From asi
Explains phase locking in oscillators from dynamical systems theory, including local/global behavior, bifurcations, stability, and Julia AlgebraicDynamics.jl integration. Useful for modeling coupled oscillators.
npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: 1 (PLUS)
Analyzes coupled phase oscillators with sinusoidal coupling using the Kuramoto model in dynamical systems theory. Covers local/global dynamics, bifurcations, stability, and Julia AlgebraicDynamics.jl integration.
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: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Fixed phase relationship in oscillators
Phase Locking is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
PHASE_LOCKING: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Phase Locking as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: phase-locking Type: Dynamical Systems / Phase Locking 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)