 3√(-27) 或类似，但解析中直接用了 -2/3，推导错误。\", \"equation\": \"3√(-278) × -√((-2)^2) = -2/3 × 1/2 - 2 = -2 1/3\"}, {\"valid\": false, \"reason\": \"√25 = 5 正确；|√3 - 3| = 3 - √3 正确；但 3√(1-6463) = 3√(-6462) 在实数范围内无意义，解析却算成 1/4，错误。\", \"equation\": \"√3 - √25 + |√3 - 3| + 3√(1-6463) = √3 - 5 + 3 - √3 + 1/4 = -7/4\"}]}","created_at":"2026-09-25T02:52:01"},{"id":427545,"import_question_id":21641,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.883,"input_snapshot":"","result_json":"{\"warnings\": [\"SOLVER\"], \"graded_gate\": true, \"hard_failed\": [\"CRITIC\", \"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-25T02:52:01"}]}