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lyapunov-function

Scalar function decreasing along trajectories

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-function

Repository

plurigrid/asi

Skill path: skills/lyapunov-function

Scalar function decreasing along trajectories

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

Works across

Claude CodeCodex CLIGemini CLIOpenCode

Favorites: 0.

Sub-skills: 0.

Aggregator: No.

Original source / Raw SKILL.md

---
name: lyapunov-function
description: Scalar function decreasing along trajectories
version: 1.0.0
---


# Lyapunov Function

**Trit**: -1 (MINUS)
**Domain**: Dynamical Systems Theory
**Principle**: Scalar function decreasing along trajectories

## Overview

Lyapunov Function 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_FUNCTION: 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 -1** (MINUS): Sinks/absorbers
- **Conservation**: Σ trits ≡ 0 (mod 3) across skill triplets

## AlgebraicDynamics.jl Connection

```julia
using AlgebraicDynamics

# Lyapunov Function 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-function
**Type**: Dynamical Systems / Lyapunov Function
**Trit**: -1 (MINUS)
**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)
```