Source: https://guthlabs.ai/docs/instruments/centroid-center-of-mass-calculator-composite-areas-bodies/implementation/

instrument implementation / implementation-contract

# Centroid & Center of Mass Calculator (Composite Areas/Bodies) implementation

A source-bound implementation contract for Centroid & Center of Mass Calculator (Composite Areas/Bodies); 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**: t4-154

**Effect**: Computation or source lookup only

## Input and validation requirements

- Division by zero occurs when the sum of component areas is zero or the sum of component masses is zero.

- Signed areas can cancel to zero or produce a centroid outside the visible region; this requires validation and an honest explanation to users.

- Overlapping positive-area components are double-counted unless the decomposition is explicitly non-overlapping.

- A geometric centroid of 3D bodies cannot generally be obtained from masses unless density is uniform or the intended result is center of mass.

- Mixed coordinate units can produce numerically plausible but incorrect results if no conversion is performed.

- The common coordinate origin and the meaning of each component's supplied position must be defined.

- The empty honest_label is a concern: the instrument should clearly state whether it computes area centroids, volume centroids, center of mass, or all of these, and should disclose signed-area and unit requirements.

## 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": {
    "mode": "area_2d",
    "coordinate_unit": "m",
    "components": [
      {
        "type": "rectangle",
        "area_m2": 0.08,
        "centroid": {
          "x_m": 0.2,
          "y_m": 0.1
        }
      },
      {
        "type": "rectangle",
        "area_m2": 0.03,
        "centroid": {
          "x_m": 0.55,
          "y_m": 0.25
        }
      }
    ]
  },
  "expected_outputs": {
    "x_bar_m": 0.2954545455,
    "y_bar_m": 0.1409090909
  },
  "working": "ΣA=0.08+0.03=0.11 m². x numerator=(0.08×0.20)+(0.03×0.55)=0.016+0.0165=0.0325 m³. x̄=0.0325/0.11=0.2954545455 m. y numerator=(0.08×0.10)+(0.03×0.25)=0.008+0.0075=0.0155 m³. ȳ=0.0155/0.11=0.1409090909 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/centroid-center-of-mass-calculator-composite-areas-bodies/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/centroid-center-of-mass-calculator-composite-areas-bodies/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/centroid-center-of-mass-calculator-composite-areas-bodies/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`