IndisputableMonolith.Economics.InequalityCeilingFromSigma
This module establishes the upper bound on the Gini coefficient as the reciprocal of the golden ratio in Recognition Science economics. Modelers of inequality under RS constraints would cite the result for its direct tie to the J-cost function. The module introduces giniCeiling together with its equality to phi minus one and its placement inside the allowed band.
claimThe Gini ceiling equals $1/phi$, where $phi$ is the golden-ratio fixed point satisfying $phi=1+1/phi$.
background
Recognition Science obtains the golden ratio phi as the unique self-similar fixed point (T6) of the forcing chain that begins with the J-uniqueness relation J(x)=(x+x^{-1})/2-1. The imported Cost module supplies the J-cost function and its symmetry properties, while Constants supplies the base time quantum tau_0=1 tick. The present module applies these objects to economic inequality, defining giniCeiling as the maximum admissible Gini coefficient consistent with J-cost symmetry.
proof idea
This is a definition module, no proofs. It introduces the constant giniCeiling, states its equality to phi minus one, and records the band membership giniCeiling_in_band together with the symmetry lemma gini_jcost_symmetric.
why it matters in Recognition Science
The module supplies the concrete numerical ceiling that any RS-derived economic model must respect. It directly implements the DOC_COMMENT claim that the Gini ceiling equals 1/phi and thereby links the phi-ladder of the forcing chain to observable inequality measures.
scope and limits
- Does not derive the Gini coefficient itself from micro-foundations.
- Does not treat time evolution or policy interventions.
- Does not extend beyond the static ceiling value.
- Does not address multi-agent or network effects.