formula-derivation

formula-derivation is a skill for Claude Code from wanshuiyin/Auto-claude-code-research-in-sleep. It costs 84 tokens per session (2,000 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.

not rated 16krepo +239 2d 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
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 · 15,970 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.

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 2,000 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 21 Mar 2026
  • Snyk pass 21 Mar 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 $0.02000
Opus 5 $0.00042 $0.01000
Sonnet 5 $0.00017 $0.00400
Haiku 4.5 $0.00008 $0.00200

Measured 12d ago against content hash 2e5f5ce66502, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-11, 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 12d 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

1 near-identical copy found in the catalogue:

skills/formula-derivation/SKILL.md · 281 lines

How it starts

The opening of the file, as written. The whole thing — 281 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 · 281 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. 12d 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 (15,970 stars, last pushed 2d ago), licensed MIT. It adds 84 tokens to every session and 2,000 once invoked, about $0.0004 per session on Opus 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.

Related

Other skills, from other repositories

remote-compute-ssh

Evaluate and use SSH Remote Compute before choosing where to run GPU, high-memory, parallel, batch, model-inference, bioinformatics, or other long-running scientific work; supports short remote commands and asynchronous jobs with automatic harvest and analysis.

aipoch/open-science · 53 tokens

paper-narrative

Judge and reshape the story told by an entire paper figure deck. Use when writing or revising a paper to derive a grounded brief from the manuscript and captions, review the full deck as a handling editor, and hand an ordered figure arc to figure-composer.

aipoch/open-science · 58 tokens

esmfold2

Biohub ESMFold2 / ESMFold2-Fast all-atom co-folding (Candido et al. 2026, github.com/Biohub/esm). Single-sequence and MSA modes; protein, DNA, RNA, ligand (CCD/SMILES), modified residues. FoldBench Ab-Ag 50-55%, PPI 70-77% DockQ-pass. Also covers the ESMC-{300M,600M,6B} protein language models from the same release…

aipoch/open-science · 223 tokens

literature-review

Find, verify, and synthesize scientific literature — from "what's the seminal paper for X" through full multi-source reviews. Covers grounding claims in real retrieved sources, avoiding fabricated citations, handling retractions, and calibrating confidence to evidence strength.

aipoch/open-science · 54 tokens

scvi-tools

Probabilistic single-cell RNA-seq with scvi-tools — scVI for a batch-corrected latent space, scANVI for semi-supervised label transfer, and Bayesian differential expression. Reach for this skill to integrate scRNA-seq batches, embed cells for clustering, transfer annotations from a reference onto a query, or score…

aipoch/open-science · 100 tokens

figure-composer

Compose one publication-grade multi-panel figure. Start from a one-line claim plus immutable data Artifact Version references, or inspect an existing figure and draft its outline directly. Plan a 12-column panel outline, delegate one worker per panel, compose and inspect the result, then run at most three adversarial…

aipoch/open-science · 93 tokens