Source: https://guthlabs.ai/docs/instruments/relativistic-doppler-effect-calculator/mechanism/

instrument mechanism / verified-clean

# Relativistic Doppler Effect Calculator mechanism

The inspectable method record for Relativistic Doppler Effect Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The supplied receding formula is standard and correct, and the honest-label warning about radial-only motion is appropriate. Implementation needs explicit wavelength, redshift, direction, beta-domain, and unit conventions before it can receive an unqualified PASS.

- The stated frequency formula is correct for radial recession when beta=v/c is positive and 0<=beta<1: f_obs=f_src*sqrt((1-beta)/(1+beta)).

- The specification does not state the formula for wavelength; under vacuum propagation it should be lambda_obs=lambda_src*sqrt((1+beta)/(1-beta))=c/f_obs.

- The specification does not define redshift z; the standard definition must be stated explicitly as z=(f_src/f_obs)-1=(lambda_obs/lambda_src)-1.

- The input includes direction, but the behavior for an approaching source is unspecified. The standard approaching formula is f_obs=f_src*sqrt((1+beta)/(1-beta)), or equivalently use signed beta with beta<0 for approach.

- The valid domain and sign convention for beta are missing: |beta|<1, with positive beta explicitly defined as recession under the supplied formula.

## Units and conventions

- Frequencies are in hertz (s^-1), wavelengths are in meters unless a display unit is explicitly applied, and velocity fraction beta is dimensionless.

- The speed of light is c=299792458 m/s in vacuum.

- The source emits light in vacuum, so c=f*lambda applies.

- The redshift convention is z=(f_src/f_obs)-1; positive z means redshift and negative z means blueshift.

- For the receding formula, beta is positive; for the approaching test vector, the reciprocal Doppler factor is assumed.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "source_frequency_hz": 600000000000000,
    "beta": 0.6,
    "direction": "receding",
    "c_m_per_s": 299792458
  },
  "expected_outputs": {
    "observed_frequency_hz": 300000000000000,
    "observed_wavelength_m": 9.993081933333334e-7,
    "redshift_z": 1
  },
  "working": "Doppler factor=sqrt((1-0.6)/(1+0.6))=sqrt(0.4/1.6)=sqrt(0.25)=0.5. f_obs=600000000000000*0.5=300000000000000 Hz. lambda_obs=c/f_obs=299792458/300000000000000=9.993081933333333e-7 m. z=f_src/f_obs-1=600000000000000/300000000000000-1=2-1=1."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The formula encounters a division-by-zero singularity at beta = -1 and should reject that input. The negative-beta plus explicit-direction case also exposes an unresolved signed-beta versus direction-field convention ambiguity.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/relativistic-doppler-effect-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/relativistic-doppler-effect-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/relativistic-doppler-effect-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`

- `BOUNDARY_HAZARD_CATALOG.json`