Source: https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/implementation/

instrument implementation / implementation-contract

# Correlation & Covariance Calculator implementation

A source-bound implementation contract for Correlation & Covariance Calculator; 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**: t4-225

**Effect**: Computation or source lookup only

## Input and validation requirements

A constant-valued input column produces a zero denominator and the undefined form 0/0. The calculator should reject it or return an explicit undefined result rather than a numeric correlation.

## 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": {
    "x": [
      1,
      2,
      3
    ],
    "y": [
      2,
      4,
      6
    ],
    "units": {
      "x": "arbitrary",
      "y": "arbitrary"
    }
  },
  "expected_outputs": {
    "pearson_r": 1,
    "covariance_population": 1.3333333333,
    "covariance_sample": 2,
    "correlation_matrix": [
      [
        1,
        1
      ],
      [
        1,
        1
      ]
    ]
  },
  "working": "x̄=(1+2+3)/3=2; ȳ=(2+4+6)/3=4. Deviations: x−x̄=(-1,0,1), y−ȳ=(-2,0,2). Cross-products: 2+0+2=4. Sum of x squared deviations=1+0+1=2. Sum of y squared deviations=4+0+4=8. r=4/√(2×8)=4/4=1. Population covariance=4/3=1.3333333333. Sample covariance=4/(3−1)=2."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/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-tranche4/tranche4-results.json`