IndisputableMonolith.Economics.WealthDistributionFromSigma
Module derives the Pareto exponent α for wealth distributions directly from Recognition Science constants. Economists and econophysicists modeling inequality would cite the result α = φ. The argument reduces the exponent via the golden-ratio identity φ² = φ + 1 together with algebraic lemmas on the inverse and admissible band.
claimThe Pareto exponent satisfies $α = 1 + 1/φ = φ$, where $φ$ obeys $φ² = φ + 1$.
background
The module resides in the Economics domain and imports the RS-native time quantum τ₀ = 1 tick from Constants. It introduces the Pareto exponent together with supporting identities that express it in terms of the self-similar fixed point φ. The local setting is the derivation of macroscopic economic distributions from the single functional equation of Recognition Science.
proof idea
This is a definition module whose core content consists of the definition paretoExponent together with the lemmas inv_phi_eq, paretoExponent_eq_phi and paretoExponent_band that establish the claimed equality to φ.
why it matters in Recognition Science
The module supplies the explicit link between the RS phi fixed point and the observed Pareto exponent in wealth distributions. It fills the step that converts the T6 fixed-point result into an economic observable; the supplied doc-comment states the reduction α = 1 + 1/φ = φ.
scope and limits
- Does not derive the full functional form of the wealth distribution.
- Does not incorporate empirical calibration or data fitting.
- Does not address other economic scaling exponents beyond Pareto.
- Does not connect to the spatial dimension D = 3 or the alpha band.