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limit-set
Asymptotic behavior of trajectories (ω/α-limit sets)
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This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.
Stars
10
Hot score
84
Updated
March 20, 2026
Overall rating
C3.2
Composite score
3.2
Best-practice grade
B81.2
Install command
npx @skill-hub/cli install plurigrid-asi-limit-set
Repository
plurigrid/asi
Skill path: skills/limit-set
Asymptotic behavior of trajectories (ω/α-limit sets)
Open repositoryBest 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 limit-set into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
- Review https://github.com/plurigrid/asi before adding limit-set to shared team environments
- Use limit-set for development workflows
Works across
Claude CodeCodex CLIGemini CLIOpenCode
Favorites: 0.
Sub-skills: 0.
Aggregator: No.
Original source / Raw SKILL.md
---
name: limit-set
description: Asymptotic behavior of trajectories (ω/α-limit sets)
version: 1.0.0
---
# Limit Set
**Trit**: 0 (ERGODIC)
**Domain**: Dynamical Systems Theory
**Principle**: Asymptotic behavior of trajectories (ω/α-limit sets)
## Overview
Limit Set is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
## Mathematical Definition
```
LIMIT_SET: 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
# Limit Set 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**: limit-set
**Type**: Dynamical Systems / Limit Set
**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)
```