Symmetric bifurcation with symmetry breaking
Trit: 1 (PLUS) Domain: Dynamical Systems Theory Principle: Symmetric bifurcation with symmetry breaking
Pitchfork is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.
PITCHFORK: Phase space × Time → Phase space
This skill participates in triadic composition:
using AlgebraicDynamics
# Pitchfork as compositional dynamical system
# Implements oapply for resource-sharing machines
Skill Name: pitchfork Type: Dynamical Systems / Pitchfork 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)