{"ok":true,"question":{"id":21572,"question_uuid":"2a472452-6970-48b0-b9f6-c8ef41539df8","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案445.pdf","source_page_start":2,"source_page_end":2,"source_bbox":"[304.31, 143.29, 440.65, 213.06]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"fill_blank","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"下列计算正确的是( ) ．( 4)^{2} = 4 ． =\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{2} \\\\sqrt{14}\"}, {\"text\": \"B ．\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{4} =\"}, {\"text\": \"2 ．\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3\\\\sqrt{8} =\"}, {\"text\": \"2 D\", \"type\": \"text\"}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"：\\\\because\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\pm \\\\sqrt{4} = \\\\pm 2, \\\\therefore (\\\\pm \\\\sqrt{4})^{2} = (\\\\pm 2)^{2} = 4\"}, {\"text\": \"，故正确；\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"A \\\\sqrt{14} = \\\\pm \\\\frac{1}{2} \\\\neq \\\\frac{1}{2}\"}, {\"text\": \"，故错误；：\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{4} = 2 \\\\neq \\\\pm 2\"}, {\"text\": \"，B C 故错误；：\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"3\\\\sqrt{8} = 2 \\\\neq \\\\pm 2\"}, {\"text\": \"，故错误．故选：．D D A\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [304.31, 143.29, 440.65, 213.06], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案445.pdf\", \"regions\": [{\"bbox\": [304.31, 143.29, 440.65, 213.06], \"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\": [304.4994812011719, 260.1634521484375, 550.406005859375, 330.9587097167969], \"page\": 2}], \"answer_original\": \"\", \"solution_original\": \"：  \\\\sqrt{4} = 2,(4)^{2} = (2)^{2} = 4，故正确； A \\\\sqrt{14} =  \\\\frac{1}{2}  \\\\frac{1}{2}，故错误；：\\\\sqrt{4} = 2 2， B C 故错误；：3\\\\sqrt{8} = 2 2，故错误．故选：． D D A\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"fill_blank\", \"content_sha256\": \"33202d7cefa86fee17b4e26ff7080138ec1a5efddf041d179a463c4161843cfc\"}","body_html":"<div>下列计算正确的是( ) ．( 4)^{2} = 4 ． =\\(\\frac{1}{2} \\sqrt{14}\\)B ．\\(\\sqrt{4} =\\)2 ．\\(3\\sqrt{8} =\\)2 D</div>","answer_html":"","ways_html":"：\\because\\(\\pm \\sqrt{4} = \\pm 2, \\therefore (\\pm \\sqrt{4})^{2} = (\\pm 2)^{2} = 4\\)，故正确；\\(A \\sqrt{14} = \\pm \\frac{1}{2} \\neq \\frac{1}{2}\\)，故错误；：\\(\\sqrt{4} = 2 \\neq \\pm 2\\)，B C 故错误；：\\(3\\sqrt{8} = 2 \\neq \\pm 2\\)，故错误．故选：．D D A","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.925,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"33202d7cefa86fee17b4e26ff7080138ec1a5efddf041d179a463c4161843cfc","created_at":"2026-09-25T02:02:54","updated_at":"2026-09-25T02:15:48","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":425902,"import_question_id":21572,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"下列计算正确的是( ) ．( 4)^{2} = 4 ． = \\frac{1}{2} \\sqrt{14} B ． \\sqrt{4} = 2 ． 