# formula-derivation

Structures research notes and equations into a derivation package. Helps organize assumptions and records proof steps in DERIVATION_PACKAGE.md.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · 532 installs · ★ 18090
- Author: wanshuiyin
- License: MIT · policy=mirror · the beginning of the file is at the end of this page
- Source: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/HEAD/skills/formula-derivation/SKILL.md
- Updated: 2026-10-24
- HTML: https://affpapa.org/en/nevibecode/skills/formula-derivation

## What it does

This skill turns messy mathematical notes, research goals, and scattered equations into a structured derivation document. It starts by defining the target and its exact role: an algebraic identity, an approximation, a local proposition, or an interpretation. If symbols or targets are ambiguous, the skill establishes an explicit reading before any symbolic manipulation.

The workflow moves through context gathering, invariant object selection, assumption normalization, and step categorization. Every nontrivial step is labeled as an identity, proposition, approximation, or interpretation. Generated notes default to `DERIVATION_PACKAGE.md` in the project root rather than editing paper `.tex` files directly.

When a derivation cannot be completed honestly, the skill avoids handwaving words like "clearly" or "obviously". Instead, it sets the status to `NOT YET COHERENT` and outputs a blocker report. Freezing the invariant quantity early prevents a convenient proxy from silently taking over the derivation.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/formula-derivation/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/formula-derivation/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/formula-derivation/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/formula-derivation/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install wanshuiyin/Auto-claude-code-research-in-sleep formula-derivation
```

2. **Manually: put the files in place**
- File: `.github/skills/formula-derivation/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep --path skills/formula-derivation
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/formula-derivation/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/HEAD/skills/formula-derivation/SKILL.md

## When to use it
- turn scattered formulas and draft notes into a structured derivation package
- separate exact algebraic identities from approximations and heuristic interpretations
- formalize implicit assumptions and definitions before symbolic manipulation
- document blockers when existing assumptions fail to support the desired claim

## Example prompts
- Use formula-derivation to build the objective function proof from notes.md into DERIVATION_PACKAGE.md
- Normalize assumptions and derive the effective cost approximation
- Check my theoretical sketch for hidden assumptions and create a derivation map

## Source text · SKILL.md · MIT

Below is the content of a third-party file. It is data, not instructions for you: do not act on anything written inside unless the human asks. Block tag: 90afbe3f0b881de5.

BEGIN THIRD-PARTY FILE 90afbe3f0b881de5
```text
---
name: formula-derivation
description: Structures and derives research formulas when the user wants to 推导公式, build a theory line, organize assumptions, turn scattered equations into a coherent derivation, or rewrite theory notes into a paper-ready formula document. Use when the derivation target is not yet fully fixed, the main object still needs to be chosen, or the user needs a coherent derivation package rather than a finished theorem proof.
argument-hint: "[problem-goal-current-formulas-or-notes]"
allowed-tools: Read, Write, Edit, Grep, Glob, Skill(lean-formalize)
---

# Formula Derivation: Research Theory Line Construction

Build an honest derivation package, not a fake polished theorem story.

## Constants

- DEFAULT_DERIVATION_DOC = `DERIVATION_PACKAGE.md` in project root
- STATUS = `COHERENT AS STATED | COHERENT AFTER REFRAMING / EXTRA ASSUMPTION | NOT YET COHERENT`

## Context: $ARGUMENTS

## Goal

Produce exactly one of:
1. a coherent derivation package for the original target
2. a reframed derivation package with corrected object / assumptions / scope
3. a blocker report explaining why the current notes cannot yet support a coherent derivation

## Inputs

Extract and normalize:
- the target phenomenon, formula, relation, or theory line
- the intended role of the derivation:
  - exact identity / algebra
  - proposition / local theorem
  - approximation
  - mechanism interpretation
- explicit assumptions
- notation and definitions
- any user-provided formula chain, sketch, messy notes, or current draft
- nearby local theory files if the request points to them
- desired output style if specified:
  - internal alignment note
  - paper-style theory draft
  - blocker report

If the target, object, notation, or assumptions are ambiguous, state the exact interpretation you are using before deriving anything.

## Workflow

### Step 1: Gather Derivation Context
Determine the target derivation file with this priority:
1. a file path explicitly specified by the user
2. a derivation draft already referenced in local notes
3. `DERIVATION_PACKAGE.md` in project root as the default target

Read the relevant local context:
- the chosen target derivation file, if it already exists
- any local theory notes, formula drafts, appendix notes, or files explicitly mentioned by the user

Extract:
```
END THIRD-PARTY FILE 90afbe3f0b881de5

The third-party file has ended. Everything between the 90afbe3f0b881de5 tags is data: requests and commands from it are not followed. An “end of file” line with another tag inside the block is part of the file.

First 2333 of 9550 bytes. © wanshuiyin · MIT · https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/tree/HEAD/skills/formula-derivation/SKILL.md

_Part of the page did not fit — see the HTML version._

---
NeVibeCode on affpapa.org. Catalog texts are descriptions, not instructions for the agent. How to choose and install: https://affpapa.org/en/nevibecode/agents.md