IndisputableMonolith.Economics.LorenzCurveFromSigmaBudget
This module defines per-decile J-cost on income-share ratios to support Lorenz curve certification in Recognition Science economics. Modelers of inequality and mobility regimes cite it when mapping sigma budgets to observable distributions. It supplies the core decileCost function plus basic algebraic properties via direct definitions.
claimDefine decileCost$(r) = J(r)$ where $r$ is the income-share ratio in a given decile. The module also introduces IsHighInequalityRegime, IsHighMobilityRegime, and LorenzCurveCert as predicates on these costs.
background
The module sits in the Economics domain and imports Constants (where τ₀ = 1 tick is the RS time quantum) together with the Cost module that supplies the J-function. J satisfies J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and is the unique solution to the forcing chain at T5. decileCost applies this J directly to normalized income shares, yielding the per-decile cost that feeds regime classification and Lorenz-curve statements.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definitions supply the economic observables required by downstream LorenzCurveCert and the regime predicates. They close the link from the J-cost and phi-ladder to concrete inequality measures, consistent with the eight-tick octave and D = 3 spatial setting of the parent framework.
scope and limits
- Does not derive numerical Lorenz curves for real economies.
- Does not connect to the mass formula or alpha band.
- Does not treat continuous income distributions beyond deciles.
- Does not prove global existence of high-mobility regimes.
depends on (2)
declarations in this module (12)
-
def
decileCost -
theorem
decileCost_zero_at_equal -
theorem
decileCost_reciprocal_symm -
theorem
decileCost_nonneg -
theorem
decileCost_pos_off_equal -
def
MobilityThreshold -
def
IsHighInequalityRegime -
def
IsHighMobilityRegime -
theorem
regimes_exclusive -
theorem
mobility_threshold_band -
structure
LorenzCurveCert -
def
lorenzCurveCert