Source: https://guthlabs.ai/docs/instruments/center-of-mass-calculator/

instrument / verified-clean

# Center of Mass Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/center-of-mass-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/center-of-mass-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/center-of-mass-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/center-of-mass-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-4

**Evidence ID**: t4-239

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formula is correct for a discrete set of point masses. The specification needs an explicit dimensionality and unit contract, validation for a nonempty list and nonzero total mass, and a clear policy for zero or negative masses. The honest_label value "n/a" does not communicate these limitations; the user-facing label should identify the result as a mass-weighted center of mass and state the unit and validation assumptions.

### Formula and scope findings

- The formula r_cm=Σm_i r_i/Σm_i is the standard formula for the center of mass of discrete point masses, but the specification does not state the required domain condition Σm_i ≠ 0.

- The specification does not state whether positions are 1D, 2D, or 3D vectors, although the formula supports any consistent coordinate dimension.

### Unit assumptions

- All masses must use a consistent mass unit; because mass units cancel in the ratio, grams or kilograms are both acceptable if used consistently.

- All position coordinates must use a consistent length unit; the output COM coordinates use that same length unit.

- Each position vector must have the same dimensionality and coordinate-unit convention as every other position vector.

- For a physical point-mass system, masses are assumed to be nonnegative, with at least one strictly positive mass.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The all-zero-mass input makes the denominator vanish and the result undefined. Because the specification does not state validation behavior, a plain arithmetic implementation could emit NaN instead of rejecting the input. The formula also has no actual piecewise branch, so the branch-switch requirement is not applicable beyond confirming that the same formula is used.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "masses_positions": [
      {
        "mass": 2,
        "position": [
          0,
          0
        ]
      },
      {
        "mass": 3,
        "position": [
          5,
          0
        ]
      }
    ],
    "mass_unit": "kg",
    "position_unit": "m"
  },
  "expected_outputs": {
    "r_cm": [
      3,
      0
    ],
    "position_unit": "m"
  },
  "working": "Total mass = 2 + 3 = 5 kg.\\nX numerator = (2×0) + (3×5) = 0 + 15 = 15 kg·m.\\nY numerator = (2×0) + (3×0) = 0 + 0 = 0 kg·m.\\nCOM = (15/5, 0/5) = (3, 0) m."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`