IndisputableMonolith.Ecology.BiodiversityIndexFromConfigDim
The module defines the five canonical ecological guilds together with guildCount and maxSimpsonDiversity measures derived from configuration dimension. It supplies the basic objects needed to construct a biodiversity index inside the Recognition Science framework. Ecologists working with RS constants would cite these definitions when mapping configuration structure to diversity metrics. The module contains only definitions and no theorems.
claimLet $G$ be the set of five canonical ecological guilds. Define guildCount as the cardinality of $G$ and maxSimpsonDiversity as the supremum of the Simpson index over configurations of given dimension.
background
The module sits in the ecology domain of Recognition Science and imports the RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It introduces EcologicalGuild as the five canonical types, guildCount as their number, and maxSimpsonDiversity as the maximum attainable Simpson diversity for a given configuration dimension. The local setting applies RS configuration structure to ecological guild models without invoking the forcing chain or phi-ladder directly.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the definitional base for biodiversity indices computed from configuration dimension. It feeds future theorems that certify biodiversity measures inside ecological applications of Recognition Science. No parent theorems appear in the current used-by graph.
scope and limits
- Does not contain empirical species data or field observations.
- Does not derive numerical values for any biodiversity index.
- Does not link guilds to specific RS constants beyond the imported time quantum.
- Does not prove maximality or uniqueness of the Simpson measure.