Explains Jacobian matrix of partial derivatives for linearizing dynamical systems near equilibria, analyzing stability, bifurcations, and local behavior. Useful for dynamical systems theory discussions.
From asi-skillsnpx claudepluginhub plurigrid/asiThis skill uses the workspace's default tool permissions.
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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.
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Trit: -1 (MINUS) Domain: Dynamical Systems Theory Principle: Matrix of partial derivatives for linearization
Jacobian is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
JACOBIAN: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Jacobian as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: jacobian Type: Dynamical Systems / Jacobian Trit: -1 (MINUS) 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)