From asi
Analyzes stability in dynamical systems using Lyapunov's direct method for equilibria, invariant sets, bifurcations, and perturbation robustness. Includes GF(3) integration and Julia examples.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 0 (ERGODIC)
Explains Lyapunov functions for stability analysis in dynamical systems theory, including properties, bifurcations, and Julia AlgebraicDynamics integration. Useful for modeling differential equations.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Guides building MCP servers enabling LLMs to interact with external services via tools. Covers best practices, TypeScript/Node (MCP SDK), Python (FastMCP).
Share bugs, ideas, or general feedback.
Trit: 0 (ERGODIC) Domain: Dynamical Systems Theory Principle: Stability via Lyapunov's direct method
Lyapunov Stability is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
LYAPUNOV_STABILITY: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Lyapunov Stability as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: lyapunov-stability Type: Dynamical Systems / Lyapunov Stability Trit: 0 (ERGODIC) GF(3): Conserved in triplet composition
Condition: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
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)