Explains unstable manifolds in dynamical systems theory, including local/global behavior near equilibria, bifurcations, stability, GF(3) integration, and Julia code via AlgebraicDynamics.jl. Useful for analyzing diverging dynamics.
From asi-skillsnpx claudepluginhub plurigrid/asiThis skill uses the workspace's default tool permissions.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Migrates code, prompts, and API calls from Claude Sonnet 4.0/4.5 or Opus 4.1 to Opus 4.5, updating model strings on Anthropic, AWS, GCP, Azure platforms.
Facilitates interactive brainstorming sessions using diverse creative techniques and ideation methods. Activates when users say 'help me brainstorm' or 'help me ideate'.
Trit: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Manifold of points diverging from equilibrium
Unstable Manifold is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
UNSTABLE_MANIFOLD: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Unstable Manifold as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: unstable-manifold Type: Dynamical Systems / Unstable Manifold Trit: 1 (PLUS) 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)