From asi
Explains synchronization as convergence to common trajectories in coupled dynamical systems, covering local/global properties, bifurcations, stability, and Julia AlgebraicDynamics.jl integration.
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**Trit**: 0 (ERGODIC)
Analyzes interacting dynamical systems, covering local/global behavior near equilibria, long-term dynamics, bifurcations, and stability analysis.
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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: 0 (ERGODIC) Domain: Dynamical Systems Theory Principle: Convergence to common trajectory in coupled systems
Synchronization is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
SYNCHRONIZATION: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Synchronization as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: synchronization Type: Dynamical Systems / Synchronization 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)