{"version":"2026-10-19.boundary.1","explanation":{"id":"answer-and-proof","taskIds":["M01"],"frontierIds":["F07","F06"],"title":"答案对了，推理就对了吗？选择数学工作的验收对象","deck":"区分答案命中、过程检查与形式核验；重复采样或模型裁判不能替代每种产物自己的门槛。","editorialAt":"2026-10-16","sourceIds":["BM11","BM12","BF06","BM06","BM13"],"sections":[{"title":"三种正确要分别说清楚","paragraphs":["答案核对检查数值是否命中；过程检查追问每一步是否由条件推出；形式证明还要核对命题语义并由证明内核检查。它们不是一条简单的自动化高低阶梯。","本次聚焦M01数值推导。M03形式命题搜索另有原始材料，不将小学答案或模型裁判成绩转成形式证明成功率。"],"sourceIds":["BM06"]},{"title":"两项研究提出了不同测量问题","paragraphs":["RLVR指可验证奖励的强化学习：训练中用可核对的奖励调整模型。本文关注训练后怎样衡量答案与推理过程，不把奖励分数直接当成现实工作验收。K是生成解答候选的数量；更大的K需要更多尝试及挑选、核验。","Yue等在Qwen2.5-7B-Base与SimpleRL-Qwen2.5-7B的指定配置中观察到：RLVR模型在较低K时更容易命中，但随着K增大，基础模型的答案覆盖可以赶上或超过它。本文引用的条件是AIME24最多1024候选、MATH500最多128候选，主设置温度0.6；这是有限预算下的答案覆盖观察，不是所有训练都没有新能力的证明。","Wen等比较Qwen2.5-32B与DAPO-Qwen-32B，在AIME24/25的高K下，两者答案覆盖可以接近，但由模型裁判接受的推理过程覆盖仍有差距。裁判为DeepSeek-R1-0528-Qwen3-8B，每条推导独立判断3次：any至少一次接受，all三次都接受，majority多数接受；生成候选K最高1024。","过程判定仍依赖裁判与聚合规则，并非形式证明内核。两项研究的模型、训练、题集与评分不同，不能合成RLVR有无新能力的统一定论。本文只保留定性方向，不把未可靠转录的曲线画成数字柱图。"],"sourceIds":["BM11","BM12"]},{"title":"对具体解题工作怎样有用","paragraphs":["先写明需要答案还是成立推导。生成草稿后独立复算数值，再审查变量、单位、边界与每一步依据；保存全部尝试和挑选规则。","把计算交给程序可让数值复算更清楚，但题意转成表达式依然可能错。数字恰好相同不足以接受完整推导；需要证明时切换到相应验证流程。"],"sourceIds":["BF06"]},{"title":"读懂Pass@K与裁判","paragraphs":["Pass@K说明K次中至少一次成功，不是每次都可靠。挑选、复核与失败的代价也属于你的工作流程。","模型裁判是另一模型对过程作判断，仍有误判与语义限制。对重要结论保留人的独立核验，不用漂亮推理文字代替证明。"],"sourceIds":[]},{"title":"训练方法迁移要逐任务判断","paragraphs":["Qwen3-14B论文v2用相同数学问题比较不同训练方式。RL在ACPBench为65.4，低于最佳SFT的69.3，却高于基础模型10.7；因此“比基础模型进步”与“该任务不如另一训练方式”可同时成立。","SFT是示范监督训练，RL是奖励驱动训练；训练问题相同不等于总算力和成本匹配。此研究是迁移条件参考，没有验证本页资源约束例；普通使用者应在需要的产物上做核验，不把训练结论换成提示技巧或职业能力分。"],"sourceIds":["BM13"]}],"evidenceStatus":"active"},"comparisonLinks":[{"label":"M01案例中的条件比较","url":"/changes?task=M01&domain=math&at=2026-10#phase-conditions"}],"sources":[{"id":"BM11","title":"RLVR答案覆盖研究（v5）","url":"https://arxiv.org/html/2504.13837v5","publishedAt":"2025-11-24","kind":"推理评测研究预印本","locator":"§3设置；表2；附录C.7覆盖与C.8温度分析","limit":"有限采样只测答案命中；特定模型/任务结果不等于所有推理机制；不与另一论文合并效应","family":"rlvr-answer-support","readAt":"2026-10-15","readingScope":"本轮直接核对所列原文位置/版本；未复跑外部实验","dateBasis":"固定v5：2025-11-24；具体结论以所引用版本为准","status":"active"},{"id":"BM12","title":"RLVR推理过程核验研究（v2）","url":"https://arxiv.org/html/2506.14245v2","publishedAt":"2025-10-02","kind":"推理评测研究预印本","locator":"§3.1图2；§3.2图3；附录A.3裁判方法","limit":"推理过程由模型裁判判定，有any/all/majority规则；不是形式证明内核，图值未可靠转录则定性","family":"rlvr-judged-traces","readAt":"2026-10-15","readingScope":"本轮直接核对所列原文位置/版本；未复跑外部实验","dateBasis":"固定v2页首：2025-10-02；不倒填首次预印本日期","status":"active"},{"id":"BF06","title":"Program of Thoughts：外部计算接口（v4）","url":"https://arxiv.org/html/2211.12588v4","publishedAt":"2023-10-23","kind":"数值任务研究预印本","locator":"§2.2；§3.1数据/实现/指标；§3.2表2","limit":"同底层模型改变提示与执行流程；未匹配完整延迟/预算；不是端到端财务工作通过率","family":"program-of-thoughts","readAt":"2026-10-15","readingScope":"本轮直接核对所列原文位置/版本；未复跑外部实验","dateBasis":"固定v4页首：2023-10-23；不把v4表格倒填v1","status":"active"},{"id":"BM06","title":"DeepSeek-Prover-V2首稿","url":"https://arxiv.org/html/2504.21801v1","publishedAt":"2025-04-30","kind":"研究基准","locator":"§3及§3.1 Experimental Results；表1（671B CoT/候选预算）、表2（题目类别）；附录C题集修订。","limit":"671B CoT的88.9%为pass@8192；82.4%为pass@32，61.9%为pass@1；不是首试成功率","family":"BM06","readAt":"2026-10-14","readingScope":"本轮直接阅读所列原文位置；未复跑实验","dateBasis":"页面标示发布日期或固定预印本v1页首日期","status":"active"},{"id":"BM13","title":"数学训练迁移的Qwen3-14B比较（v2）","url":"https://arxiv.org/html/2507.00432v2","publishedAt":"2025-10-20","kind":"训练方法研究预印本","locator":"表1；§2.2；附录A.3","limit":"训练问题相同不代表总算力相同；ACPBench并非真实工作交付","family":"math-training-transfer","readAt":"2026-10-16","readingScope":"本轮直接阅读所列原文和固定版本；未复跑外部实验","dateBasis":"固定v2实际修订2025-10-20；v1发表于2025-07-01","status":"active"}],"scope":"现今编辑解释；不是按历史月份筛选的证据快照；实际覆盖未知"}