Bifurcation creating/destroying equilibrium pair
/plugin marketplace add plurigrid/asi/plugin install asi-skills@asi-skillsThis skill inherits all available tools. When active, it can use any tool Claude has access to.
Trit: -1 (MINUS) Domain: Dynamical Systems Theory Principle: Bifurcation creating/destroying equilibrium pair
Saddle-node is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
SADDLE-NODE: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Saddle-node as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: saddle-node Type: Dynamical Systems / Saddle-node 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)
This skill should be used when the user asks to "create a hookify rule", "write a hook rule", "configure hookify", "add a hookify rule", or needs guidance on hookify rule syntax and patterns.
Create distinctive, production-grade frontend interfaces with high design quality. Use this skill when the user asks to build web components, pages, or applications. Generates creative, polished code that avoids generic AI aesthetics.