SkillHub ClubShip Full StackFull Stack

lyapunov-stability

Stability via Lyapunov's direct method

Packaged view

This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.

Stars

Hot score

Updated

March 20, 2026

Overall rating

C3.5

Composite score

3.5

Best-practice grade

B78.7

Install command

npx @skill-hub/cli install plurigrid-asi-lyapunov-stability

Repository

plurigrid/asi

Skill path: skills/lyapunov-stability

Stability via Lyapunov's direct method

Open repository

Best for

Primary workflow: Ship Full Stack.

Technical facets: Full Stack.

Target audience: everyone.

License: Unknown.

Original source

Catalog source: SkillHub Club.

Repository owner: plurigrid.

This is still a mirrored public skill entry. Review the repository before installing into production workflows.

What it helps with

Install lyapunov-stability into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
Review https://github.com/plurigrid/asi before adding lyapunov-stability to shared team environments
Use lyapunov-stability for development workflows

Works across

Claude CodeCodex CLIGemini CLIOpenCode

Favorites: 0.

Sub-skills: 0.

Aggregator: No.

Original source / Raw SKILL.md

---
name: lyapunov-stability
description: Stability via Lyapunov's direct method
version: 1.0.0
---


# Lyapunov Stability

**Trit**: 0 (ERGODIC)
**Domain**: Dynamical Systems Theory
**Principle**: Stability via Lyapunov's direct method

## Overview

Lyapunov Stability is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.

## Mathematical Definition

```
LYAPUNOV_STABILITY: Phase space × Time → Phase space
```

## Key Properties

1. **Local behavior**: Analysis near equilibria and invariant sets
2. **Global structure**: Long-term dynamics and limit sets  
3. **Bifurcations**: Parameter-dependent qualitative changes
4. **Stability**: Robustness under perturbation

## Integration with GF(3)

This skill participates in triadic composition:
- **Trit 0** (ERGODIC): Neutral/ergodic
- **Conservation**: Σ trits ≡ 0 (mod 3) across skill triplets

## AlgebraicDynamics.jl Connection

```julia
using AlgebraicDynamics

# Lyapunov Stability as compositional dynamical system
# Implements oapply for resource-sharing machines
```

## Related Skills

- equilibrium (trit 0)
- stability (trit +1)  
- bifurcation (trit +1)
- attractor (trit +1)
- lyapunov-function (trit -1)

---

**Skill Name**: lyapunov-stability
**Type**: Dynamical Systems / Lyapunov Stability
**Trit**: 0 (ERGODIC)
**GF(3)**: Conserved in triplet composition

## Non-Backtracking Geodesic Qualification

**Condition**: μ(n) ≠ 0 (Möbius squarefree)

This skill is qualified for non-backtracking geodesic traversal:

1. **Prime Path**: No state revisited in skill invocation chain
2. **Möbius Filter**: Composite paths (backtracking) cancel via μ-inversion
3. **GF(3) Conservation**: Trit sum ≡ 0 (mod 3) across skill triplets
4. **Spectral Gap**: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion

```
Geodesic Invariant:
  ∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
  
Möbius Inversion:
  f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)
```