Length Contraction Calculator mechanism

Model scope

The contraction relation L=L0/γ is standard and correct for special relativity when L0 is the proper length and γ=1/√(1−β²). The honest label correctly limits the result to the direction of motion. Verdict is NEEDS_REVIEW because the supplied formula does not explicitly define γ and the input notation v is potentially ambiguous unless documented as a fraction of c.

• The formula is incomplete as written because γ is not defined. It must specify γ=1/√(1−(v/c)^2), or γ=1/√(1−v^2) only when v is explicitly the dimensionless fraction of c.

Units and conventions

• L0 and L use the same length unit; no length-unit conversion is performed.
• The input v is a dimensionless speed fraction β=v/c, not a speed in m/s.
• If v is supplied as a physical speed, the calculator must first divide by c=299792458 m/s.
• Contraction applies only to the component of length parallel to the motion; transverse dimensions are unchanged.
• c is unnecessary when v is already supplied as a fraction of c.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "L0": 2,
    "L0_unit": "m",
    "v": 0,
    "v_unit": "fraction_of_c"
  },
  "expected_outputs": {
    "L": 2,
    "L_unit": "m",
    "gamma": 1
  },
  "working": "β=0.00. γ=1/√(1−β²)=1/√(1−0)=1/√1=1. L=L0/γ=2.0/1=2.0 m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formula is undefined at exactly |v/c|=1 and for |v/c|>1. An implementation that does not validate the domain can produce division-by-zero, NaN, or misleading outputs. The input convention must also enforce that v is a dimensionless fraction of c.

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