How to use the Formula Derivation agent skill (formula-derivation)

What is an agent skill, and what does this one make the agent do?

An agent skill is a folder containing a SKILL.md file that gives an AI agent specific instructions for a task. When the skill is installed and your request matches its description, the agent follows those instructions instead of its default approach.

This skill makes the agent behave like a careful theory collaborator. Given messy formulas, notes or a research goal, it first fixes exactly what is being derived, identifies the core quantity that should organise the argument, and writes out assumptions and notation.

It then labels every nontrivial step as an identity (exact algebraic reformulation), a proposition (needs stated conditions), an approximation, or an interpretation. The result is saved as a structured Markdown file, by default DERIVATION_PACKAGE.md in the project root. If the notes cannot support a coherent derivation, the skill writes a blocker report instead of a polished but misleading story.

Install the formula-derivation skill

There are two routes. In Claude Code, download the ZIP of the skill from this page and unzip it into ~/.claude/skills/ to make it available to all your projects, or into a project's .claude/skills/ folder to limit it to that project. In the Claude apps, upload the skill under Settings → Capabilities → Skills.

Check that the unzipped folder contains SKILL.md. The skill's files reviewed here consist of that single file.

• Personal install: ~/.claude/skills/
• Project install: .claude/skills/ inside your project folder
• Claude apps: Settings → Capabilities → Skills (upload)

What does the agent need to run it?

The agent must support SKILL.md skills and have file read and write and search tools (Read, Write, Edit, Grep, Glob). The skill is designed to write the derivation file, so it needs write access to your project folder.

The skill's allowed-tools list also references an optional lean-formalize skill. That skill is not included in the files reviewed for this page, so the formula-derivation skill works without it but cannot call it.

• Agent with SKILL.md skill support
• File read, write, edit and search tools (Read, Write, Edit, Grep, Glob)
• Optional: lean-formalize skill (not included here)

Trigger the skill with a natural request

The skill activates when your request matches its description: deriving a formula (推导公式), building a theory line, organising assumptions, turning scattered equations into a coherent derivation, or rewriting theory notes into a paper-ready formula document. It is also suited to cases where the derivation target is not yet fixed or you need a derivation package rather than a finished theorem proof.

Give the agent the goal, the current formulas or notes, and any file paths. You can also pass a short description as an argument, since the skill accepts a problem goal, current formulas or notes as its argument hint.

Good requests name the target and the output you want. For example: 'Use the formula-derivation skill to turn the equations in notes/theory_draft.md into a derivation package for the effective cost bound, and flag every approximation.'

• Name the target quantity or relation you want derived.
• Point to the files holding your notes or formula drafts.
• State the output mode if you have one: internal alignment note, paper-style theory draft, or blocker report.
• Say which steps you suspect are approximations so they get flagged.

Read and use the output

The skill writes a derivation package with a fixed structure: Target, Status, Invariant Object, Assumptions, Notation, Derivation Strategy, Derivation Map, Main Derivation, Remarks and Interpretation, Boundaries and Non-Claims, and Open Risks. The Status field is one of COHERENT AS STATED, COHERENT AFTER REFRAMING / EXTRA ASSUMPTION, or NOT YET COHERENT.

Check every step labelled as an approximation or proposition before relying on it. The skill is told not to write into paper or appendix .tex files unless you explicitly ask, so you move the content across yourself.

• Status tells you how far the notes support the target.
• Approximation and proposition labels show where conditions still need checking.
• Open Risks lists what is still unresolved.

Safety notes: scripts and network

According to the skill's documentation, it runs no scripts and uses no network access. Its activity is limited to reading and writing files through the agent's file tools in your project.

Because it writes files, review what it changes, especially when it updates an existing derivation file. The skill is instructed to read an existing file first and update the relevant section rather than duplicating content.

• Runs scripts: no
• Uses network: no
• Writes derivation files in your project; review changes before committing.

Tips for better derivation packages

Give the skill the messiest version of your notes rather than a cleaned-up summary, because the skill is designed to surface hidden assumptions and undefined notation. Name the object you believe organises the argument, and the skill will check whether it is a true top-level object, a proxy, a local slice or an approximation.

Expect a blocker report when the notes do not support the claim. That is the intended behaviour, not a failure.

• Provide the original notation; the skill preserves it unless cleanup is needed for coherence.
• Ask for the blocker report explicitly if you want a gap analysis instead of a derivation.
• Use the output as a checkable outline and have an expert verify it before publication.