IndisputableMonolith.Sociology.UrbanizationFromPhiLadder
This module defines types and functions modeling urban hierarchies via the phi-ladder of Recognition Science. Quantitative sociologists examining self-similar population scaling would reference these constructs. It supplies level enumerations, rung-based population counts, ratios, and a certification predicate as pure definitions with no internal proofs.
claimLet $U$ denote the type of urban levels indexed by phi-ladder rungs. Define population at rung $r$ by base scaling with $\phi^r$, the ratio between consecutive levels, and a predicate $C$ certifying that the resulting structure obeys the Recognition Composition Law.
background
Recognition Science derives discrete scaling from the J-functional equation, with phi as the self-similar fixed point and the phi-ladder supplying rung-indexed quantities. The upstream Constants module fixes the base time quantum $ au_0 = 1$ tick in RS-native units. This module applies the same ladder pattern to sociology, defining discrete urban levels together with population counts and ratios that mirror the yardstick scaling used for masses.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module extends the phi-ladder formalism (T6 fixed point, T7 octave) into the sociology domain by supplying the core objects for urbanization hierarchies. It sits directly on the Constants import and prepares definitions that later results could invoke for social scaling laws, though the current dependency graph lists no downstream users.
scope and limits
- Does not derive the phi-ladder or J-equation.
- Does not include time evolution or migration flows.
- Does not match numerical outputs to census data.
- Does not incorporate economic or policy variables.