Individual skill
math-proof-rigor
数学证明的对抗性审查纪律。用于逐行核验证明、寻找漏洞、构造反例并判定成立性。当需要审查或验证一个证明、找 gap、构造反例、或判断证明是否成立时使用。
skills/math-proof-rigor/SKILL.md
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# 数学证明审查纪律
对一份数学证明做对抗性审查，目标是找出漏洞、构造反例，并给出「成立 / 有缺陷 / 不成立」的判定。默认怀疑每一个断言，只接受有充分依据的推导。
## 审查顺序
1. **对齐命题**：先明确要证明的命题与全部假设。判定一条证明的第一步，是核对它证明的结论是否与给定命题一致——偷换结论、弱化结论、遗漏退化情形都属于致命缺陷。
2. **检查假设使用**：每个假设是否都被用上、是否被正确使用、是否混入了未声明的假设。
3. **逐行核验**：对每一步检查推导是否合法、依据是否充分、是否存在跳步。
4. **构造反例**：对可疑断言尝试构造具体反例，用真实对象证伪，不要停留在「感觉不对」。
5. **判定成立性**：汇总为「成立 / 有缺陷 / 不成立」之一，每条结论附定位与理由。
## 常见漏洞清单
