Source: https://guthlabs.ai/docs/instruments/redshift-velocity-distance/

instrument / verified-clean

# Redshift ↔ Velocity/Distance

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/redshift-velocity-distance/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/redshift-velocity-distance/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/redshift-velocity-distance/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/redshift-velocity-distance/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Earth & Space (astronomy, orbital mechanics, meteorology, geology, geodesy, oceanography)

**Tranche**: tranche-4

**Evidence ID**: t4-065

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core arithmetic is correct under the stated low-z approximation and consistent units, but the specification needs review before release. It must define the wavelength conversion, exact H0 presets and units, validation constraints, and the precise meaning of velocity and distance. The honest label should explicitly state that v=cz and d=v/H0 are low-redshift approximations and that H0 is user-selectable and contested.

### Formula and scope findings

- v=cz is the correct first-order non-relativistic approximation only when z is much less than 1; it is not a general redshift-to-velocity formula.

- d=v/H0 is the low-redshift linear Hubble-law distance, not a general cosmological distance such as comoving, luminosity, or angular-diameter distance.

- The wavelength-input path is underspecified: it must explicitly define z=(observed_wavelength-rest_wavelength)/rest_wavelength.

- The exact selectable H0 values are not specified, and the result depends materially on that choice.

### Unit assumptions

- Redshift z is dimensionless.

- c is taken as 299792.458 km/s.

- H0 must be supplied in km/s/Mpc for d=v/H0 to return Mpc.

- Observed and rest wavelengths must use the same units; nanometers cancel in their ratio.

- The reported velocity is in km/s and the reported Hubble-law distance is in Mpc.

- The approximation assumes z is sufficiently small; z=0.1 is already only a low-redshift illustrative case, not a generally accurate cosmological-velocity calculation.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The distance calculation is undefined when the user selects H0=0, and the specification provides no explicit high-redshift branch or threshold even though v=cz is only a low-z approximation. Wavelength-field reversal also produces a materially different signed result.

## 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": {
    "z": 0.01,
    "H0_km_s_Mpc": 67.4,
    "c_km_s": 299792.458
  },
  "expected_outputs": {
    "velocity_km_s": 2997.92458,
    "distance_Mpc": 44.47959317
  },
  "working": "v = cz = 299792.458 km/s × 0.01 = 2997.92458 km/s. d = v/H0 = 2997.92458 km/s ÷ 67.4 km/s/Mpc = 44.47959317 Mpc."
}
````

## 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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`