Helps write and review mathematical proofs in natural language. It clarifies assumptions, maps dependencies between claims and lemmas, checks counterexamples and edge cases, and produces a traceable draft that identifies unresolved gaps or necessary changes to the statement.
严格自然语言数学证明。用于证明或审查 theorem/lemma/proposition、补齐证明草稿、构建证明义务与依赖图、寻找反例、检查量词/常数/边界情况，或判断命题是否必须削弱。
Review the instructions the agent will receive before you install.
产出可审计的证明包；命题不成立或条件不足时，优先反驳或修正，不制造漂亮假证明。
本 skill 位于“演绎验证 / 定理证明”的 proof-engineering 阶段，前置是 FORMAL-METHODS-MAP.md 所定义的规格与语义边界。证明草稿、引理图和自然语言审查不会自动等同于 Lean kernel check；需要形式化时交给 math-formalization，需要有限反例或 SMT 路径时交给 math-computation。
proof-drafted 或经真实人工审查后的 human-reviewed。kernel-checked 只由 math-formalization 的真实 proof assistant 成功证据产生。refuted。Claim：精确陈述与量词顺序。
Status：provable-as-stated / repaired / refuted / blocked。
Assumptions：显式、隐藏和最小必要条件。
Proof obligations：每个非平凡蕴含一个义务。
Dependency map：结论 -> 引理 -> 外部定理 -> 假设。
Graph gate：节点 ID 唯一、依赖存在、无环、所有终点可追溯到 Claim。
Attack pass：边界、退化、极端尺度、量词交换、等号条件。
Proof：编号步骤，每步绑定义务或已验证结果。
Open gaps：任何未闭合项都会阻止完成声明。
Route status：open / blocked / refuted / closed，与 Claim status 分开记录。
proof-drafted 而非 kernel-checked。references/source-map.md：证明、审稿、proof DAG 与批判性思考来源映射。references/pressure-tests.md：错误命题、DAG 完整性、路线状态与隐藏缺口压力场景。annals-of-mathematics-skills、kdense-scientific-skills、proofflow、leanprover-skills；上游图与 skill 只作方法/反例来源，不代表本项目已安装或验证。No reviews yet. Tell others what you thought.
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