equilibriumRatio
plain-language theorem explainer
Equilibrium prey-predator ratio equals phi at recognition equilibrium. Ecologists calibrating Lotka-Volterra models to the phi-ladder cite this definition to fix the population ratio. It is introduced by direct assignment to the constant phi from the Recognition Science constants.
Claim. The equilibrium ratio of prey to predator populations is defined as $phi$.
background
The module links predator-prey dynamics to the phi-ladder. In a stable ecosystem at recognition equilibrium, prey and predator populations oscillate at frequencies in the ratio phi to 1. The RS prediction states that the prey to predator population ratio at equilibrium equals phi when the growth rates are calibrated to the canonical band. The five canonical predator-prey interaction types correspond to configDim D = 5. This supplies the ratio for model certification.
proof idea
Direct definition assigning the constant phi to equilibriumRatio. No lemmas or reductions are applied.
why it matters
This definition is used by the theorem equilibriumRatio_gt_one and the structure PredatorPreyCert. It realizes the RS prediction in the module that the prey-predator ratio equals phi at equilibrium. It connects ecological modeling to the phi-ladder in the Recognition Science framework.
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