What is the significance of the Trit -1 value in this skill?

In the context of triadic composition, Trit -1 (MINUS) represents sinks or absorbers, contributing to the conservation law where the sum of trits across a skill triplet must be zero mod 3.

How does this skill help with system perturbations?

It provides the tools to determine if the qualitative behavior of a differential equation or flow on a manifold remains unchanged when the system is subjected to small perturbations.

Does this skill support Julia's AlgebraicDynamics library?

Yes, it provides implementation patterns for AlgebraicDynamics.jl, specifically for compositional dynamical systems and resource-sharing machines.

What is a non-backtracking geodesic qualification?

It is a mathematical constraint ensuring that no states are revisited during a skill invocation chain, using Möbius inversion filters to cancel out composite paths.

Structural Stability Analysis

Name: Structural Stability Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes the robustness of qualitative dynamics in complex systems to ensure stability under perturbations.

About

The Structural Stability skill empowers Claude with specialized expertise in dynamical systems theory, specifically focusing on how qualitative behaviors persist despite small changes in system parameters. It provides the mathematical framework to analyze local equilibria, global limit sets, and bifurcation points within phase space. By integrating with AlgebraicDynamics.jl and utilizing triadic composition (GF(3)), this skill is essential for developers building topological computing models, complex simulations, or resource-sharing machines where maintaining invariant behavior under noise is a critical requirement.

Key Features

AlgebraicDynamics.jl integration for compositional modeling
Bifurcation detection for parameter-dependent changes
Qualitative dynamic robustness analysis for complex systems
Non-backtracking geodesic qualification via Möbius filters
Phase space evaluation of local and global invariant sets
2 GitHub stars

Use Cases

Designing robust control systems that maintain specific qualitative behaviors under noise
Validating the structural integrity of complex state-space models against perturbations
Modeling topological 'chemputers' and chemical reaction networks using algebraic dynamics

About

Key Features

AlgebraicDynamics.jl integration for compositional modeling
Bifurcation detection for parameter-dependent changes
Qualitative dynamic robustness analysis for complex systems
Non-backtracking geodesic qualification via Möbius filters
Phase space evaluation of local and global invariant sets
2 GitHub stars

Use Cases

Designing robust control systems that maintain specific qualitative behaviors under noise
Validating the structural integrity of complex state-space models against perturbations
Modeling topological 'chemputers' and chemical reaction networks using algebraic dynamics