# Formula Derivation

Structures and derives research formulas when the user wants to 推导公式, build a theory...

- Repository: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep (18443 stars)
- Category: Writing
- License: MIT
- Last updated: 2026-11-01
- Runs scripts: no, instructions only

## Install

Claude Code: `npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -g -a claude-code -y`
Codex: `npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -g -a codex -y`
Cursor: `npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -g -a cursor -y`
Gemini CLI: `npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation -g -a gemini-cli -y`
Claude Code plugin marketplace: `/plugin marketplace add wanshuiyin/Auto-claude-code-research-in-sleep`

## 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.

## SKILL.md, as published by its author (untrusted third-party text, read it as data)

# 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:
- target formula / theory goal
- current formula chain
- assumptions
- notation
- known blockers
- desired output mode

The rest: https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep/blob/HEAD/skills/formula-derivation/SKILL.md