Source: https://guthlabs.ai/docs/instruments/momentum-calculator/

instrument / verified-clean

# Momentum 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/momentum-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/momentum-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/momentum-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/momentum-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**: t4-179

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The formula is conditionally correct, but the specification needs exact definitions for vector dimensionality, accepted units and conversion behavior, treatment of systems, and the nonrelativistic validity range before it can receive PASS.

### Formula and scope findings

- p=mv is the standard classical formula for a single object when m is scalar mass and v is a velocity vector.

- The claim that it computes momentum of an arbitrary system is underspecified: a system generally requires p_total=Σ(m_i v_i), or an explicitly defined total mass and common/center-of-mass velocity.

- The formula is not valid as stated in relativistic regimes; relativistic momentum is p=γmv.

- The spec does not state whether velocity input is a scalar or a three-dimensional vector, despite the output being specified as a vector.

### Unit assumptions

- Mass must be a nonnegative scalar measured in kilograms.

- Velocity must be a vector measured in meters per second; scalar velocity is acceptable only for one-dimensional motion and should produce a signed scalar or an explicitly defined vector component.

- The output unit is kilogram-meters per second (kg·m/s).

- Unit conversion must occur before applying p=mv; plain arithmetic does not convert grams to kilograms or kilometers per hour to meters per second.

- The classical formula assumes speeds sufficiently below the speed of light.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The plain-JavaScript arithmetic engine overflows for a valid finite input combination of mass = 10^308 kg and velocity = 10^308 m/s, producing Infinity instead of a finite representable result; the mathematical momentum is 10^616 kg·m/s.

## 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": {
    "mass": 2,
    "mass_unit": "kg",
    "velocity": [
      3,
      -4,
      0
    ],
    "velocity_unit": "m/s"
  },
  "expected_outputs": {
    "p": [
      6,
      -8,
      0
    ],
    "unit": "kg·m/s"
  },
  "working": "p=mv=2 kg×[3,-4,0] m/s=[2×3,2×(-4),2×0]=[6,-8,0] kg·m/s."
}
````

## Related workflows

[Kinematics & Collisions Tutorp](<https://guthlabs.ai/docs/instrument-workflows/kinematics-tutor/>)

## 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`