Source: https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/implementation/

instrument implementation / implementation-contract

# Chi-Square Goodness-of-Fit (Genetics) implementation

A source-bound implementation contract for Chi-Square Goodness-of-Fit (Genetics); 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**: t6-079

**Effect**: Computation or source lookup only

## Input and validation requirements

An expected ratio containing a zero produces an expected count E = 0 and a 0/0 χ² term when the corresponding observed count is also zero. The instrument must reject this input or explicitly define handling; otherwise the statistic and p-value are undefined.

## 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": {
    "observed_counts": [
      75,
      25
    ],
    "expected_ratio": [
      3,
      1
    ],
    "df": 1,
    "alpha": 0.05
  },
  "expected_outputs": {
    "expected_counts": [
      75,
      25
    ],
    "chi_square": 0,
    "p_value": 1,
    "critical_value_at_alpha": 3.841459,
    "decision": "fail to reject"
  },
  "working": "Observed total = 75+25 = 100. Ratio total = 3+1 = 4. Expected counts = 100×[3/4,1/4] = [75,25]. χ² = (75−75)²/75 + (25−25)²/25 = 0/75 + 0/25 = 0. For df=1, p=P(Χ²₁≥0)=1. Since 0 < 3.841459, fail to reject at α=0.05."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/chi-square-goodness-of-fit-genetics/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`