Source: https://guthlabs.ai/docs/instruments/relativistic-momentum-kinetic-energy-calculator/implementation/

instrument implementation / implementation-contract

# Relativistic Momentum & Kinetic Energy Calculator implementation

A source-bound implementation contract for Relativistic Momentum & Kinetic Energy Calculator; 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**: t5-221

**Effect**: Computation or source lookup only

## Input and validation requirements

An exact input of v_fraction_c=1 makes 1-v^2/c^2 equal zero, so gamma and all relativistic outputs depending on it are undefined or divergent. The calculator should reject |v_fraction_c|>=1. Momentum also has a sign-convention ambiguity if a negative input is interpreted as a speed rather than a signed velocity.

## 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": {
    "m_kg": 1,
    "v_fraction_of_c": 0.6,
    "c_m_per_s": 299792458
  },
  "expected_outputs": {
    "gamma": 1.25,
    "p_kg_m_per_s": 224844343.5,
    "E_total_J": 112344397342102200,
    "KE_J": 22468879468420440,
    "classical_KE_J": 16177593217262718
  },
  "working": "beta=0.6. gamma=1/sqrt(1-0.6^2)=1/sqrt(0.64)=1/0.8=1.25. Physical velocity u=beta*c=0.6*299792458=179875474. p=gamma*m*beta*c=1.25*1*0.6*299792458=224844343.5 kg*m/s. E_total=gamma*m*c^2=1.25*1*(299792458)^2=1.25*89875517873681764=112344397342102205 J. KE=(gamma-1)*m*c^2=0.25*89875517873681764=22468879468420441 J. Classical KE=0.5*m*(beta*c)^2=0.5*1*0.6^2*c^2=0.18*89875517873681764=16177593217262717.52 J."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/relativistic-momentum-kinetic-energy-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/relativistic-momentum-kinetic-energy-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/relativistic-momentum-kinetic-energy-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-tranche5/tranche5-results.json`