{"ok":true,"question":{"id":21384,"question_uuid":"bd71f325-8649-4f63-81df-135204b980be","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案415.pdf","source_page_start":2,"source_page_end":2,"source_bbox":"[30.22, 392.67, 249.66, 405.5]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"fill_blank","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"写出一个 −6~ −5之间的无理数： _____.\", \"type\": \"text\"}, {\"type\": \"answer\", \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"-2\\\\sqrt{6},\\\\ -3\\\\sqrt{3},\\\\ -2\\\\sqrt{7}\\\\cdots\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"因为\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"-6=-\\\\sqrt{36}-5=-\\\\sqrt{25}\"}, {\"text\": \"，\\\\therefore 只要写被开方数在25和36之间，且不是完全平方数并加上负号的都可，如：\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"-2\\\\sqrt{6}\"}, {\"text\": \"，\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"-3\\\\sqrt{3}\"}, {\"text\": \"，\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"-2\\\\sqrt{7}\\\\cdots\"}]}], \"source\": {\"bbox\": [30.22, 392.67, 249.66, 405.5], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案415.pdf\", \"regions\": [{\"bbox\": [30.22, 392.67, 249.66, 405.5], \"page\": 2}], \"section\": \"generic\", \"page_end\": 2, \"page_start\": 2, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [43.99800109863281, 563.3077392578125, 438.0333557128906, 603.5216674804688], \"page\": 4}], \"answer_original\": \"−2√6,   −3√3,   −2√7 ⋯\", \"solution_original\": \"因为−6 = −√36 −5 = −√25， ∴ 只要写被开方数在25和36之间，且不是完全 平方数并加上负号的都可，如：−2√6,   −3√3,   −2√7 ⋯\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"9\", \"subject_code\": \"math\", \"question_type\": \"fill_blank\", \"content_sha256\": \"9b1f5dabfbbb7abe601da6245e29ed66bcce856a04f51b7717e9984165e2410d\"}","body_html":"<div>写出一个 −6~ −5之间的无理数： _____.</div>","answer_html":"\\(-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots\\)","ways_html":"因为\\(-6=-\\sqrt{36}-5=-\\sqrt{25}\\)，\\therefore 只要写被开方数在25和36之间，且不是完全平方数并加上负号的都可，如：\\(-2\\sqrt{6}\\)，\\(-3\\sqrt{3}\\)，\\(-2\\sqrt{7}\\cdots\\)","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":"9b1f5dabfbbb7abe601da6245e29ed66bcce856a04f51b7717e9984165e2410d","created_at":"2026-09-25T00:43:18","updated_at":"2026-09-25T00:59:10","answer_missing":false,"formula_fallback":false,"_number":"9","_section":"generic","_section_label":""},"assets":[],"knowledge":[],"audits":[{"id":421377,"import_question_id":21384,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"写出一个 −6~ −5之间的无理数： _____.","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T00:49:14"},{"id":421378,"import_question_id":21384,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots; -6=-\\sqrt{36}-5=-\\sqrt{25}; -2\\sqrt{6}; -3\\sqrt{3}; -2\\sqrt{7}\\cdots","result_json":"{\"risky\": 5, \"issues\": [], \"checked\": 5, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T00:49:14"},{"id":421379,"import_question_id":21384,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"写出一个 −6~ −5之间的无理数： _____.","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T00:49:14"},{"id":421383,"import_question_id":21384,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n写出一个 −6~ −5之间的无理数： _____.\n答案：\n\\(-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots\\)\n解析：\n因为\\(-6=-\\sqrt{36}-5=-\\sqrt{25}\\)，\\therefore 只要写被开方数在25和36之间，且不是完全平方数并加上负号的都可，如：\\(-2\\sqrt{6}\\)，\\(-3\\sqrt{3}\\)，\\(-2\\sqrt{7}\\cdots\\)","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"解析中‘只要写被开方数在25和36之间’表述可优化为‘只要写被开方数在25到36之间（不含25和36）’，以更准确反映无理数定义要求\"]}","created_at":"2026-09-25T00:49:39"},{"id":421387,"import_question_id":21384,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"写出一个 −6~ −5之间的无理数： _____.","result_json":"{\"basis\": \"要找一个在 -6 到 -5 之间的无理数，可以考虑负数的平方根形式。