gpd-derive-equation

Performs rigorous physics derivations with step-by-step verification and dimensional analysis.

Updated Mar 18, 2026
One-click install
npx skills add https://github.com/MichaelsEngineering/sentinel-multiscale-field-dynamics --skill gpd-derive-equation-michaelsengineering
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: gpd-derive-equation
Source: https://github.com/MichaelsEngineering/sentinel-multiscale-field-dynamics/tree/main/.agents/skills/gpd-derive-equation
Command: npx skills add https://github.com/MichaelsEngineering/sentinel-multiscale-field-dynamics --skill gpd-derive-equation-michaelsengineering

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve? Physics derivations often contain hidden assumptions, unjustified approximations, and silent convention errors (sign flips, missing factors of 2pi) that propagate undetected. This Skill enforces a rigorous derivation workflow where every step is verified, every assumption is explicit, and every approximation is bounded with error estimates. ## Core Features & Use Cases - Convention Locking: Loads project convention locks (metric signature, Fourier convention, normalization) and asserts them per-step via machine-readable ASSERT_CONVENTION markers to catch convention drift. - Systematic Verification: Performs dimensional analysis, limiting-case checks, symmetry preservation tests, and numerical spot-checks at each major derivation step. - Documented Output: Produces a complete, self-contained derivation document with numbered assumptions, boxed final result, error analysis, and connection to known results, saved to phase-scoped or standalone analysis directories. - Use Case: Derive the effective mass from a self-energy expression in a quantum field theory project, with each intermediate result checked against the free-theory limit and Peskin & Schroeder reference values. ## Quick Start Ask the AI to derive an equation, for example: derive the dispersion relation for the current system with full step-by-step verification.

Frequently Asked Questions about gpd-derive-equation

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

FAQPage Schema
How do I derive a physics equation with step-by-step verification?▼

Provide the equation or topic as an argument, such as deriving effective mass from self-energy. The workflow states assumptions, establishes notation, performs each algebraic step with dimensional checks, and verifies results against known limits before producing a boxed final expression.

What makes a physics derivation rigorous and verifiable?▼

A rigorous derivation numbers every assumption, defines all notation before use, names each mathematical operation, justifies approximations with error bounds, and checks intermediate results dimensionally and against limiting cases. No step may rely on unstated intuition.

How does the skill prevent convention errors like sign flips?▼

It loads a project convention lock covering metric signature, Fourier convention, and normalization, then inserts machine-readable ASSERT_CONVENTION comments in the document header and each derivation step. Any drift from the lock halts the derivation immediately.

Can I use this derivation workflow without an existing project?▼

Yes, standalone usage is supported. If project initialization fails or no state exists, all conventions must be declared explicitly in Step 1, and the derivation document is written to .gpd/analysis/ instead of a phase-scoped directory.

What are common physics derivation pitfalls to avoid?▼

Common pitfalls include flipped metric signatures, dropped boundary terms in integration by parts, missing factors of i from Wick rotation, wrong integration measures, and summing divergent series. The workflow prevents these through explicit convention declarations and per-step dimensional analysis.