From asi
Analyzes time average of observables along trajectories in dynamical systems theory for studying local/global behavior, stability, and bifurcations.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 1 (PLUS)
Explains ergodicity in dynamical systems theory, where time averages equal space averages. Useful for analyzing qualitative behavior of differential equations, flows on manifolds, bifurcations, and stability.
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).
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Trit: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Time average of observable along trajectory
Birkhoff Average is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
BIRKHOFF_AVERAGE: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Birkhoff Average as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: birkhoff-average Type: Dynamical Systems / Birkhoff Average 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)