Relativistic Momentum & Kinetic Energy Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

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
• BOUNDARY_HAZARD_CATALOG.json