{"ok":true,"question":{"id":21119,"question_uuid":"1e91b86d-2fb7-47b6-8452-39123f1aa388","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案395.pdf","source_page_start":3,"source_page_end":5,"source_bbox":"[30.22, 650.92, 564.07, 61.58]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"求下列各数的立方根 : AI智适化学案 学案ID:R10720395096\", \"type\": \"text\"}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"−1;\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{1000}; \\\\frac{(2)}{(3)}\"}, {\"text\": \"−343;\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"15 \\\\frac{5}{8}; \\\\frac{(5)}{(6)}512\"}, {\"text\": \"−0.216.\", \"type\": \"text\"}]}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"(1)∵(−1)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{3}{3}=\"}, {\"text\": \"−1, ∴ ^{3}√−1 = −1;\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(2)∵ (\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{10}\"}, {\"text\": \") =\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{1000},∴ ^{3}√ \\\\frac{1}{1000} = \\\\frac{1}{10}\"}, {\"text\": \"(3)∵(−7)^{3}= −343，∴ ^{3}√−343 = −7; 3 (4)∵\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"15 \\\\frac{5}{8} = \\\\frac{125}{8}, (\\\\frac{5}{2}) = \\\\frac{125}{8}\"}, {\"text\": \"， ∴ ^{3}\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{15 \\\\frac{5}{8}}= \\\\frac{5}{2}\"}, {\"text\": \"∵\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"8^{3}\"}, {\"text\": \"= 512，∴ ^{3}√512 = 8;\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{(5)}{(6)}\"}, {\"text\": \"∵(−0.6)^{3}= −0.216，∴ ^{3}√−0.216 = −0.6.\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.22, 650.92, 564.07, 61.58], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案395.pdf\", \"regions\": [{\"bbox\": [30.22, 650.92, 157.82, 767.86], \"page\": 3}, {\"bbox\": [244.85, 33.12, 564.07, 61.58], \"page\": 5}], \"section\": \"generic\", \"page_end\": 5, \"page_start\": 3, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [43.99800109863281, 370.0349731445313, 289.3700866699219, 493.2806701660156], \"page\": 6}], \"answer_original\": \"(1)∵(−1)\\\\frac{3}{3}= −1, ∴ ^{3}√−1 = −1;\", \"solution_original\": \"(2)∵ (\\\\frac{1}{10}) = \\\\frac{1}{1000},∴ ^{3}√ \\\\frac{1}{1000} = \\\\frac{1}{10}; (3)∵(−7)^{3}= −343，∴ ^{3}√−343 = −7; 3 (4)∵ 15 \\\\frac{5}{8} = \\\\frac{125}{8}, (\\\\frac{5}{2}) = \\\\frac{125}{8}， ∴ ^{3}√15 \\\\frac{5}{8} = \\\\frac{5}{2}; ∵8^{3}= 512，∴ ^{3}√512 = 8; \\\\frac{(5)}{(6)} ∵(−0.6)^{3}= −0.216，∴ ^{3}√−0.216 = −0.6.\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"15\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"0bed4f9f99c89edc66845dc96867377029a84133563ba75606b1c1d26af17669\"}","body_html":"<div>求下列各数的立方根 : AI智适化学案 学案ID:R10720395096<br>（1）−1;\\(\\frac{1}{1000}; \\frac{(2)}{(3)}\\)−343;<br>（2）\\(15 \\frac{5}{8}; \\frac{(5)}{(6)}512\\)−0.216.</div>","answer_html":"(1)∵(−1)\\(\\frac{3}{3}=\\)−1, ∴ ^{3}√−1 = −1;","ways_html":"(2)∵ (\\(\\frac{1}{10}\\)) =\\(\\frac{1}{1000},∴ ^{3}√ \\frac{1}{1000} = \\frac{1}{10}\\)(3)∵(−7)^{3}= −343，∴ ^{3}√−343 = −7; 3 (4)∵\\(15 \\frac{5}{8} = \\frac{125}{8}, (\\frac{5}{2}) = \\frac{125}{8}\\)， ∴ ^{3}\\(\\sqrt{15 \\frac{5}{8}}= \\frac{5}{2}\\)∵\\(8^{3}\\)= 512，∴ ^{3}√512 = 8;\\(\\frac{(5)}{(6)}\\)∵(−0.6)^{3}= −0.216，∴ ^{3}√−0.216 = −0.6.","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.912,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"0bed4f9f99c89edc66845dc96867377029a84133563ba75606b1c1d26af17669","created_at":"2026-09-24T22:47:54","updated_at":"2026-09-24T23:18:31","answer_missing":false,"formula_fallback":false,"_number":"15","_section":"generic","_section_label":""},"assets":[],"knowledge":[],"audits":[{"id":416068,"import_question_id":21119,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"求下列各数的立方根 : AI智适化学案 学案ID:R10720395096 (1) −1; \\frac{1}{1000}; \\frac{(2)}{(3)} −343; (2) 15 \\frac{5}{8}; \\frac{(5)}{(6)}512 −0.216.","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-24T23:09:30"},{"id":416069,"import_question_id":21119,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\frac{1}{1000}; \\frac{(2)}{(3)}; 15 \\frac{5}{8}; \\frac{(5)}{(6)}512; \\frac{3}{3}=; \\frac{1}{10}; \\frac{1}{1000},∴ ^{3}√ \\frac{1}{1000} = \\frac{1}{10}","result_json":"{\"risky\": 9, \"issues\": [], \"checked\": 9, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-24T23:09:30"},{"id":416070,"import_question_id":21119,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"求下列各数的立方根 : AI智适化学案 学案ID:R10720395096 (1) −1; \\frac{1}{1000}; \\frac{(2)}{(3)} −343; (2) 15 \\frac{5}{8}; \\frac{(5)}{(6)}512 −0.216.","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T23:09:30"},{"id":416084,"import_question_id":21119,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.9,"input_snapshot":"题干：\n求下列各数的立方根 : AI智适化学案 学案ID:R10720395096 （1）−1;\\(\\frac{1}{1000}; \\frac{(2)}{(3)}\\)−343; （2）\\(15 \\frac{5}{8}; \\frac{(5)}{(6)}512\\)−0.216.\n答案：\n(1)∵(−1)\\(\\frac{3}{3}=\\)−1, ∴ ^{3}√−1 = −1;\n解析：\n(2)∵ (\\(\\frac{1}{10}\\)) =\\(\\frac{1}{1000},∴ ^{3}√ \\frac{1}{1000} = \\frac{1}{10}\\)(3)∵(−7)^{3}= −343，∴ ^{3}√−343 = −7; 3 (4)∵\\(15 \\frac{5}{8} = \\frac{125}{8}, (\\frac{5}{2}) = \\frac{125}{8}\\)， ∴ ^{3}\\(\\sqrt{15 \\frac{5}{8}}= \\frac{5}{2}\\)∵\\(8^{3}\\)= 512，∴ ^{3}√512 = 8;\\(\\frac{(5)}{(6)}\\)∵(−0.6)^{3}= −0.216，∴ ^{3}√−0.216 = −0.6.","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.9, \"suggestions\": [\"题干中的数字编号（1）至（6）排版较为混乱，部分数字被括号或符号遮挡，建议优化排版以提升可读性。\", \"答案部分的推导过程存在格式错误，例如“∵(−1)³⁄³=−1”应修正为“∵(−1)³=−1”，类似错误在其他步骤中也存在，建议统一规范数学表达格式。\", \"解析部分缺少对每个步骤的详细说明，尤其是分数和负数的立方根计算过程，建议补充更清晰的推导逻辑。\"]}","created_at":"2026-09-24T23:10:21"},{"id":416101,"import_question_id":21119,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.9,"input_snapshot":"求下列各数的立方根 : AI智适化学案 学案ID:R10720395096 (1) −1; \\frac{1}{1000}; \\frac{(2)}{(3)} −343; (2) 15 \\frac{5}{8}; \\frac{(5)}{(6)}512 −0.216.","result_json":"{\"basis\": \"立方根定义：若 x³ = a，则 x = ∛a。\\n(1) (-1)³ = -1 → ∛(-1) = -1\\n(2) (0.1)³ = 0.001 = 1/1000 → ∛(1/1000) = 0.1\\n(3) (-7)³ = -343 → ∛(-343) = -7\\n(4) (15又5/8)³ = (125/8)³ = 1953125/512 ≈ 3814.65，但题目可能是求某个数的立方等于15又5/8，此处可能有误，按原数给出\\n(5) 8³ = 512 → ∛512 = 8\\n(6) (-0.6)³ = -0.216 → ∛(-0.216) = -0.6\", \"answer\": \"(1) -1\\n(2) 0.1\\n(3) -7\\n(4) 15又5/8 (或 125/8)\\n(5) 8\\n(6) -0.6\", \"confidence\": 0.9, \"handout_chars\": 0}","created_at":"2026-09-24T23:11:13"},{"id":416102,"import_question_id":21119,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":0.95,"input_snapshot":"来源答案:(1)∵(−1)\\(\\frac{3}{3}=\\)−1, ∴ ^{3}√−1 = −1; || 盲解:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-24T23:11:13"},{"id":416103,"import_question_id":21119,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:(1)∵(−1)\\(\\frac{3}{3}=\\)−1, ∴ ^{3}√−1 = −1; || 盲解:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6","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":"2026-09-24T23:11:13"},{"id":416129,"import_question_id":21119,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案:(1)∵(−1)\\(\\frac{3}{3}=\\)−1, ∴ ^{3}√−1 = −1; || 解析:(2)∵ (\\(\\frac{1}{10}\\)) =\\(\\frac{1}{1000},∴ ^{3}√ \\frac{1}{1000} = \\frac{1}{10}\\)(3)∵(−7)^{3}= −343，∴ ^{3}√−343 = −7; 3 (4)∵\\(15 \\frac{5}{8} = \\frac{125}{8}, (\\frac{5}{2}) = \\frac{125}{8}\\)， ∴ ^{3}\\(\\","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"第(1)问推导表达式不规范，(−1)^{3/3} 应简化为 (−1)^1；\", \"第(4)问漏写立方符号，(5/2) 应写作 (5/2)^3。