Wavelength Scaling Law

The Wavelength Scaling Law is the rule that the nth generation of a recursive structure has a wavelength equal to the base wavelength divided by n, so each generation packs its structure more finely. In chapter 9's π-based geometry, wavelength contraction and geometric recursion together produce self-similar structure across generations. BPT Recursive Scaling follows this law: emergence arcs grow as EA_n = EA_0 × π^(n/2) × Φ(n) [𝕃] while their wavelengths contract, and the resulting structure has a fractal dimension D_f = log(π)/log(2) ≈ 1.65, between one and two dimensions. Growth is thus nested rather than linear, each generation adding structural depth while keeping proportion. The current lexicon statement also applies the law to branching in one-dimensional linear chains, whose sequential logic keeps temporal order on the ①⥂⧗⌂ cycle of two Pulse Rhythms, ①⥂⧖⌂ = ①⥂⧗⌂/2. The book writes λ_n = λ_0/n, where λ_n is the wavelength of generation n [𝕃], λ_0 the base wavelength [𝕃] and n the generation or harmonic number [∅]. The Wavelength Scaling Law connects to BPT Recursive Scaling, Fractal Dimension, Self-Similar Structure, Alpha Wavelength of Harmonics, Emergence Arc and 1D Emergence Layer - Linear Chains.