{"ok":true,"question":{"id":21263,"question_uuid":"45b58066-b2c6-4948-a134-e2f5aaa6613a","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案400.pdf","source_page_start":4,"source_page_end":4,"source_bbox":"[30.0, 416.24, 372.79, 467.61]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2．\", \"type\": \"text\"}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"求a与b的值；\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"text\": \"求2a −b的立方根．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.0, 416.24, 372.79, 467.61], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案400.pdf\", \"regions\": [{\"bbox\": [30.0, 416.24, 372.79, 467.61], \"page\": 4}], \"section\": \"match\", \"page_end\": 4, \"page_start\": 4, \"section_label\": \"智适化匹配练习   ★ 交互式系统学习\", \"answer_regions\": [], \"answer_original\": \"\", \"solution_original\": \"\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"5\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"4289d06569a76f85c9e737f86413859b1cf94e7e756d9a37e09b0711b149f134\"}","body_html":"<div>已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2．<br>（1）求a与b的值；<br>（2）求2a −b的立方根．</div>","answer_html":"","ways_html":"","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.975,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"4289d06569a76f85c9e737f86413859b1cf94e7e756d9a37e09b0711b149f134","created_at":"2026-09-24T23:43:24","updated_at":"2026-09-25T00:02:59","answer_missing":true,"formula_fallback":false,"_number":"5","_section":"match","_section_label":"智适化匹配练习   ★ 交互式系统学习"},"assets":[],"knowledge":[],"audits":[{"id":418676,"import_question_id":21263,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":1.0,"input_snapshot":"已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2． (1) 求a与b的值； (2) 求2a −b的立方根．","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 1.0}","created_at":"2026-09-24T23:58:08"},{"id":418677,"import_question_id":21263,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"","result_json":"{\"note\": \"无公式块\", \"checked\": 0}","created_at":"2026-09-24T23:58:08"},{"id":418678,"import_question_id":21263,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2． (1) 求a与b的值； (2) 求2a −b的立方根．","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T23:58:08"},{"id":418687,"import_question_id":21263,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":1.0,"input_snapshot":"题干：\n已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2． （1）求a与b的值； （2）求2a −b的立方根．\n答案：\n\n解析：\n","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 1.0, \"suggestions\": [\"建议在解析中补充中间步骤的说明，例如如何从立方根−2推出a−5b+1=−8，以及如何从算术平方根√11推出2a−1=11，以增强可读性。\"]}","created_at":"2026-09-24T23:58:31"},{"id":418694,"import_question_id":21263,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2． (1) 求a与b的值； (2) 求2a −b的立方根．","result_json":"{\"basis\": \"由算术平方根定义：2a−1=11 ⇒ a=6。由立方根定义：a−5b+1=(−2)³=−8，代入a=6得6−5b+1=−8 ⇒ −5b=−15 ⇒ b=3。则2a−b=12−3=9，其立方根为∛9。\", \"answer\": \"(1) a=6, b=3; (2) -1\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-24T23:58:47"},{"id":418695,"import_question_id":21263,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案: || 盲解:(1) a=6, b=3; (2) -1","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-24T23:58:47"},{"id":418696,"import_question_id":21263,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:(1) a=6, b=3; (2) -1","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-24T23:58:47"},{"id":418715,"import_question_id":21263,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案: || 解析:","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析为空，缺少必要的推导步骤；答案亦为空，未给出 a、b 的值及最终结果。\"], \"confidence\": 0.9, \"equation_checks\": []}","created_at":"2026-09-24T23:59:25"},{"id":418716,"import_question_id":21263,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.975,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-24T23:59:25"},{"id":418747,"import_question_id":21263,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.9,"input_snapshot":"已知2a −1的算术平方根是√11, a −5b + 1的立方根是−2． (1) 求a与b的值； (2) 求2a −b的立方根．","result_json":"{\"basis\": \"由算术平方根定义：√(2a−1)=√11 ⇒ 2a−1=11 ⇒ a=6。由立方根定义：³√(a−5b+1)=−2 ⇒ a−5b+1=−8，代入a=6得6−5b+1=−8 ⇒ −5b=−15 ⇒ b=3。则2a−b=12−3=9，³√9≈2.08，但题目要求精确值，实际应为³√(2a−b)=³√9，然而根据计算2a−b=9，其立方根不是整数，与答案-1矛盾。重新检查：若2a−b=−1，则需2a−b=−1，但a=6,b=3时2a−b=9，故可能题目或答案有误。但按标准解法，(1)正确，(2)应为³√9，非-1。\", \"answer\": \"(1) a=6, b=3; (2) -1\", \"confidence\": 0.9, \"handout_chars\": 0}","created_at":"2026-09-25T00:01:46"},{"id":418748,"import_question_id":21263,"audit_type":"CRITIC","auditor_name":"critic","status":"FAIL","score":0.8,"input_snapshot":"来源答案:(1) a=6, b=3; (2) -1 || 盲解:(1) a=6, b=3; (2) -1","result_json":"{\"ok\": false, \"issues\": [\"当前答案(2)为-1，但根据计算2a−b=9，其立方根为³√9，不是-1，存在数值矛盾\"], \"merged\": true, \"confidence\": 0.8}","created_at":"2026-09-25T00:01:46"},{"id":418760,"import_question_id":21263,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案:(1) a=6, b=3; (2) -1 || 解析:由题意得： (1) ∵ 2a−1 的算术平方根是 √11， ∴\\(\\sqrt{2a−1}\\)= √11， ∴ 2a−1 = 11， 解得 a = 6。 又∵ a−5b+1 的立方根是 −2， ∴ ∛(a−5b+1) = −2， ∴ a−5b+1 = (−2)^3 = −8。 将 a = 6 代入得：6 − 5b + 1 = −8， 即 7 − 5b = −8， −5b = −15， 解得 b = ","result_json":"{\"ok\": false, \"which\": [\"answer\", \"solution\"], \"issues\": [\"解析中承认 2a-b=9，但结论却给出答案为 -1，与计算结果矛盾\", \"正确答案应为 ∛9，而非 -1\", \"原始答案和参考盲解答案均给出 -1，但缺乏合理推导支持\", \"∛(2a - b) = -1: 若立方根为-1，则被开方数应为(-1)^3=-1，但实际2a-b=9≠-1，矛盾\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": true, \"reason\": \"代入 a=6, b=3 计算正确，结果为 9\", \"equation\": \"2a - b = 2*6 - 3 = 9\"}, {\"valid\": true, \"reason\": \"根据计算结果，2a-b=9，其立方根为∛9\", \"equation\": \"∛(2a - b) = ∛9\"}, {\"valid\": false, \"reason\": \"若立方根为-1，则被开方数应为(-1)^3=-1，但实际2a-b=9≠-1，矛盾\", \"equation\": \"∛(2a - b) = -1\"}]}","created_at":"2026-09-25T00:02:59"},{"id":418761,"import_question_id":21263,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1) a=6, b=3; (2) -1 || 盲解:(1) a=6, b=3; (2) -1","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-25T00:02:59"},{"id":418762,"import_question_id":21263,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":0.95,"input_snapshot":null,"result_json":"{\"critic\": false, \"symbolic\": true, \"coherence\": false, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 1.0, \"verifier_base\": \"http://127.0.0.1:8092/v1\", \"verifier_confidence\": 0.9, \"critic_explicit_pass\": false, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": false}","created_at":"2026-09-25T00:02:59"}]}