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formula-derivation

formula-derivation is a skill for Claude Code from wanshuiyin/Auto-claude-code-research-in-sleep. It costs 84 tokens per session (2,064 once invoked), scanned A, original, MIT.

A structured method for turning scattered equations and assumptions into a coherent research derivation. A derivation is a step-by-step explanation of how a formula or result follows from definitions and assumptions.

In plain words
What is it for?
It helps organize theory notes, derive formulas, state assumptions, and prepare a paper-ready derivation or a blocker report.
Why use it?
It reveals when a proposed theory is incomplete, uses unclear notation, or needs an extra assumption. It can produce either a corrected derivation or a plain explanation of why the current material is not yet sufficient.

Skill for Claude Code

Written for Claude Code: allowed-tools in frontmatter.

Part of the aris plugin — 87 skills, 1 command, 1 agent shipped together

not rated 19krepo +287 changed 1mo ago A scan Socket: passSnyk: passSkillSpector: pass 84 tokens original MIT

Good fit It helps organize theory notes, derive formulas, state assumptions, and prepare a paper-ready derivation or a blocker report.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation
View source ↗ wanshuiyin/Auto-claude-code-research-in-sleep
About the project

ARIS is a collection of Markdown-based skills that define a workflow for autonomous machine-learning research, including idea discovery, experiment automation, and review loops. Researchers and AI coding agents use it across tools such as Claude Code, Codex, Cursor, and OpenClaw without depending on a single framework. The catalogue entries are ARIS workflow skills and agents.

wanshuiyin/Auto-claude-code-research-in-sleep · 19,107 stars · on GitHub

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add wanshuiyin/Auto-claude-code-research-in-sleep --skill formula-derivation
Clone the repo
git clone --depth 1 https://github.com/wanshuiyin/Auto-claude-code-research-in-sleep

Made for: Claude Code.

Or install aris, the plugin that ships this one along with the rest of its 87 skills, 1 command, 1 agent.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for formula-derivation

README.md
[![agentmods](https://agentmods.dev/badge/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation/github.svg)](https://agentmods.dev/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation)
Your own site
<a href="https://agentmods.dev/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation"><img src="https://agentmods.dev/badge/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for formula-derivation

Your own site · 80×15
<a href="https://agentmods.dev/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation"><img src="https://agentmods.dev/badge/skills/wanshuiyin/auto-claude-code-research-in-sleep/formula-derivation.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 84 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 2,064 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe. Third-party audits
  • Socket pass 6 Oct 2026
  • Snyk pass 6 Oct 2026
  • NVIDIA SkillSpector pass 7 Sept 2026
How audits are shown
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00084 $0.02064
Opus 5.5 $0.00034 $0.00826
Sonnet 5.5 $0.00017 $0.00413
Haiku 4.5 $0.00008 $0.00206

Measured 1mo ago against content hash c428e321dd2d, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

Grade A, and why

formula-derivation scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 1mo ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

Origin

Copies of this mod

2 near-identical copies found in the catalogue:

skills/formula-derivation/SKILL.md · 286 lines

How it starts

The opening of the file, as written. The whole thing — 286 lines — stays where its author put it; the contents beside it link to each section on GitHub.

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

Step 2: Freeze the Target

State explicitly:

  • what is being explained, derived, or supported
  • whether the immediate goal is:
    • identity / algebra
    • proposition
    • approximation
    • interpretation
  • what the derivation is expected to output in the end

Read the full file on GitHub · 286 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 1mo ago Changed · +5 lines c428e321dd2d
  2. 2mo ago First seen · 281 lines · 84 tokens per session scan A 2e5f5ce66502

Subscribe to this mod's changes

formula-derivation is a skill published in the GitHub repository wanshuiyin/Auto-claude-code-research-in-sleep (19,107 stars, last pushed 2d ago), licensed MIT. It adds 84 tokens to every session and 2,064 once invoked, about $0.0003 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

Claude CodeResearchScientificai-researchautonomous-agentcodexmcpml-research
Related

formula-derivation compared with skills from other repositories

formula-derivation next to 6 skills from other repositories
ModTypeStarsLast pushLicenceScanTokensWorks with
formula-derivationwanshuiyin/Auto-claude-code-research-in-sleepSkill19k2d agoMITA84Claude Code
remote-compute-sshaipoch/open-scienceSkill5.5ktodayApache-2.0A52Claude Code, Codex
figure-styleaipoch/open-scienceSkill5.5ktodayApache-2.0A91Claude Code, Codex
paper-narrativeaipoch/open-scienceSkill5.5ktodayApache-2.0A58Claude Code, Codex
literature-reviewaipoch/open-scienceSkill5.5ktodayApache-2.0A54Claude Code, Codex
scvi-toolsaipoch/open-scienceSkill5.5ktodayApache-2.0A100Claude Code, Codex
esmfold2aipoch/open-scienceSkill5.5ktodayApache-2.0A223Claude Code, Codex