例如，√36=6，√25=5，因此 √(30) 在 5 和 6 之间，取负号即 -√30 也在 -6 到 -5 之间，且为无理数。类似地，-2√6 = -√24，也满足条件。\", \"answer\": \"-2√6\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T00:50:03"},{"id":421388,"import_question_id":21384,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:\\(-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots\\) || 盲解:-2√6","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T00:50:03"},{"id":421389,"import_question_id":21384,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:\\(-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots\\) || 盲解:-2√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":"2026-09-25T00:50:03"},{"id":421765,"import_question_id":21384,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案:\\(-2\\sqrt{6},\\ -3\\sqrt{3},\\ -2\\sqrt{7}\\cdots\\) || 解析:因为\\(-6=-\\sqrt{36}-5=-\\sqrt{25}\\)，\\therefore 只要写被开方数在25和36之间，且不是完全平方数并加上负号的都可，如：\\(-2\\sqrt{6}\\)，\\(-3\\sqrt{3}\\)，\\(-2\\sqrt{7}\\cdots\\)","result_json":"{\"ok\": false, \"which\": [\"solution\", \"解析\"], \"issues\": [\"解析中连等式错误：-6 = -√36 - 5 = -√25 不成立，导致推导基础错误。\", \"虽然最终举例的数（如 -2√6）确实在 -6 到 -5 之间且为无理数，但解析过程存在逻辑断裂。\", \"-6 = -√36 - 5 = -√25: 等式不成立：-√36 = -6，因此 -√36 - 5 = -11，而非 -6；同理 -√25 = -5，故 -6 ≠ -√25。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"等式不成立：-√36 = -6，因此 -√36 - 5 = -11，而非 -6；同理 -√25 = -5，故 -6 ≠ -√25。\", \"equation\": \"-6 = -√36 - 5 = -√25\"}]}","created_at":"2026-09-25T00:53:02"},{"id":421766,"import_question_id":21384,"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":"2026-09-25T00:53:02"},{"id":421847,"import_question_id":21384,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.9,"input_snapshot":"写出一个 −6~ −5之间的无理数： _____.","result_json":"{\"basis\": \"要找一个在 -6 到 -5 之间的无理数，可以考虑负数的平方根。由于 6 介于 5 和 7 之间，√6 约为 2.45，因此 -2√6 ≈ -4.9，落在 -6 到 -5 区间内，且为无理数。\", \"answer\": \"-2√6\", \"confidence\": 0.9, \"handout_chars\": 0}","created_at":"2026-09-25T00:57:35"},{"id":421848,"import_question_id":21384,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:-2√6 || 盲解:-2√6","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T00:57:35"},{"id":421862,"import_question_id":21384,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.95,"input_snapshot":"答案:-2√6 || 解析:要找到一个介于 -6 和 -5 之间的无理数，可以考虑负数的平方根形式。由于 -6 = -√36，-5 = -√25，因此任何形如 -√n 的数，若 n 在 25 和 36 之间且不是完全平方数，则其值必在 -6 与 -5 之间且为无理数。例如，取 n=26，则 -√26 满足条件；同理，-2√6 = -√(\\(4\\times 6\\)) = -√24，但 24&lt;25，故 -2√6 ≈ -4.","result_json":"{\"ok\": false, \"which\": [\"answer\", \"solution\"], \"issues\": [\"答案 -2√6 约为 -4.899，不在 -6 至 -5 之间，不符合题意。\", \"解析中虽指出 -2√6 不在范围内，但最终仍将其作为候选答案，逻辑矛盾。\", \"正确示例应为 -√26 等（-6 < -√26 < -5），但答案未修正。\", \"-4.899 在 -6 到 -5 之间: -4.899 > -5，不在 [-6, -5] 区间内。\"], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": true, \"reason\": \"(-2)^2 * 6 = 4 * 6 = 24，等式成立。\", \"equation\": \"-2√6 = -√24\"}, {\"valid\": true, \"reason\": \"√24 ≈ 4.899，故 -√24 ≈ -4.899，计算正确。\", \"equation\": \"-√24 ≈ -4.899\"}, {\"valid\": false, \"reason\": \"-4.899 > -5，不在 [-6, -5] 区间内。\", \"equation\": \"-4.899 在 -6 到 -5 之间\"}]}","created_at":"2026-09-25T00:59:10"},{"id":421863,"import_question_id":21384,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:-2√6 || 盲解:-2√6","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": 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