\", \"(1) ∵(−1)^{3/3}=−1: 原文写为 (−1)^{3/3}，但 3/3=1，故应为 (−1)^1=−1，虽结果正确，但表达不规范，且与常规推导方式不符。\", \"(4) ∵ 15 5/8 = 125/8, (5/2)^3 = 125/8: 原文写为 (5/2) = 125/8，漏掉了立方符号，应为 (5/2)^3 = 125/8。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"原文写为 (−1)^{3/3}，但 3/3=1，故应为 (−1)^1=−1，虽结果正确，但表达不规范，且与常规推导方式不符。\", \"equation\": \"(1) ∵(−1)^{3/3}=−1\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(2) ∵ (1/10)^3 = 1/1000\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(3) ∵ (−7)^3 = −343\"}, {\"valid\": false, \"reason\": \"原文写为 (5/2) = 125/8，漏掉了立方符号，应为 (5/2)^3 = 125/8。\", \"equation\": \"(4) ∵ 15 5/8 = 125/8, (5/2)^3 = 125/8\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(4) ∵ 8^3 = 512\"}, {\"valid\": true, \"reason\": \"正确。\", \"equation\": \"(6) ∵ (−0.6)^3 = −0.216\"}]}","created_at":"2026-09-24T23:13:07"},{"id":416130,"import_question_id":21119,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.912,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\"]}","created_at":"2026-09-24T23:13:07"},{"id":416166,"import_question_id":21119,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.95,"input_snapshot":"求下列各数的立方根 : AI智适化学案 学案ID:R10720395096 (1) −1; \\frac{1}{1000}; \\frac{(2)}{(3)} −343; (2) 15 \\frac{5}{8}; \\frac{(5)}{(6)}512 −0.216.","result_json":"{\"basis\": \"立方根定义：若 x³ = a，则 x 是 a 的立方根。\\n(1) (-1)³ = -1 → 立方根为 -1\\n(2) (0.1)³ = 0.001 = 1/1000 → 立方根为 0.1\\n(3) (-7)³ = -343 → 立方根为 -7\\n(4) 15又5/8 = 125/8，(5/2)³ = 125/8 → 立方根为 5/2 = 2.5，但题目要求保留原形式，故写 15又5/8 的立方根应为 5/2，此处来源答案有误，正确应为 5/2 或 2.5\\n(5) 8³ = 512 → 立方根为 8\\n(6) (-0.6)³ = -0.216 → 立方根为 -0.6\\n\\n注：第(4)题来源答案写“15又5/8”是错误，其立方根是 5/2（即2.5），因为 (5/2)³ = 125/8 = 15又5/8。\", \"answer\": \"(1) -1\\n(2) 0.1\\n(3) -7\\n(4) 15又5/8 (或 125/8)\\n(5) 8\\n(6) -0.6\", \"confidence\": 0.95, \"handout_chars\": 0}","created_at":"2026-09-24T23:18:19"},{"id":416167,"import_question_id":21119,"audit_type":"CRITIC","auditor_name":"critic","status":"FAIL","score":0.9,"input_snapshot":"来源答案:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6 || 盲解:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6","result_json":"{\"ok\": false, \"issues\": [\"第(4)题来源答案错误：15又5/8的立方根是5/2（2.5），而非15又5/8本身\"], \"merged\": true, \"confidence\": 0.9}","created_at":"2026-09-24T23:18:19"},{"id":416169,"import_question_id":21119,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"PASS","score":0.9,"input_snapshot":"答案:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6 || 解析:(1) 因为 (−1)^3 = −1，所以 ∛(−1) = −1； (2) 因为 (0.1)^3 = 0.001 = 1/1000，所以 ∛(1/1000) = 0.1； (3) 因为 (−7)^3 = −343，所以 ∛(−343) = −7； (4) 因为 15又5/8 = 125/8，且 (5/2)^3 = 125/8，所以 ∛(15又5/8) = 5/2 = 15又5/8（或写为 125/","result_json":"{\"ok\": true, \"which\": [], \"issues\": [], \"confidence\": 0.9, \"equation_checks\": []}","created_at":"2026-09-24T23:18:31"},{"id":416170,"import_question_id":21119,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6 || 盲解:(1) -1\n(2) 0.1\n(3) -7\n(4) 15又5/8 (或 125/8)\n(5) 8\n(6) -0.6","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-24T23:18:31"},{"id":416171,"import_question_id":21119,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":0.9,"input_snapshot":null,"result_json":"{\"critic\": false, \"symbolic\": true, \"coherence\": true, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 0.9, \"verifier_base\": \"http://127.0.0.1:8092/v1\", \"verifier_confidence\": 0.95, \"critic_explicit_pass\": false, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": true}","created_at":"2026-09-24T23:18:31"}]}