IndisputableMonolith.Archaeology.UrbanDensityFromPhiLadder
This module defines five canonical settlement levels forced by configDim=5 and derives their rung spacing, population ratios, and costs from the Recognition Science phi-ladder. Archaeologists applying self-similar scaling to historical urban data would cite these objects. The module consists of successive definitions and basic equalities that build the density certificate from imported constants and cost functions.
claimFive canonical settlement levels with rung spacing given by the phi-ladder, population ratios lying in the Christaller band, and a certified urban density model, all forced by configDim = 5.
background
Recognition Science derives scaling laws from the phi fixed point (T6) and the eight-tick octave (T7). The module imports the RS time quantum τ₀ = 1 tick from Constants and the J-cost function from the Cost module. It introduces settlementLevelCount as the number of levels, settlementRungSpacing as the phi-based interval on the ladder, settlementPopRatio as the self-similar population multiplier, and UrbanDensityCert as the object that packages these into a density model.
proof idea
This is a definition module, no proofs. The structure proceeds by defining settlementLevelCount, proving its equality to 5, then defining the associated spacing, ratio, and cost objects, and finally packaging them into the UrbanDensityCert certificate.
why it matters in Recognition Science
The module applies the phi-ladder (T6) to archaeology, supplying the self-similar hierarchy that aligns with D = 3 spatial dimensions (T8) and the Recognition Composition Law. It provides the concrete objects needed for any downstream model of urban density in the Recognition framework, even though no direct used-by theorems are recorded yet.
scope and limits
- Does not derive configDim = 5 from the forcing chain.
- Does not compare predicted ratios against specific archaeological site data.
- Does not extend the model beyond five levels or vary configDim.
- Does not incorporate defectDist or Berry creation threshold.