IndisputableMonolith.Economics.InequalityCeilingFromSigma
This module establishes the Gini coefficient ceiling as 1/φ within Recognition Science economics models. Researchers applying RS to inequality bounds would cite it to constrain distribution metrics. The structure consists of definitions and equalities built directly on J-cost symmetry and the phi fixed point from imported modules.
claimThe Gini coefficient satisfies an upper bound of $1/φ$, where $φ$ denotes the golden ratio fixed point.
background
Recognition Science starts from the J-uniqueness relation J(x) = (x + x^{-1})/2 - 1 and the Recognition Composition Law. The Constants module fixes the base time quantum τ₀ = 1 tick. The Cost module supplies the J-cost function and defect measures that this economics module applies to derive an inequality ceiling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the inequality ceiling that feeds economic applications of the phi-ladder and eight-tick octave in Recognition Science. It directly instantiates the T6 self-similar fixed point as a bound on observable distributions. No downstream theorems are recorded in the current dependency graph.
scope and limits
- Does not derive the Gini coefficient from raw transaction data.
- Does not model time-dependent evolution of inequality.
- Does not connect the ceiling to the fine-structure constant band.
- Does not address multi-agent or network extensions.