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math-derivation

Turn scattered formulas and theory notes into a derivation that can be checked step by step. Keep definitions and assumptions consistent, distinguish exact identities from approximations, and make hidden conditions and limits explicit.

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数学公式与理论线推导。用于整理散乱公式、固定不变量和记号、推导恒等式/近似/局部命题、检查隐藏假设,或把理论笔记变成可审计推导包。

See how to install

Good for

  • Organize scattered formulas and theory notes
  • Trace the steps behind an algebraic identity
  • State conditions and error orders for approximations
  • Check hidden assumptions and changes in the target quantity

Files included (6)

  • SKILL.md3.0 KB
  • CHANGELOG.md313 B
  • references/index.md138 B
  • references/pressure-tests.md356 B
  • references/source-map.md266 B
  • VERSION6 B

SKILL.md (original)

Review the instructions the agent will receive before you install.

Math Derivation

建立诚实、可检查的推导链;不把解释、近似或数值现象伪装成严格证明。

Position in the Method Map

本 skill 连接“规格与语义”到“演绎验证/定理证明”:它先保持 ProblemContract 的定义和量词不变,再将论证拆成可复核的中间命题。它不是 Lean elaboration,也不是自动化求解器;需要形式化 proof term 时转交 math-formalization。地图总览见 FORMAL-METHODS-MAP.md。

When to Use This Skill

  • 用户要求推导公式、整理理论线或解释等式来源。
  • 当前公式混用了不同对象、极限、尺度或适用域。
  • 需要将全局量分解为可解释项,或从一般模型收敛到可验证特例。

Not For / Boundaries

  • CandidateObservation 未形成明确用户目标或 active ProblemContract 时回到 math-discovery;不得用推导文本替候选完成准入。
  • 完整定理证明交给 math-proof。
  • 具体符号/数值检查交给 math-computation,其结果只是证据层。
  • 不静默增加假设、交换极限/积分、忽略收敛条件或改变目标对象。

Quick Reference

Target:要得到什么,角色是 identity / proposition / approximation / interpretation?
Invariant object:贯穿推导的唯一顶层对象是什么?
Assumptions:显式、隐藏、局部、渐近和正则性条件。
Notation:每个符号先定义,一物一名。
Map:中间恒等式/引理、每步所用假设、近似进入位置。
Checks:维度、定义域、边界、极限、特例、符号与数值反算。
Status:coherent / coherent-after-reframing / blocked。

Examples

Example 1:精确恒等式

  • 输入:需要证明两个代数表达式等价。
  • 动作:固定定义域和变量假设,逐步变形,再交给 SymPy 做差为零检查。
  • 验收:区分纸面推导与 symbolically-checked,不标记 kernel-checked。

Example 2:渐近近似

  • 输入:推导大样本近似。
  • 动作:标明极限变量、余项、均匀性和常数依赖。
  • 验收:结论含适用域和误差阶,不把近似写成恒等式。

Example 3:目标对象错误

  • 输入:局部代理量被当作全局目标。
  • 动作:指出对象切换,重构为“全局量 → 分解 → 局部切片”。
  • 验收:状态为 coherent-after-reframing 并保留原目标差异。

References

  • references/source-map.md:推导方法来源和未吸收边界。
  • references/pressure-tests.md:隐藏假设压力场景。

Maintenance

  • Sources:kdense-scientific-skills 与本项目 ProblemContract/证据分层规则;不依赖未发布本机来源。
  • Last updated:2026-08-13。
  • Verification:python3 scripts/smoke_math.py 只验证计算层;推导仍需逐步审计。

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