3\\sqrt{8} = 2 D","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T02:10:16"},{"id":425903,"import_question_id":21572,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\frac{1}{2} \\sqrt{14}; \\sqrt{4} =; 3\\sqrt{8} =; \\pm \\sqrt{4} = \\pm 2, \\therefore (\\pm \\sqrt{4})^{2} = (\\pm 2)^{2} = 4; A \\sqrt{14} = \\pm \\frac{1}{2} \\neq \\frac{1}{2}","result_json":"{\"risky\": 7, \"issues\": [], \"checked\": 7, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T02:10:16"},{"id":425904,"import_question_id":21572,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"下列计算正确的是( ) ．( 4)^{2} = 4 ． = \\frac{1}{2} \\sqrt{14} B ． \\sqrt{4} = 2 ． 3\\sqrt{8} = 2 D","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T02:10:16"},{"id":425907,"import_question_id":21572,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"下列计算正确的是( ) ．( 4)^{2} = 4 ． = \\frac{1}{2} \\sqrt{14} B ． \\sqrt{4} = 2 ． 3\\sqrt{8} = 2 D","result_json":"{\"basis\": \"逐项验证：A. (±√4)² = (±2)² = 4，正确；B. ±√(1/4) = ±1/2，而非仅 1/2，错误；C. √4 = 2（算术平方根），不是 ±2，错误；D. ³√8 = 2（实数范围内立方根唯一），不是 ±2，错误。\", \"answer\": \"A\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T02:10:36"},{"id":425908,"import_question_id":21572,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案: || 盲解:A","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T02:10:36"},{"id":425914,"import_question_id":21572,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.9,"input_snapshot":"题干：\n下列计算正确的是( ) ．( 4)^{2} = 4 ． =\\(\\frac{1}{2} \\sqrt{14}\\)B ．\\(\\sqrt{4} =\\)2 ．\\(3\\sqrt{8} =\\)2 D\n答案：\n\n解析：\n：\\because\\(\\pm \\sqrt{4} = \\pm 2, \\therefore (\\pm \\sqrt{4})^{2} = (\\pm 2)^{2} = 4\\)，故正确；\\(A \\sqrt{14} = \\pm \\frac{1}{2} \\neq \\frac{1}{2}\\)，故错误；：\\(\\sqrt{4} = 2 \\neq \\pm 2\\)，B C 故错误；：\\(3\\sqrt{8} = 2 \\neq \\pm 2\\)，故错误．故选：．D D A","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.9, \"suggestions\": [\"解析部分排版混乱，建议重新整理为清晰的步骤说明。\", \"答案选项标记（如A、B、C、D）在题干中未正确对齐，建议调整格式以增强可读性。\"]}","created_at":"2026-09-25T02:10:51"},{"id":425915,"import_question_id":21572,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:A","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-25T02:10:51"},{"id":425941,"import_question_id":21572,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案: || 解析:：\\because\\(\\pm \\sqrt{4} = \\pm 2, \\therefore (\\pm \\sqrt{4})^{2} = (\\pm 2)^{2} = 4\\)，故正确；\\(A \\sqrt{14} = \\pm \\frac{1}{2} \\neq \\frac{1}{2}\\)，故错误；：\\(\\sqrt{4} = 2 \\neq \\pm 2\\)，B C 故错误；：\\(3\\sqrt{8} = 2 \\neq","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中把 A 项写成 \\\\sqrt{14}=\\\\pm\\\\frac{1}{2}，明显错误；B 项 \\\\sqrt{4}=\\\\pm2 错误；C 项 3\\\\sqrt{8}=2 错误；D 项未给出完整表达式，但根据题干应为 (\\\\pm\\\\sqrt{4})^2=4，该式正确。因此正确答案应为 D，但解析推理混乱，多处等式不成立。\", \"\\\\sqrt{14} = \\\\pm \\\\frac{1}{2}: \\\\sqrt{14} 是正数，约等于 3.74，而 \\\\pm 1/2 是 ±0.5，显然不相等。\", \"\\\\sqrt{4} = \\\\pm 2: \\\\sqrt{4}=2，算术平方根只取正值，不能写成 ±2。\", \"3\\\\sqrt{8} = 2: 3\\\\sqrt{8}=3×2\\\\sqrt{2}=6\\\\sqrt{2}≈8.485，不等于 2。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": true, \"reason\": \"左边：\\\\pm\\\\sqrt{4}=\\\\pm2，平方后(\\\\pm2)^2=4，成立。\", \"equation\": \"(\\\\pm \\\\sqrt{4})^{2} = (\\\\pm 2)^{2} = 4\"}, {\"valid\": false, \"reason\": \"\\\\sqrt{14} 是正数，约等于 3.74，而 \\\\pm 1/2 是 ±0.5，显然不相等。\", \"equation\": \"\\\\sqrt{14} = \\\\pm \\\\frac{1}{2}\"}, {\"valid\": false, \"reason\": \"\\\\sqrt{4}=2，算术平方根只取正值，不能写成 ±2。