{"ok":true,"question":{"id":21532,"question_uuid":"9d20a6a9-0d26-439c-ae57-af8a93b06ff8","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案440.pdf","source_page_start":1,"source_page_end":1,"source_bbox":"[303.07, 441.97, 453.2, 463.59]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"fill_blank","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"x −\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2} =1\"}, {\"text\": \"则x = _______\", \"type\": \"text\"}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"x=1+\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2}\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"由题设方程 x -\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2} = 1\"}, {\"text\": \"，直接移项得 x = 1 +\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2}\"}, {\"text\": \"。原解析误将方程理解为绝对值方程 |x -\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2}| = 1\"}, {\"text\": \"，从而多出一个解 x = 1 -\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{2}\"}, {\"text\": \"，该解不满足原方程，应舍去。\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [303.07, 441.97, 453.2, 463.59], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案440.pdf\", \"regions\": [{\"bbox\": [303.07, 441.97, 453.2, 463.59], \"page\": 1}], \"section\": \"memory\", \"page_end\": 1, \"page_start\": 1, \"section_label\": \"巩固记忆学习        请认真填写，不会的地方及时查看上方核心知识点！\", \"answer_regions\": [], \"answer_original\": \"\", \"solution_original\": \"\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"14\", \"subject_code\": \"math\", \"question_type\": \"fill_blank\", \"content_sha256\": \"107ae4a7daaba49286af275d8d2a05e39c9f6be4f9f2967c8a3701e2d528b69e\"}","body_html":"<div>x −\\(\\sqrt{2} =1\\)则x = _______</div>","answer_html":"x=1+\\(\\sqrt{2}\\)","ways_html":"由题设方程 x -\\(\\sqrt{2} = 1\\)，直接移项得 x = 1 +\\(\\sqrt{2}\\)。原解析误将方程理解为绝对值方程 |x -\\(\\sqrt{2}| = 1\\)，从而多出一个解 x = 1 -\\(\\sqrt{2}\\)，该解不满足原方程，应舍去。","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: VISION","published_question_id":null,"content_sha256":"107ae4a7daaba49286af275d8d2a05e39c9f6be4f9f2967c8a3701e2d528b69e","created_at":"2026-09-25T01:49:49","updated_at":"2026-09-25T01:56:41","answer_missing":false,"formula_fallback":false,"_number":"14","_section":"memory","_section_label":"巩固记忆学习        请认真填写，不会的地方及时查看上方核心知识点！"},"assets":[],"knowledge":[],"audits":[{"id":424958,"import_question_id":21532,"audit_type":"STRUCTURE","auditor_name":"structure-rule","status":"PASS","score":0.9,"input_snapshot":"x − \\sqrt{2} =1 则x = _______","result_json":"{\"ok\": true, \"rule\": \"clean-override\", \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-25T01:52:26"},{"id":424959,"import_question_id":21532,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\sqrt{2} =1","result_json":"{\"risky\": 1, \"issues\": [], \"checked\": 1, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T01:52:26"},{"id":424960,"import_question_id":21532,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"x − \\sqrt{2} =1 则x = _______","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T01:52:26"},{"id":424966,"import_question_id":21532,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"x − \\sqrt{2} =1 则x = _______","result_json":"{\"basis\": \"由绝对值定义，|A|=B(B≥0)等价于A=B或A=-B。此处A=x−√2，B=1，故x−√2=1或x−√2=−1，解得x=1+√2或x=1−√2。\", \"answer\": \"x=1+\\\\sqrt{2}或x=1-\\\\sqrt{2}\", \"confidence\": 1.0, \"handout_chars\": 81}","created_at":"2026-09-25T01:52:36"},{"id":424967,"import_question_id":21532,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案: || 盲解:x=1+\\sqrt{2}或x=1-\\sqrt{2}","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T01:52:36"},{"id":424983,"import_question_id":21532,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.9,"input_snapshot":"题干：\nx −\\(\\sqrt{2} =1\\)则x = _______\n答案：\n\n解析：\n","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.9, \"suggestions\": [\"建议补充完整答案和解析内容\"]}","created_at":"2026-09-25T01:53:01"},{"id":424984,"import_question_id":21532,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:x=1+\\(\\sqrt{2}\\)或x=1-\\(\\sqrt{2}\\) || 盲解:x=1+\\sqrt{2}或x=1-\\sqrt{2}","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":"2026-09-25T01:53:01"},{"id":425033,"import_question_id":21532,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案:x=1+\\(\\sqrt{2}\\)或x=1-\\(\\sqrt{2}\\) || 解析:由绝对值定义，|A|=B(B≥0)等价于A=B或A=-B。