IndisputableMonolith.Economics.InequalityFromSigmaBudget
The module supplies the economics domain certificate deriving inequality bounds from the sigma budget constraint via the J-cost band. Econophysics researchers applying Recognition Science to resource allocation would cite it within the master cert chain. It instantiates the reusable six-clause template imported from CanonicalJBand to establish matched-zero and nonnegativity for the relevant ratio.
claimThe central object is the inequality certificate asserting $J(1)=0$ and $J(r)≥0$ for $r>0$, where $r$ is the normalized sigma budget ratio and $J$ is the canonical cost function.
background
The module sits in the economics domain of Recognition Science and imports the Canonical J-Cost Band template. That template supplies the six-clause structure used across B-tier domain certs: matched-zero at $J(1)=0$ together with nonnegativity $J(x)≥0$ for $x>0$. The sigma budget ratio is the economic quantity to which this J-cost is applied, yielding an inequality certificate consistent with the master cert chain.
proof idea
This is a definition module, no proofs. It defines InequalityCert as the six-clause instance and inequalityCert as its concrete realization by specializing the imported CanonicalJBand template to the sigma budget ratio.
why it matters in Recognition Science
The module supplies the economics entry in the Plan v7 domain certs and feeds the master cert chain. It extends the CanonicalJBand template to the sigma budget, producing the inequality certificate required for whole-science openings that treat economic distributions under J-cost constraints.
scope and limits
- Does not derive numerical inequality indices such as Gini coefficients.
- Does not address time-dependent or stochastic economic processes.
- Does not incorporate external market parameters beyond the sigma budget ratio.
- Does not establish uniqueness of the resulting inequality bound.