IndisputableMonolith.Ecology.PredatorPreyFromPhiLadder
The module shows that Recognition Science forces the equilibrium prey-to-predator ratio to equal the golden ratio phi. Ecologists working with population models under RS constraints would cite the result. It supplies type definitions for interaction classes together with a direct certification that the ratio equals phi.
claimAt equilibrium the prey-to-predator ratio equals $\phi$, where $\phi$ is the unique positive fixed point of the self-similar map.
background
Recognition Science obtains all constants from the forcing chain that terminates at the self-similar fixed point phi. The module imports Constants, whose sole documented object is the fundamental RS time quantum $\tau_0 = 1$ tick. It introduces InteractionType to label predator-prey relations and equilibriumRatio to record the phi value on the ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module realizes the phi fixed point (T6) inside ecological equilibria. It supplies the concrete ratio required by any downstream application of the phi-ladder to biological scaling. No parent theorems are recorded among the used-by edges.
scope and limits
- Does not derive the ratio without the phi-ladder hypothesis.
- Does not treat transient or non-equilibrium population trajectories.
- Does not address stochastic forcing or spatial heterogeneity.
- Does not extend the result to multi-trophic food webs.