\", \"equation\": \"\\\\sqrt{4} = \\\\pm 2\"}, {\"valid\": false, \"reason\": \"3\\\\sqrt{8}=3×2\\\\sqrt{2}=6\\\\sqrt{2}≈8.485，不等于 2。\", \"equation\": \"3\\\\sqrt{8} = 2\"}]}","created_at":"2026-09-25T02:12:37"},{"id":425942,"import_question_id":21572,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.925,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-25T02:12:37"},{"id":425968,"import_question_id":21572,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"下列计算正确的是( ) ．( 4)^{2} = 4 ． = \\frac{1}{2} \\sqrt{14} B ． \\sqrt{4} = 2 ． 3\\sqrt{8} = 2 D","result_json":"{\"basis\": \"逐项验证：A. (±√4)² = (±2)² = 4，正确；B. ±√(1/4) = ±1/2，而非仅1/2，错误；C. √4 = 2（算术平方根），不是±2，错误；D. ³√8 = 2（实数范围内立方根唯一），不是±2，错误。\", \"answer\": \"A\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T02:14:20"},{"id":425969,"import_question_id":21572,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:D || 盲解:A","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T02:14:20"},{"id":425982,"import_question_id":21572,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案:D || 解析:逐项验证：A项：\\((\\pm\\sqrt{4})^2=(\\pm2)^2=4\\)，等式成立；B项：\\(\\sqrt{4}=2\\neq\\pm2\\)，等式不成立；C项：\\(3\\sqrt{8}=3\\times2\\sqrt{2}=6\\sqrt{2}\\neq\\pm2\\)，等式不成立；D项：题干中\\(\\sqrt{14}=\\pm\\frac{1}{2}\\)明显错误，但根据选项排列及解析意图，正确选项应为A。然而，原题选","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中承认D项题干错误，却仍选D；同时盲解答案为A，说明正确答案应为A，但解析结论与事实矛盾。\", \"解析未明确指出A项才是唯一正确的计算，反而因选项标注错位问题推导出D，逻辑不严谨。\", \"B项：$\\\\sqrt{4}=\\\\pm2$: 错误：算术平方根$\\\\sqrt{4}=2$，不是$\\\\pm2$\", \"C项：$3\\\\sqrt{8}=\\\\pm2$: 错误：$3\\\\sqrt{8}=3\\\\times2\\\\sqrt{2}=6\\\\sqrt{2}\\\\neq\\\\pm2$\", \"D项：题干中$\\\\sqrt{14}=\\\\pm\\\\frac{1}{2}$: 错误：$\\\\sqrt{14}\\\\approx3.74$，显然不等于$\\\\pm0.5$\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": true, \"reason\": \"计算正确：$\\\\sqrt{4}=2$，故$(\\\\pm2)^2=4$\", \"equation\": \"A项：$(\\\\pm\\\\sqrt{4})^2=(\\\\pm2)^2=4$\"}, {\"valid\": false, \"reason\": \"错误：算术平方根$\\\\sqrt{4}=2$，不是$\\\\pm2$\", \"equation\": \"B项：$\\\\sqrt{4}=\\\\pm2$\"}, {\"valid\": false, \"reason\": \"错误：$3\\\\sqrt{8}=3\\\\times2\\\\sqrt{2}=6\\\\sqrt{2}\\\\neq\\\\pm2$\", \"equation\": \"C项：$3\\\\sqrt{8}=\\\\pm2$\"}, {\"valid\": false, \"reason\": \"错误：$\\\\sqrt{14}\\\\approx3.74$，显然不等于$\\\\pm0.5$\", \"equation\": \"D项：题干中$\\\\sqrt{14}=\\\\pm\\\\frac{1}{2}$\"}]}","created_at":"2026-09-25T02:15:48"},{"id":425983,"import_question_id":21572,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:D || 盲解:A","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案存在字面差异，需 Critic 复核\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-25T02:15:48"},{"id":425984,"import_question_id":21572,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":1.0,"input_snapshot":null,"result_json":"{\"critic\": true, \"symbolic\": true, \"coherence\": false, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 1.0, \"verifier_base\": \"http://127.0.0.1:8091/v1\", \"verifier_confidence\": 1.0, \"critic_explicit_pass\": true, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": false, \"coherence_explicit_pass\": false}","created_at":"2026-09-25T02:15:48"}]}