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Math Derivation

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tradecatlabs
math-derivation

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。

Overview

Publishertradecatlabs
Repositoryvibe-coding-cn
Skill namemath-derivation
Stars
17.4K
Forks
1.8K
Bundled files
5
LicenseMIT
Links
Skill sourceRepositoryHomepage
  • Markdown instructions

    A SKILL.md file the model loads on demand, so it only costs tokens when a request actually matches.

  • Works with any LLM

    AI skills are plain Markdown, not provider-specific code, so this works with GPT, Claude, Gemini, Grok, or a local model.

  • 5 bundled files

    Scripts, templates, and references the model can read while it works. Files are read-only and never executed.

  • Open source

    Published by tradecatlabs on GitHub. Read the source before you install it.

Installation

Install the Math Derivation AI skill in TypingMind to use it with any LLM, or drop it into another agent that reads SKILL.md.

1

Install in TypingMind

TypingMind installs a skill straight from its GitHub folder — it reads SKILL.md, bundles the resource files, and stores the result locally.

  1. Open the app and go to Plugins → Skills.
  2. Choose "Install from GitHub".
  3. Paste the skill folder URL below and confirm.
    https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-derivation
  4. Enable the skill in any chat where you want it available.
Plugins → Skills → Add skill → From GitHub URL, then paste the folder URL and press Continue.
2

Install in another agent

Any agent that reads the Agent Skills format can use this skill — copy the folder into that agent's skills directory.

Claude Code — .claude/skills
git clone --depth 1 https://github.com/tradecatlabs/vibe-coding-cn.git /tmp/vibe-coding-cn
mkdir -p .claude/skills
cp -r /tmp/vibe-coding-cn/research/vibe-mathing-cn-public/.codex/skills/math-derivation .claude/skills/math-derivation
Restart Claude Code after copying so it picks up the new skill.

Use it in TypingMind

Enable Math Derivation in any TypingMind chat and the model takes it from there. Its name and description sit in the system prompt, and the moment a request matches, the model loads the full instructions itself — you never invoke it by hand, and it costs no tokens until it is actually used.

The model loads Math Derivation on its own as soon as a request matches it.

Works with any AI model

AI skills are plain Markdown instructions rather than provider-specific code, so Math Derivation is not tied to the model it was written for. Install it once in TypingMind and use it with GPT-5, Claude, Gemini, Grok, DeepSeek, Mistral, Llama, or a local model you run yourself — all on your own API keys.

  • Loaded only when it is needed

    The system prompt carries just the name and description. The instructions are fetched on the first matching request, so an idle skill costs nothing.

  • Switch models mid-chat

    Because the skill is instructions rather than code, changing model does not break it — the next model reads the same SKILL.md.

Skill instructions

This is the SKILL.md content the model loads. Read it before installing — a skill is instructions your model will follow.

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

text
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。

Bundled files

The model reads these on demand while the skill is loaded. They are exposed as readable files and are never executed.

Frequently asked questions

What does the Math Derivation AI skill do?

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。

Why use Math Derivation on TypingMind?

Because you install it once and use it with any model. Math Derivation is plain Markdown rather than provider-specific code, so the same skill runs on GPT-5, Claude, Gemini, Grok, or a local model — and you can switch model mid-chat without it breaking. TypingMind runs on your own API keys, so you pay providers directly instead of a per-seat subscription, and your skills and chats stay in your own storage.

How do I install Math Derivation in TypingMind?

Open Plugins → Skills → Install from GitHub in TypingMind and paste https://github.com/tradecatlabs/vibe-coding-cn/tree/develop/research/vibe-mathing-cn-public/.codex/skills/math-derivation. TypingMind reads its SKILL.md and bundles its files and installs it as a skill you can enable per chat.

Which AI models can use Math Derivation?

Any model you connect in TypingMind. AI skills are plain Markdown instructions rather than provider-specific code, so GPT, Claude, Gemini, Grok, and local models can all load this skill when a request matches it.

How many AI models can I use with Math Derivation?

As many as you like. As long as a model supports skills, you can use Math Derivation with it — GPT, Claude, Gemini, Grok, DeepSeek, Mistral, Llama and more — all on TypingMind with your own API keys.

Is the Math Derivation AI skill free?

Yes. It is published on GitHub by tradecatlabs under the MIT license. You only pay your own AI provider for the tokens you use.

What are AI skills?

An AI skill is a reusable instruction bundle that teaches an AI model how to do one specific task. It follows the open Agent Skills format: a SKILL.md file with a name and description, plus any scripts, templates or reference files the model may need. The model reads the instructions only when your request matches the skill, so an installed skill costs nothing until it is used.

How are AI skills different from plugins or MCP servers?

A plugin or MCP server gives a model new tools to call — code that runs somewhere and returns a result. An AI skill gives the model knowledge and process instead: how to approach a task, which steps to follow, what good output looks like. Skills are plain Markdown, so they need no server, no API key and no runtime, and they work with any model.

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