Source: https://guthlabs.ai/docs/instruments/relative-velocity-composition-classical/implementation/

instrument implementation / implementation-contract

# Relative Velocity Composition (classical) implementation

A source-bound implementation contract for Relative Velocity Composition (classical); 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**: t2-047

**Effect**: Computation or source lookup only

## Input and validation requirements

The extreme-magnitude vector pair overflows JavaScript Number arithmetic to Infinity, so the instrument must reject or explicitly report a non-finite result. The specification also leaves angular sign and heading-wrap conventions unspecified, producing reflected or differently represented headings.

## 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": {
    "v_AB": {
      "magnitude": 8,
      "unit": "m/s",
      "direction_deg_from_east_ccw": 0
    },
    "v_BC": {
      "magnitude": 3,
      "unit": "m/s",
      "direction_deg_from_east_ccw": 90
    }
  },
  "expected_outputs": {
    "resultant_x": 8,
    "resultant_y": 3,
    "resultant_magnitude_m_per_s": 8.544004,
    "resultant_heading_deg_from_east_ccw": 20.556045
  },
  "working": "v_AB = (8 cos 0°, 8 sin 0°) = (8, 0) m/s. v_BC = (3 cos 90°, 3 sin 90°) = (0, 3) m/s. Sum = (8 + 0, 0 + 3) = (8, 3) m/s. Magnitude = sqrt(8^2 + 3^2) = sqrt(64 + 9) = sqrt(73) = 8.544004 m/s. Heading = atan2(3, 8) = 20.556045°."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/relative-velocity-composition-classical/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/relative-velocity-composition-classical/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/relative-velocity-composition-classical/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-tranche2/tranche2-results.json`