Relativistic Doppler Effect Calculator mechanism

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

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