Source: https://guthlabs.ai/docs/instruments/length-contraction-calculator/

instrument / verified-clean

# Length Contraction 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](<https://guthlabs.ai/docs/instruments/length-contraction-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/length-contraction-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/length-contraction-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/length-contraction-calculator/qualification/>)

## 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**: t5-215

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## 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`