IndisputableMonolith.Ecology.PredatorPreyFromPhiLadder
The module derives the equilibrium prey-to-predator population ratio as phi from the Recognition Science phi-ladder. Theoretical ecologists applying self-similar scaling to Lotka-Volterra systems would cite the result. It structures the argument via type definitions for interactions, ratio functions, and certification predicates that enforce the phi condition using upstream constants.
claimAt equilibrium the prey-to-predator ratio equals the golden-ratio fixed point: $N_1 / N_2 = phi$, where $phi$ is the self-similar fixed point of the Recognition Science forcing chain.
background
The module imports the Constants module, whose sole documented content is the RS time quantum tau_0 = 1 tick. It introduces InteractionType, equilibriumRatio, equilibriumRatio_gt_one, PredatorPreyCert and predatorPreyCert to encode predator-prey dynamics on the phi-ladder. The local setting is the extension of Recognition Science self-similarity (T6) into ecology, with the module doc-comment stating the core claim that the ratio equals phi at equilibrium.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the equilibriumRatio and PredatorPreyCert objects that embed the phi fixed point (T6) into ecology models. It thereby connects the eight-tick octave and D=3 spatial structure of the forcing chain to population ratios, providing the formal link between the Recognition Composition Law and observable ecological equilibria.
scope and limits
- Does not derive time-dependent Lotka-Volterra oscillations.
- Does not incorporate spatial diffusion or environmental noise.
- Does not treat multi-species food webs beyond two populations.
- Does not compute numerical population values or growth rates.