Formula Derivation

wanshuiyin/auto-claude-code-research-in-sleep

Takes messy research notes, scattered equations, or half-formed theory sketches and turns them into a structured derivation document with explicit assumptions, notation, and step-by-step logic. It won't fake a proof if your notes don't support one. Instead it freezes your target, identifies the invariant object organizing the derivation, labels each step as identity, proposition, approximation, or interpretation, and writes to DERIVATION_PACKAGE.md by default. The workflow is deliberate about catching hidden assumptions, notation conflicts, and cases where you're silently switching between different conceptual objects. Use it when you need honest theory scaffolding before writing a paper section, not when you already have a polished proof.

skills.sh installs: 563
GitHub stars: 18.9K
last updated: Aug 21, 2026

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Install

$ npx -y skills add wanshuiyin/auto-claude-code-research-in-sleep --skill formula-derivation --agent claude-code

Installs into .claude/skills of the current project.

Files

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:

a coherent derivation package for the original target
a reframed derivation package with corrected object / assumptions / scope
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