InequalityCeilingCert
plain-language theorem explainer
The InequalityCeilingCert structure packages three facts about the Gini ceiling: equality to the golden-ratio conjugate phi minus one, membership in the open interval (0.617, 0.623), and equality of J-cost values with phi itself. RS economists cite the certificate when stating the maximum sustainable Gini under zero sigma before institutional collapse occurs. The declaration is a plain structure definition whose fields are filled by three already-proved sibling lemmas.
Claim. A structure whose fields assert that the Gini ceiling equals $phi - 1$, satisfies $0.617 <$ Gini ceiling $< 0.623$, and obeys $J($Gini ceiling$) = J(phi)$, where $phi$ is the golden ratio and $J$ is the J-cost function.
background
The module defines the Gini ceiling as the reciprocal of the golden ratio, $phi^{-1}$, which equals $phi - 1$ by the identity $phi^2 = phi + 1$. This definition is imported from the CrossDomain.PhiInverseInvariants module where giniCeiling is set to phiInv. The J-cost function is taken from the Cost module and records recognition cost under the Recognition Composition Law. The module documentation states that the ceiling marks the threshold above which a sigma-cascade produces institutional collapse and below which stable recognition equilibrium is maintained.
proof idea
The declaration is a structure definition whose three fields are propositions already established by the sibling lemmas giniCeiling_eq_phi_minus_one, giniCeiling_in_band, and gini_jcost_symmetric. No tactics or reductions are performed inside the structure itself.
why it matters
The structure supplies the bundled certificate consumed by the downstream inequalityCeilingCert definition, which assembles the RS prediction for the economic inequality ceiling at $1/phi$. It closes the F3 economic step by linking the phi-ladder, the eight-tick octave, and J-cost symmetry. No open scaffolding remains inside the module.
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