giniCeiling
plain-language theorem explainer
Recognition Science sets the Gini ceiling to the reciprocal of the golden ratio. Economists working in this framework cite the value as the upper bound on sustainable inequality when recognition variance sigma equals zero. The definition is a direct assignment of phi inverse drawn from the upstream invariants module.
Claim. The Gini ceiling equals $phi^{-1}$, where $phi$ is the golden ratio fixed point satisfying $phi^2 = phi + 1$.
background
The Economics.InequalityCeilingFromSigma module predicts that the maximum sustainable Gini coefficient under sigma equals zero is one over phi, approximately 0.618. Above this threshold the recognition system undergoes a sigma-cascade and institutional collapse; below it the system maintains stable recognition equilibrium. The definition imports phi inverse from CrossDomain.PhiInverseInvariants, where the same quantity is named phiInv, and aligns with the zero J-cost identity event from ObserverForcing.
proof idea
The declaration is a direct noncomputable definition that assigns phi inverse. It inherits the golden ratio reciprocal identity from the upstream phi inverse definition and the equality theorem proved in the same module.
why it matters
This definition supplies the core constant for the inequality ceiling theorems, including equality to phi minus one, band membership in (0.617, 0.622), and J-cost symmetry. It feeds the PhiInverseInvariantsCert structure and the unification theorem that equates all five instances of one over phi. In the Recognition framework it instantiates the T6 self-similar fixed point phi as an economic observable, consistent with the RCL and the eight-tick octave.
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