此处A=x−√2，B=1，故x−√2=1或x−√2=−1，解得x=1+√2或x=1−√2。","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中错误地应用了绝对值定义，将 x - √2 = 1 错误地理解为 |x - √2| = 1，从而多出了一个解 x = 1 - √2。\", \"x - √2 = -1: 原方程是 x - √2 = 1，而不是 x - √2 = -1。解析中错误地引入了 x - √2 = -1 这一情况，导致多出一个解 x = 1 - √2。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": true, \"reason\": \"这是题目给出的原始方程，无需验证。\", \"equation\": \"x - √2 = 1\"}, {\"valid\": false, \"reason\": \"原方程是 x - √2 = 1，而不是 x - √2 = -1。解析中错误地引入了 x - √2 = -1 这一情况，导致多出一个解 x = 1 - √2。\", \"equation\": \"x - √2 = -1\"}]}","created_at":"2026-09-25T01:54:14"},{"id":425034,"import_question_id":21532,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.925,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\"]}","created_at":"2026-09-25T01:54:14"},{"id":425085,"import_question_id":21532,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"x − \\sqrt{2} =1 则x = _______","result_json":"{\"basis\": \"根据绝对值的定义，|a|=b(b≥0)则a=±b。这里a=x-√2，b=1，所以x-√2=±1，解得x=1+√2或x=-1+√2。\", \"answer\": \"1+√2或-1+√2\", \"confidence\": 1.0, \"handout_chars\": 81}","created_at":"2026-09-25T01:55:17"},{"id":425086,"import_question_id":21532,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:x=1+\\(\\sqrt{2}\\) || 盲解:1+√2或-1+√2","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T01:55:17"},{"id":425095,"import_question_id":21532,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:x=1+\\(\\sqrt{2}\\) || 解析:由题设方程 x -\\(\\sqrt{2} = 1\\)，直接移项得 x = 1 +\\(\\sqrt{2}\\)。原解析误将方程理解为绝对值方程 |x -\\(\\sqrt{2}| = 1\\)，从而多出一个解 x = 1 -\\(\\sqrt{2}\\)，该解不满足原方程，应舍去。","result_json":"{\"ok\": true, \"which\": [], \"issues\": [], \"confidence\": 1.0, \"equation_checks\": []}","created_at":"2026-09-25T01:55:47"},{"id":425096,"import_question_id":21532,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:x=1+\\(\\sqrt{2}\\) || 盲解:1+√2或-1+√2","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":"2026-09-25T01:55:47"},{"id":425097,"import_question_id":21532,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"PASS","score":1.0,"input_snapshot":null,"result_json":"{\"critic\": true, \"symbolic\": true, \"coherence\": true, \"consensus\": \"two_solvers+symbolic_literal_warn+critic_and_coherence\", \"confidence\": 1.0, \"verifier_base\": \"http://127.0.0.1:8091/v1\", \"verifier_confidence\": 1.0, \"critic_explicit_pass\": true, \"symbolic_literal_warn\": true, \"symbolic_explicit_pass\": false, \"coherence_explicit_pass\": true}","created_at":"2026-09-25T01:55:47"},{"id":425098,"import_question_id":21532,"audit_type":"AUTO_REPAIR","auditor_name":"answer-repair","status":"PASS","score":1.0,"input_snapshot":null,"result_json":"{\"basis\": \"由绝对值定义，|A|=B(B≥0)等价于A=B或A=-B。此处A=x−√2，B=1，故x−√2=1或x−√2=−1，解得x=1+√2或x=1−√2。\", \"answer\": \"x=1+\\\\sqrt{2}或x=1-\\\\sqrt{2}\", \"critic\": {\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}, \"reason\": \"当前题干与来源答案冲突，使用高置信盲解修复并通过二次校验\", \"symbolic\": {\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案存在字面差异，需 Critic 复核\"}, \"status\": \"WARN\", \"applicable\": true}, \"coherence\": {\"ok\": true, \"which\": [], \"issues\": [], \"confidence\": 1.0, \"equation_checks\": []}}","created_at":"2026-09-25T01:55:47"},{"id":425118,"import_question_id":21532,"audit_type":"VISION","auditor_name":"vision-auditor","status":"FAIL","score":0.9,"input_snapshot":"当前答案解析经过独立复算修正了来源错误。题干、条件、选项和配图仍必须忠实原图；答案解析与来源不同时须独立验证修正是否成立，不能仅因不同就否决，也不能因已修正就通过。\n题干：\nx −\\(\\sqrt{2} =1\\)则x = _______\n答案：\nx=1+\\(\\sqrt{2}\\)\n解析：\n由题设方程 x -\\(\\sqrt{2} = 1\\)，直接移项得 x = 1 +\\(\\sqrt{2}\\)。原解析误将方程理解为绝对值方程 |x -\\(\\sqrt{2}| = 1\\)，从而多出一个解 x = 1 -\\(\\sqrt{2}\\)，该解不满足原方程，应舍去。","result_json":"{\"ok\": false, \"hard\": true, \"issues\": [\"题干显示为绝对值方程 |x - √2| = 1，但当前题干文本遗漏了绝对值符号，写作 x - √2 = 1，导致方程含义改变\", \"由于题干缺失绝对值符号，当前答案 x = 1 + √2 虽为原方程的一个解，但并非全部解，且无法体现原方程的完整解集\", \"解析中承认原方程被误读，但未在题干层面修正，造成题干与解析不一致\"], \"confidence\": 0.9, \"suggestions\": [\"题干应恢复为 |x - √2| = 1，以准确反映原卷内容\", \"若保持当前题干，则答案应仅给出满足该方程的解，并说明原卷可能存在印刷遗漏\"]}","created_at":"2026-09-25T01:56:41"}]}