{"ok":true,"question":{"id":21651,"question_uuid":"c064657d-008c-43ec-8c72-6b850260da73","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案455.pdf","source_page_start":1,"source_page_end":1,"source_bbox":"[30.22, 235.47, 177.75, 342.21]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"single_choice","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"下列计算中，正确的是(    )\", \"type\": \"text\"}, {\"type\": \"option\", \"label\": \"A\", \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{4 \\\\frac{1}{9}}= 2 \\\\frac{1}{3}\"}], \"source_bbox\": [47.57, 262.84, 105.34, 291.17], \"source_page\": 1}, {\"type\": \"option\", \"label\": \"B\", \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{−2}^{2}\"}, {\"text\": \"= 2\", \"type\": \"text\"}], \"source_bbox\": [47.57, 292.3, 108.82, 313.66], \"source_page\": 1}, {\"type\": \"option\", \"label\": \"C\", \"blocks\": [{\"text\": \"√16 = ±4\", \"type\": \"text\"}], \"source_bbox\": [47.57, 316.29, 99.0, 328.43], \"source_page\": 1}, {\"type\": \"option\", \"label\": \"D\", \"blocks\": [{\"text\": \"^{3}√−8 = ±2\", \"type\": \"text\"}], \"source_bbox\": [47.57, 329.56, 102.22, 342.21], \"source_page\": 1}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"B\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"√37 对于A： ∵\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"4 \\\\frac{1}{9} = \\\\frac{37}{9},∴\"}, {\"text\": \"√\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{37}{9} =\"}, {\"text\": \"≠\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{7}{3}\"}, {\"text\": \"（即\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2 \\\\frac{1}{3}）\"}, {\"text\": \"，故A不符合题意；对于 3 B：∵(−2)^{2}= 4, ∴ √4 = 2，故B符合题意；对于C： ∵ √16 = 4 ≠±4，故 C不符合题意；对于D：∵(−2)^{3}= −8,   ∴ 3√−8 = −2 ≠±2，故D不符合题意；故选：B．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.22, 235.47, 177.75, 342.21], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案455.pdf\", \"regions\": [{\"bbox\": [30.22, 235.47, 177.75, 342.21], \"page\": 1}], \"section\": \"generic\", \"page_end\": 1, \"page_start\": 1, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [43.99800109863281, 165.7989501953125, 502.8270568847656, 241.6659393310547], \"page\": 4}], \"answer_original\": \"B\", \"solution_original\": \"√37 对于A： ∵ 4 \\\\frac{1}{9} = \\\\frac{37}{9},∴ √ \\\\frac{37}{9} = ≠ \\\\frac{7}{3} （即2 \\\\frac{1}{3}），故A不符合题意；对于 3 B：∵(−2)^{2}= 4, ∴ √4 = 2，故B符合题意；对于C： ∵ √16 = 4 ≠±4，故 C不符合题意；对于D：∵(−2)^{3}= −8,   ∴ 3√−8 = −2 ≠±2，故D不符合题意；故选：B．\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"2\", \"subject_code\": \"math\", \"question_type\": \"single_choice\", \"content_sha256\": \"bfb1916aff680143ded6ab6a50276a621c803a0f0b664f99ea71d8e76dac7028\"}","body_html":"<div>下列计算中，正确的是(    )<br>A. \\(\\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3}\\)<br>B. \\(\\sqrt{−2}^{2}\\)= 2<br>C. √16 = ±4<br>D. ^{3}√−8 = ±2</div>","answer_html":"B","ways_html":"√37 对于A： ∵\\(4 \\frac{1}{9} = \\frac{37}{9},∴\\sqrt{\\frac{37}{9}}=\\)≠\\(\\frac{7}{3}\\)（即\\(2 \\frac{1}{3}）\\)，故A不符合题意；对于 3 B：∵(−2)^{2}= 4, ∴ √4 = 2，故B符合题意；对于C： ∵ √16 = 4 ≠±4，故 C不符合题意；对于D：∵(−2)^{3}= −8,   ∴ 3√−8 = −2 ≠±2，故D不符合题意；故选：B．","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.938,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"bfb1916aff680143ded6ab6a50276a621c803a0f0b664f99ea71d8e76dac7028","created_at":"2026-09-25T02:52:33","updated_at":"2026-09-25T03:04:34","answer_missing":false,"formula_fallback":false,"_number":"2","_section":"generic","_section_label":""},"assets":[],"knowledge":[],"audits":[{"id":427993,"import_question_id":21651,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"下列计算中，正确的是( ) A. \\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3} B. \\sqrt{−2}^{2} = 2 C. √16 = ±4 D. ^{3}√−8 = ±2","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T03:01:17"},{"id":427994,"import_question_id":21651,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3}; \\sqrt{−2}^{2}; 4 \\frac{1}{9} = \\frac{37}{9},∴; \\frac{37}{9} =; \\frac{7}{3}","result_json":"{\"risky\": 6, \"issues\": [], \"checked\": 6, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T03:01:17"},{"id":427995,"import_question_id":21651,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"下列计算中，正确的是( ) A. \\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3} B. \\sqrt{−2}^{2} = 2 C. √16 = ±4 D. ^{3}√−8 = ±2","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T03:01:17"},{"id":427996,"import_question_id":21651,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n下列计算中，正确的是( ) A. \\(\\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3}\\) B. \\(\\sqrt{−2}^{2}\\)= 2 C. √16 = ±4 D. ^{3}√−8 = ±2\n答案：\nB\n解析：\n√37 对于A： ∵\\(4 \\frac{1}{9} = \\frac{37}{9},∴\\)√\\(\\frac{37}{9} =\\)≠\\(\\frac{7}{3}\\)（即\\(2 \\frac{1}{3}）\\)，故A不符合题意；对于 3 B：∵(−2)^{2}= 4, ∴ √4 = 2，故B符合题意；对于C： ∵ √16 = 4 ≠±4，故 C不符合题意；对于D：∵(−2)^{3}= −8, ∴ 3√−8 = −2 ≠±2，故D不符合题意；故选：B．","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"解析中‘√37’疑似为误写，可能应为‘对于A’或其他说明，建议核对原文确认。\"]}","created_at":"2026-09-25T03:01:30"},{"id":427997,"import_question_id":21651,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"下列计算中，正确的是( ) A. \\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3} B. \\sqrt{−2}^{2} = 2 C. √16 = ±4 D. ^{3}√−8 = ±2","result_json":"{\"basis\": \"A错：√(4又1/9)=√(37/9)=√37/3≈2.01，而2又1/3≈2.33，不相等。B对：√(−2)²=√4=2。C错：√16表示算术平方根，结果为4，不是±4。D错：³√(−8)=−2，立方根只有一个实数值，不是±2。\", \"answer\": \"B\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T03:01:38"},{"id":427998,"import_question_id":21651,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:B || 盲解:B","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T03:01:38"},{"id":427999,"import_question_id":21651,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:B || 盲解:B","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-25T03:01:38"},{"id":428003,"import_question_id":21651,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案:B || 解析:√37 对于A： ∵\\(4 \\frac{1}{9} = \\frac{37}{9},∴\\)√\\(\\frac{37}{9} =\\)≠\\(\\frac{7}{3}\\)（即\\(2 \\frac{1}{3}）\\)，故A不符合题意；对于 3 B：∵(−2)^{2}= 4, ∴ √4 = 2，故B符合题意；对于C： ∵ √16 = 4 ≠±4，故 C不符合题意；对于D：∵(−2)^{3}= −8, ∴ 3√−8 =","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中对于选项A的推导错误：将√(37/9) 错误地化简为 7/3，实际上√(37/9) = √37 / 3，而√37 无法进一步化简，且显然不等于 7/3。