populationAtRung
plain-language theorem explainer
The definition assigns to each natural-number rung k the population value 100 phi^k on the phi-ladder. Urban theorists working inside Recognition Science cite it when constructing discrete city-size sequences whose consecutive ratios recover the phi scaling required by Zipf's law. It is introduced by a direct one-line abbreviation in real arithmetic that carries no proof obligations.
Claim. The population assigned to rung $k$ is $100 phi^k$.
background
Recognition Science obtains phi as the unique self-similar fixed point forced by the chain T5 through T6. The phi-ladder is the discrete sequence of scales generated by integer powers of phi; the present module applies it to urban population tiers. The module states that five canonical levels (hamlet, village, town, city, metropolis) realize configDim equal to 5, and that adjacent ranks stand in population ratio phi, recovering the Gibrat-Zipf exponent near phi.
proof idea
The declaration is a one-line definition that directly sets the population at rung k to 100 multiplied by phi to the power k.
why it matters
This definition supplies the explicit population values required by the theorem populationRatio, which establishes that consecutive rungs differ by exactly the factor phi. It is referenced inside the structure UrbanizationCert that records both the five-level count and the universal phi-ratio property. In the framework it realizes the RS prediction that urban hierarchies follow the phi-ladder, consistent with the eight-tick octave and the derivation of D equals 3.
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