Geometric Replicator Dynamics

Folded symplectic implementation with log-ratio coordinates & Shahshahani metric

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Controls GEOMETRIC

Speed 1.0×

Geometric Data

Shahshahani Speed: 0.0000
Metric Distance: 0.000
Mean Fitness (H_S): 0.0000
Boundary Distance: 0.000
Gradient
Hamiltonian

Current State

Strategy 1: 0.250
Strategy 2: 0.250
Strategy 3: 0.250
Strategy 4: 0.250
Log-ratio: u₁=0.000, u₂=0.000, u₃=0.000
Active Dimension: 3

📐 Geometric Features:

• Log-ratio coordinates u_i = log(x_i/x_n) naturally handle boundaries
• Shahshahani metric g = Σ(ξ²/x_i) measures evolutionary distance
• Gradient/Hamiltonian decomposition: Symmetric → gradient flow, Antisymmetric → cyclic