IndisputableMonolith.Economics.InequalityCeilingFromSigma
The module establishes the Gini ceiling as 1/φ in the Recognition Science treatment of economics. Researchers modeling inequality bounds under RS constraints would cite these results. The module collects definitions and equalities that apply the J-cost symmetry and phi fixed point imported from Constants and Cost.
claimThe Gini ceiling equals $\phi^{-1}$, where $\phi$ is the golden-ratio fixed point of the J-cost function.
background
Recognition Science extends its core functional equation to economics through the J-cost and phi-ladder. The imported Constants module fixes the base time quantum $\tau_0 = 1$ tick. The Cost module supplies the J-cost definition $J(x) = (x + x^{-1})/2 - 1$ together with the Recognition Composition Law.
The present module applies these objects to inequality, introducing the Gini ceiling as the upper bound implied by the self-similar fixed point $\phi$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the inequality ceiling required by the RS economics layer. It realizes the bound from the phi self-similar fixed point (T6) and places the result inside the allowed band. No downstream theorems are recorded yet, but the results support later economic applications of the framework.
scope and limits
- Does not derive the Gini coefficient from empirical distributions.
- Does not treat time evolution of inequality.
- Does not incorporate policy or external shocks.
- Does not address multi-agent or network effects.