\", \"√(37/9) = 7/3: √(37/9) = √37 / 3，而 √37 ≠ 7（因为 7²=49），所以 √(37/9) ≠ 7/3。解析中错误地认为 √37 = 7。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"√(37/9) = √37 / 3，而 √37 ≠ 7（因为 7²=49），所以 √(37/9) ≠ 7/3。解析中错误地认为 √37 = 7。\", \"equation\": \"√(37/9) = 7/3\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(−2)² = 4\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"√4 = 2\"}, {\"valid\": true, \"reason\": \"正确，算术平方根是非负的。\", \"equation\": \"√16 = 4 ≠ ±4\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(−2)³ = −8\"}, {\"valid\": true, \"reason\": \"正确，立方根在实数范围内是唯一的。\", \"equation\": \"³√(−8) = −2 ≠ ±2\"}]}","created_at":"2026-09-25T03:02:21"},{"id":428004,"import_question_id":21651,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.938,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\"]}","created_at":"2026-09-25T03:02:21"},{"id":428026,"import_question_id":21651,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"下列计算中，正确的是( ) A. \\sqrt{4 \\frac{1}{9}}= 2 \\frac{1}{3} B. \\sqrt{−2}^{2} = 2 C. √16 = ±4 D. ^{3}√−8 = ±2","result_json":"{\"basis\": \"A项：√(4 1/9)=√(37/9)=√37/3，而2 1/3=7/3，√37≠7，故错误。B项：√(−2)²=√4=2，正确。C项：√16表示算术平方根，结果为4，不是±4，错误。D项：³√(−8)=−2，立方根只有一个实数值，不是±2，错误。\", \"answer\": \"B\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T03:03:41"},{"id":428027,"import_question_id":21651,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:B || 盲解:B","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T03:03:41"},{"id":428033,"import_question_id":21651,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案:B || 解析:对于A：\\(4\\frac{1}{9}=\\frac{37}{9}\\)，\\(\\sqrt{\\frac{37}{9}}=\\frac{\\sqrt{37}}{3}\\)，而\\(\\frac{\\sqrt{37}}{3}\\neq\\frac{7}{3}\\)（因为\\(\\sqrt{37}\\neq7\\)），故A错误； 对于B：\\(\\sqrt{(-2)^2}=\\sqrt{4}=2\\)，故B正确； 对于C：\\(\\sqrt{16}","result_json":"{\"ok\": false, \"which\": [], \"issues\": [\"\\\\sqrt{4 \\\\frac{1}{9}} = 2 \\\\frac{1}{3}: 左边 = \\\\sqrt{37/9} = \\\\sqrt{37}/3 ≈ 2.027，右边 = 7/3 ≈ 2.333，不相等。\", \"\\\\sqrt{16} = \\\\pm 4: \\\\sqrt{16} 表示算术平方根，结果为 4，不是 ±4。\", \"\\\\sqrt[3]{-8} = \\\\pm 2: 立方根在实数范围内唯一，\\\\sqrt[3]{-8} = -2，不是 ±2。\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": false, \"reason\": \"左边 = \\\\sqrt{37/9} = \\\\sqrt{37}/3 ≈ 2.027，右边 = 7/3 ≈ 2.333，不相等。\", \"equation\": \"\\\\sqrt{4 \\\\frac{1}{9}} = 2 \\\\frac{1}{3}\"}, {\"valid\": true, \"reason\": \"(-2)^2 = 4，\\\\sqrt{4} = 2，正确。\", \"equation\": \"\\\\sqrt{(-2)^2} = 2\"}, {\"valid\": false, \"reason\": \"\\\\sqrt{16} 表示算术平方根，结果为 4，不是 ±4。\", \"equation\": \"\\\\sqrt{16} = \\\\pm 4\"}, {\"valid\": false, \"reason\": \"立方根在实数范围内唯一，\\\\sqrt[3]{-8} = -2，不是 ±2。\", \"equation\": \"\\\\sqrt[3]{-8} = \\\\pm 2\"}]}","created_at":"2026-09-25T03:04:34"},{"id":428034,"import_question_id":21651,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:B || 盲解:B","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-25T03:04:34"},{"id":428035,"import_question_id":21651,"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://127.0.0.1:8092/v1\", \"verifier_confidence\": 1.0, \"critic_explicit_pass\": true, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": false}","created_at":"2026-09-25T03:04:34"}]}