formula-derivation

Derive structured research formulas from problem statements with classified steps.

Updated Apr 18, 2026
One-click install
npx skills add https://github.com/THUFanZd/Sewed_pipeline --skill formula-derivation-thufanzd
Or copy as Structured Prompt for Agent
Please help me install this Agent Skill.
Skill: formula-derivation
Source: https://github.com/THUFanZd/Sewed_pipeline/tree/main/.agents/skills/formula-derivation
Command: npx skills add https://github.com/THUFanZd/Sewed_pipeline --skill formula-derivation-thufanzd

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This skill helps users structure and derive research formulas when they need to derive a theory line, build equations from a problem statement, clarify assumptions, separate formal derivation from remarks, or turn messy notes into a paper-ready derivation skeleton. Use for research-style formula development, not for fully rigorous theorem proving once the claim is already fixed.

Core Features & Use Cases

  • One invariant object as the central anchor across regimes.
  • Explicitly list assumptions, notations, and regime boundaries before starting derivation.
  • Classify each step as identity, proposition, approximation, or interpretation to preserve clarity.
  • Produce multiple output formats (mainline derivation note, paper-style theory draft, blocker report) from a single derivation.
  • Attach helpful guidance for translating derivations into manuscript sections or presentation materials.

Quick Start

Provide a complete derivation starting from the invariant object and annotate each step with its type (identity, proposition, approximation, interpretation).

Frequently Asked Questions about formula-derivation

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I structure research formula derivations from a problem statement?

To derive research formulas, first establish an invariant object as the central anchor, explicitly list assumptions and notations, then classify each derivation step as an identity, proposition, approximation, or interpretation. This yields structured outputs for paper drafts.

What is the best way to turn messy research notes into a paper-ready derivation?

Transforming messy notes into a paper-ready derivation requires separating formal steps from remarks and generating a paper-style theory draft. You define regime boundaries upfront and annotate each step by type to preserve manuscript clarity.

Can I use this approach for fully rigorous theorem proving?

No, this approach is not intended for fully rigorous theorem proving once a mathematical claim is already fixed. It is designed specifically for research-style formula development, theoretical modeling, and proof sketching from initial problem statements.

How do I define invariants and assumptions before starting a theoretical modeling derivation?

To define invariants and assumptions for theoretical modeling, establish one invariant object as the central anchor across regimes and explicitly list all notations, assumptions, and regime boundaries before starting the mainline derivation.

What output formats can I generate for a research formula derivation?

You can generate multiple unified output formats from a single derivation, including a mainline derivation note, a paper-style theory draft, or a blocker report. These formats are suitable for both internal research notes and manuscript drafts.

Why do I need to classify each step when building equations from a problem statement?

Classifying each step when building equations preserves clarity by distinguishing whether a step is an identity, proposition, approximation, or interpretation. This separation is essential for generating paper-ready derivations and avoiding logical ambiguity.