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Xi Network

A decentralized knowledge network modeled on topological graph theory with mathematical foundation structures.

Xi Network applies advanced mathematical concepts to create a self-organizing information system. Through recursive graph transformations and dynamic node relationship algorithms, this project visualizes complex knowledge systems in an interactive 3D space.

Core Architecture

  • • Hierarchical hypergraph model
  • • Knowledge persistence through topological invariants
  • • Distributed node reconciliation algorithm
  • • Context-aware information propagation

Interactive Capabilities

  • • Multi-dimensional node manipulation
  • • Temporal information visualization
  • • Dynamic relationship mapping
  • • Network simulation controls

Network Visualization

Interactive network topology simulation (JavaScript required)

Mathematical Framework

Network Formation

The system utilizes hypergraph theory to model multi-relational systems using this foundational equation:

H = (V, E) where E ⊆ ∪i=1n ℙ(V)

H: hypergraph, V: vertices, E: hyperedges

Dynamic Parameters

  • • Dimensionality range: 3 ≤ D ≤ 6
  • • Connection density: 0.2 ≤ α ≤ 0.7
  • • Evolution rate parameter: γ = 0.01-0.5
  • • Knowledge decay factor: λ = 0.1-1.0

Interaction Model

Interactive elements follow this transformation model for user manipulation:

Mt+1 = Mt • exp(-ρt) + N(0,σ2)

ρ: interaction dampening rate, σ: noise coefficient

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