Source: https://guthlabs.ai/docs/instruments/relativistic-momentum-kinetic-energy-calculator/
instrument / verified-clean
# Relativistic Momentum & Kinetic Energy 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]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## 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-5
**Evidence ID**: t5-221
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The core relativistic formulas are standard when v denotes physical velocity and c is in consistent units. Because the specification instead defines v as a fraction of c, and because gamma and classical KE formulas plus domain constraints are omitted, the instrument needs an explicit input convention and formula completion before passing verification.
### Formula and scope findings
- The Lorentz factor formula gamma=1/sqrt(1-beta^2) is missing even though gamma is an output.
- The input is specified as v (fraction of c), so v is dimensionless beta; in that case momentum must be written p=gamma*m*beta*c, not gamma*m*v unless v is first converted to the physical velocity beta*c.
- The classical kinetic-energy comparison formula KE_classical=0.5*m*(beta*c)^2 is missing.
- The valid input domain is not stated: for a massive particle, m>=0 and |beta|<1 are required.
### Unit assumptions
- m is in kilograms.
- The velocity input is beta=v/c, dimensionless; the physical velocity is u=beta*c in meters per second.
- c is the exact SI speed of light, 299792458 m/s.
- p is reported in kg*m/s.
- E_total, KE, and classical KE are reported in joules.
- Gamma is dimensionless.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
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.
## 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": {
"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."
}
````
## 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-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`