IndisputableMonolith.Sociology.DunbarLayersFromPhi
This module derives Dunbar social layers from the phi constant in Recognition Science. It introduces definitions for layer indices, sizes scaled by phi ratios, and a certification structure. Social physicists and network theorists would cite it for grounding empirical group sizes in the forcing chain fixed point. The module is purely definitional with supporting properties for positivity and ratios.
claimThe type of social strata is indexed by integers, with the size of layer $n$ satisfying $s(n+1)/s(n) = (1 + 5^{1/2})/2$, a total layer count function, and a certification predicate for the resulting hierarchy.
background
Recognition Science derives phi as the self-similar fixed point (T6) in the T0-T8 forcing chain. The module imports the base constant where the time quantum is the fundamental RS time quantum (RS-native), τ₀ = 1 tick. It defines the type of social strata, the function giving size to each layer index, the count of layers, and the certification predicate, all built on phi scaling from the upstream Constants module.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module extends the Recognition framework into sociology by grounding Dunbar layers in the phi constant from the forcing chain. It supplies the definitional base for any future theorems on social scaling, though no downstream dependencies are recorded.
scope and limits
- Does not derive specific empirical values such as 5, 15, 50, 150.
- Does not include dynamic evolution or stability analysis of layers.
- Does not connect to the mass formula or alpha band constants.
- Does not prove uniqueness from the Recognition Composition Law.