IndisputableMonolith.Economics.WealthDistributionFromSigma
The module introduces the Pareto exponent for wealth distributions as a direct consequence of the Recognition Science phi constant. It supplies definitions such as paretoExponent and WealthDistributionCert for use in economic modeling. Researchers analyzing power laws in wealth would cite this when applying RS to sigma-based distributions. The content consists of algebraic definitions and equalities derived from phi squared equals phi plus one.
claimThe Pareto exponent satisfies $\alpha = 1 + \phi^{-1} = \phi$, where $\phi$ is the unique positive solution to $\phi^2 = \phi + 1$.
background
Recognition Science derives all physics and extensions from one functional equation, with phi as the self-similar fixed point forced at T6 of the UnifiedForcingChain. This module operates in the Economics domain and imports the base time quantum tau_0 = 1 tick from Constants. It introduces paretoExponent as the exponent in the Pareto law for wealth, along with WealthDistributionCert as the certifying object and related band and equality statements.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies paretoExponent and WealthDistributionCert to parent results on economic distributions in the Recognition framework. It completes the link from the phi-ladder to wealth statistics, consistent with the RCL and eight-tick octave. No downstream uses are listed, indicating it serves as a foundational block for further economic applications.
scope and limits
- Does not compute numerical values for specific sigma inputs.
- Does not prove uniqueness of the resulting distribution.
- Does not address time evolution or dynamics of wealth.