How does this skill use GF(3) triadic logic?

It assigns a 'trit' value of -1 (MINUS) to represent sinks and absorbers, ensuring that the sum of trits remains conserved (≡ 0 mod 3) across skill triplets in a compositional system.

What is the significance of the Möbius Filter in this skill?

The Möbius Filter ensures non-backtracking geodesic qualification, where composite or backtracking paths in a skill invocation chain are cancelled via inversion, ensuring state efficiency.

Is this skill compatible with Julia programming?

Yes, it is specifically designed to connect with AlgebraicDynamics.jl for treating invariant measures as compositional dynamical systems and resource-sharing machines.

What is an invariant measure in this context?

An invariant measure is a mathematical tool used to describe a measure on a phase space that remains unchanged under the action of a flow or transformation, which is crucial for understanding the qualitative behavior of differential equations.

Invariant Measure Analysis

Name: Invariant Measure Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes and defines measures preserved by flows in dynamical systems to understand long-term qualitative behavior.

The Invariant Measure skill provides specialized tools for Dynamical Systems Theory, enabling Claude to model and analyze how phase space measures are preserved over time. It leverages triadic logic (GF(3)) and non-backtracking geodesic qualification to assess local behavior near equilibria, identify global structures, and predict parameter-dependent bifurcations. This skill is particularly useful for researchers and engineers working with complex systems, AlgebraicDynamics.jl integrations, and topological computing architectures where conservation laws and stability are paramount.

Key Features

012 GitHub stars

02Analyzes phase space measures preserved by system flows

03Identifies local behavior near equilibria and invariant sets

04Supports non-backtracking geodesic traversal for state space exploration

05Implements triadic composition (GF(3)) for conserved system states

06Integrates with AlgebraicDynamics.jl for compositional modeling

Use Cases

01Analyzing the long-term stability and limit sets of differential equations

02Detecting parameter-dependent bifurcations in complex physical models

03Modeling resource-sharing machines using compositional dynamical systems

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi invariant-measure

For use in Claude.ai and ChatGPT

Download Skill