What is the Möbius filter mentioned in the documentation?

It is a qualification for non-backtracking geodesic traversal, ensuring that skill invocation chains do not revisit states or create redundant loops.

How does this skill relate to the 'asi' repository?

It is part of the 'asi' plugin which views everything as a topological chemputer, using GF(3) logic to categorize system components like sinks and absorbers.

Can this skill be used for automated coding in Julia?

Yes, it specifically includes connections to AlgebraicDynamics.jl for implementing compositional dynamical systems and resource-sharing machines.

What is the importance of the Trit -1 designation?

In the context of this skill, Trit -1 represents 'MINUS' or 'Sinks/Absorbers', indicating a state where system energy or trajectories converge.

Lyapunov Function Analysis

Name: Lyapunov Function Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes the stability and qualitative behavior of dynamical systems using scalar functions that decrease along trajectories.

The lyapunov-function skill provides a rigorous mathematical framework for Claude to evaluate the stability of equilibria and invariant sets within dynamical systems. Built for the 'asi' topological computing environment, it leverages triadic composition (GF(3)) and integrates with AlgebraicDynamics.jl to model sinks and absorbers. This skill is essential for researchers and engineers working with differential equations, control theory, and complex flows on manifolds, ensuring that system trajectories evolve toward predictable, stable states.

Key Features

018 GitHub stars

02Non-backtracking geodesic qualification via Möbius squarefree filtering

03GF(3) triadic logic support for identifying system sinks (Trit -1)

04Bifurcation analysis for parameter-dependent qualitative changes

05Stability analysis for local equilibria and global limit sets

06Integration with AlgebraicDynamics.jl for compositional modeling

Use Cases

01Modeling resource-sharing machines in topological chemputer environments

02Verifying the global asymptotic stability of control system architectures

03Analyzing qualitative long-term behavior in complex differential equations

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi lyapunov-function

For use in Claude.ai and ChatGPT

Download Skill