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

instrument mechanism / verified-clean

# Correlation & Covariance Calculator mechanism

The inspectable method record for Correlation & Covariance Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The causal disclaimer is honest and appropriate: correlation does not imply causation. The Pearson formula itself passes verification, but the covariance denominator convention, missing-data policy, multi-column matrix construction, and minimum/variance constraints must be specified before release.

- The supplied Pearson correlation formula is standard and correct for complete paired observations.

- The covariance formula is not specified; population covariance uses Σ((x−x̄)(y−ȳ))/n, while sample covariance uses Σ((x−x̄)(y−ȳ))/(n−1).

- The construction rules for a multi-variable correlation matrix are not specified, including whether all variables must use the same complete rows or whether pairwise deletion is used for missing values.

- The formula requires at least two observations and nonzero variance in both variables; these constraints are not stated.

## Units and conventions

- Pearson correlation is dimensionless and is unchanged by consistent positive linear unit conversions.

- Covariance retains the product of the input units; for example, meters-centimeters produces m·cm, not m².

- Expected covariance values below report both population covariance, dividing by n, and sample covariance, dividing by n−1, because the specification does not choose one convention.

- The arithmetic assumes complete paired observations with ordinary arithmetic means and no missing-value handling.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "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."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

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.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/correlation-covariance-calculator/implementation/>)[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`

- `BOUNDARY_HAZARD_CATALOG.json`