Source: https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/implementation/

instrument implementation / implementation-contract

# Gini Coefficient / Lorenz Curve Estimator implementation

A source-bound implementation contract for Gini Coefficient / Lorenz Curve Estimator; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-091

**Effect**: Computation or source lookup only

## Input and validation requirements

The zero-total input produces an undefined normalization denominator and must be rejected. The specification also does not state how group ordering or percentage-versus-fraction units are interpreted; reversed ordering can yield an invalid negative formal Gini.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "grouping": "10 equal-population deciles",
    "income_shares": [
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1
    ],
    "sampled_x": [
      0,
      0.5,
      1
    ]
  },
  "expected_outputs": {
    "gini": 0,
    "lorenz_sampled_points": [
      {
        "x": 0,
        "y": 0
      },
      {
        "x": 0.5,
        "y": 0.5
      },
      {
        "x": 1,
        "y": 1
      }
    ],
    "curve_features": {
      "equality_intersections": "Every point on 0<=x<=1",
      "maximum_gap_from_equality": 0,
      "asymptotes": "None"
    }
  },
  "working": "Cumulative Lorenz y-values: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. Each trapezoid has width 0.1 and average height 0.1. B=10*(0.1*((0.1+0.1)/2))=10*0.01=0.10? Including the endpoint formula directly: B=0.1*(0.5*0+0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9+0.5*1)=0.1*(5.0)=0.5. A=0.5-B=0.5-0.5=0. Gini=A/(A+B)=0/0.5=0. The Lorenz curve is y=x, so y(0.5)=0.5 and its maximum gap from equality is 0."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`