Agent skill

Formula Derivation

by AI4Scientist in AI4Scientist/nano-scientist

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…

No licenceAuto-check passed

Install Formula Derivation

skills CLI
$ npx skills add AI4Scientist/nano-scientist --skill formula-derivation -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install AI4Scientist/nano-scientist formula-derivation --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/AI4Scientist/nano-scientist.git skills-src && mkdir -p .claude/skills && cp -r skills-src/skills/formula-derivation .claude/skills/formula-derivation && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
formula-derivation
GitHub stars
128
Used in
5 other repos
Token cost
~2.3k tokens
SKILL.md length
1,070 words
Files
1
Skills in repo
74
Repo updated
First seen
Licence
None found

At a glance

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…

  • Works in 8 steps: Gather Derivation Context → Freeze the Target → Choose the Invariant Object → …
  • Build a theory line
  • SKILL.md covers Constants, Context: $ARGUMENTS, Goal and Inputs, plus 6 more sections
  • Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md

What it does

Formula Derivation is an agent skill from AI4Scientist/nano-scientist. 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.

Its SKILL.md is about 2.3k tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

The repository describes itself as: An autonomous research agent that turns a topic into a peer-reviewed technical report.

When your agent uses it

  • Build a theory line
  • Organize assumptions
  • Turn scattered equations into a coherent derivation
  • Rewrite theory notes into a paper-ready formula document

Example prompts

  • “Use the formula-derivation skill to structure and derives research formulas when the user wants to 推导公式, build a theory line, organize assumptions…”
  • “/formula-derivation”

Requirements

  • Pre-approved tools (allowed-tools): Read, Write, Edit, Grep, Glob

Workflow steps

8 steps, taken from the step headings in SKILL.md.

  1. Gather Derivation Context
  2. Freeze the Target
  3. Choose the Invariant Object
  4. Normalize Assumptions and Notation
  5. Classify the Derivation Steps
  6. Build a Derivation Map
  7. Write the Derivation Document
  8. Final Verification

What it can do on your machine

Read from SKILL.md and the folder at commit 7132192. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Read
    • Write
    • Edit
    • Grep
    • Glob

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    No scripts in the folder and no shell commands in SKILL.md (its code samples are markdown).

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Formula Derivation loads about 2.3k tokens when it runs. Until then it costs about 107 tokens; SKILL.md has 1,070 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~107
When it runs · the whole SKILL.md, loaded when a task matches
~2.3k

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check passed

The automated check found no risky patterns in SKILL.md.

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

Without a licence we can't republish the file, so here is its outline and opening line. It has 1,070 words (~2,278 tokens).

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

— opening of SKILL.md by AI4Scientist
name
formula-derivation
allowed-tools
Read, Write, Edit, Grep, Glob
argument-hint
problem-goal-current-formulas-or-notes

Read the full SKILL.md on GitHub

Files

Just SKILL.md in skills/formula-derivation of AI4Scientist/nano-scientist.

Open the folder on GitHubat commit 7132192

Used in 5 other repositories

We found 9 copies of this SKILL.md (exact, near-identical or edited) in other folders, from 5 other GitHub owners. This page covers the copy in AI4Scientist/nano-scientist, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Formula Derivation next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Formula Derivation compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Formula Derivation this skillAI4Scientist/nano-scientist1285 repos~2.3kAutomated safety check: PassNone
Formula Derivationbrycewang-stanford/Auto-Empirical-Research-Skills4.5k—~1.7kAutomated safety check: PassCustom licence
Structured Datathedaviddias/Front-End-Checklist74k—~420Automated safety check: PassMIT
Bio Structural Biology Modern Structure PredictionFreedomIntelligence/OpenClaw-Medical-Skills3.1k1 repos~2.5kAutomated safety check: PassNone
Crypto Derivatives StrategiesHKUDS/Vibe-Trading35k—~2.4kAutomated safety check: PassMIT
List Structurethedaviddias/Front-End-Checklist74k—~438Automated safety check: PassMIT

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Questions about Formula Derivation

What does Formula Derivation do?

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…. Formula Derivation is an agent skill from AI4Scientist/nano-scientist. 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.

When should I use Formula Derivation?

Formula Derivation fits situations like: build a theory line; organize assumptions; turn scattered equations into a coherent derivation; rewrite theory notes into a paper-ready formula document.

How do I install Formula Derivation in Claude Code?

Run `npx skills add AI4Scientist/nano-scientist --skill formula-derivation -a claude-code`. Or copy the skill folder (skills/formula-derivation in AI4Scientist/nano-scientist) into .claude/skills/formula-derivation in your project. Claude Code loads it when a task matches its description.

How do I install Formula Derivation in Codex?

Run `npx skills add AI4Scientist/nano-scientist --skill formula-derivation -a codex`. Or copy the skill folder (skills/formula-derivation in AI4Scientist/nano-scientist) into .agents/skills/formula-derivation in your project. Codex loads it when a task matches its description.

Can I use Formula Derivation in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add AI4Scientist/nano-scientist --skill formula-derivation -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/formula-derivation, .gemini/skills/formula-derivation, .github/skills/formula-derivation and .opencode/skills/formula-derivation in your project.

What does Formula Derivation need to run?

SKILL.md names no scripts, command-line tools or credentials: Formula Derivation is instructions for the agent only. Its frontmatter pre-approves these tools: Read, Write, Edit, Grep, Glob.

Does Formula Derivation access the network?

SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.

Is Formula Derivation safe to install?

Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.

What licence does Formula Derivation use?

No licence was found for Formula Derivation or its repository. Without one, default copyright applies: ask the author before reusing or redistributing it.

How many tokens does Formula Derivation use?

About 2.3k tokens (SKILL.md is roughly 9.1k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Formula Derivation?

Skills that share tags, products or a category with Formula Derivation: Formula Derivation (brycewang-stanford/Auto-Empirical-Research-Skills, 4.5k stars), Structured Data (thedaviddias/Front-End-Checklist, 74k stars), Bio Structural Biology Modern Structure Prediction (FreedomIntelligence/OpenClaw-Medical-Skills, 3.1k stars) and Crypto Derivatives Strategies (HKUDS/Vibe-Trading, 35k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Formula Derivation?

AI4Scientist (a GitHub organization) maintains it in AI4Scientist/nano-scientist, which has 128 GitHub stars. The repository holds 74 skills in this directory. The repository was last updated on June 3, 2026.

Source: AI4Scientist/nano-scientist on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.