From asi
Explains periodic orbits in dynamical systems theory, covering definitions, local/global behavior, bifurcations, stability, GF(3) integration, and Julia AlgebraicDynamics.jl usage. Useful for qualitative dynamics analysis.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 0 (ERGODIC)
Explains trajectories as paths traced by solutions through phase space in dynamical systems theory, covering local/global behavior, stability, bifurcations, and Julia examples. Useful for differential equation modeling.
Guides Next.js Cache Components and Partial Prerendering (PPR): 'use cache' directives, cacheLife(), cacheTag(), revalidateTag() for caching, invalidation, static/dynamic optimization. Auto-activates on cacheComponents: true.
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: Closed trajectory in phase space
Periodic Orbit is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
PERIODIC_ORBIT: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Periodic Orbit as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: periodic-orbit Type: Dynamical Systems / Periodic Orbit 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)