center-manifold

Original：🇺🇸 English

Translated

Invariant manifold tangent to center eigenspace

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Sourceplurigrid/asi

Added on2026-02-22

NPX Install

npx skill4agent add plurigrid/asi center-manifold

SKILL.md Content

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Center Manifold

Trit: -1 (MINUS) Domain: Dynamical Systems Theory Principle: Invariant manifold tangent to center eigenspace

Overview

Center Manifold is a fundamental concept in dynamical systems theory, providing tools for understanding the qualitative behavior of differential equations and flows on manifolds.

Mathematical Definition

CENTER_MANIFOLD: Phase space × Time → Phase space

Key Properties

Local behavior: Analysis near equilibria and invariant sets
Global structure: Long-term dynamics and limit sets
Bifurcations: Parameter-dependent qualitative changes
Stability: Robustness under perturbation

Integration with GF(3)

This skill participates in triadic composition:

Trit -1 (MINUS): Sinks/absorbers
Conservation: Σ trits ≡ 0 (mod 3) across skill triplets

AlgebraicDynamics.jl Connection

julia

using AlgebraicDynamics

# Center Manifold as compositional dynamical system
# Implements oapply for resource-sharing machines

Related Skills

equilibrium (trit 0)
stability (trit +1)
bifurcation (trit +1)
attractor (trit +1)
lyapunov-function (trit -1)

Skill Name: center-manifold Type: Dynamical Systems / Center Manifold Trit: -1 (MINUS) GF(3): Conserved in triplet composition

Non-Backtracking Geodesic Qualification

Condition: μ(n) ≠ 0 (Möbius squarefree)

This skill is qualified for non-backtracking geodesic traversal:

Prime Path: No state revisited in skill invocation chain
Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
Spectral Gap: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion

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)