Source: https://guthlabs.ai/docs/instruments/habitable-zone-distance-rough/

instrument / verified-clean

# Habitable-Zone Distance (rough)

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/habitable-zone-distance-rough/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/habitable-zone-distance-rough/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/habitable-zone-distance-rough/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/habitable-zone-distance-rough/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-7

**Evidence ID**: t7-006

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The core inverse-square luminosity relation is standard, but the instrument needs review before implementation because the conservative/optimistic boundary mapping, Kopparapu polynomial coefficients, Teff-plus-radius luminosity conversion, and valid-temperature policy are not explicitly specified. Honest label should remain: simplified 1-D climate estimate, not a full climate model.

### Formula and scope findings

- The distance formula d = sqrt((L*/L_sun)/S_eff) is correct when luminosity is bolometric and S_eff is the dimensionless incident stellar flux required by the selected Kopparapu limit.

- The specification does not define which boundaries are meant by conservative and optimistic. The standard interpretation is conservative = runaway-greenhouse inner edge to maximum-greenhouse outer edge, and optimistic = recent-Venus inner edge to early-Mars outer edge.

- The specification names Kopparapu coefficients but does not state the required polynomial S_eff = S_sun + a*T' + b*T'^2 + c*T'^3 + d*T'^4, where T' = Teff - 5780 K, nor does it provide the coefficients.

- For Teff-plus-radius input, the luminosity conversion is unspecified. A standard implementation should use L*/L_sun = (R*/R_sun)^2*(Teff/5780 K)^4, assuming blackbody bolometric luminosity.

- The Kopparapu polynomial is an approximate climate-boundary fit with a stated stellar-temperature applicability range of approximately 2600 K to 7200 K; inputs outside that range require an explicit warning or rejection.

### Unit assumptions

- L*/L_sun is a dimensionless bolometric luminosity ratio, not apparent brightness or monochromatic luminosity.

- S_eff is dimensionless and represents stellar irradiance divided by the present solar constant at 1 AU.

- Distance output is in AU.

- Teff is in kelvin and must be absolute temperature.

- When radius is supplied, radius and R_sun must use the same length unit; the ratio is dimensionless.

- The table values used below are the standard Kopparapu solar-temperature values at Teff = 5780 K, so T' = 0 K.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

A negative luminosity produces negative square-root arguments and therefore an undefined real HZ distance. The instrument must validate luminosity as nonnegative and reject the input explicitly.

## 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": {
    "stellar_luminosity_L_sun": 1,
    "Teff_K": 5780,
    "requested_boundaries": "conservative_and_optimistic"
  },
  "expected_outputs": {
    "conservative_inner_AU": 0.950443,
    "conservative_outer_AU": 1.676004,
    "optimistic_inner_AU": 0.750312,
    "optimistic_outer_AU": 1.767767
  },
  "reference_data": {
    "runaway_greenhouse_S_eff": 1.107,
    "maximum_greenhouse_S_eff": 0.356,
    "recent_Venus_S_eff": 1.7763,
    "early_Mars_S_eff": 0.32,
    "source_convention": "Widely tabulated standard values from Kopparapu et al. 2013 Table 3, evaluated at Teff = 5780 K"
  },
  "working": "At Teff = 5780 K, T' = 5780 - 5780 = 0 K, so each S_eff equals its tabulated solar-temperature value. Conservative inner = sqrt(1.0 / 1.107) = sqrt(0.903342367) = 0.950443 AU. Conservative outer = sqrt(1.0 / 0.356) = sqrt(2.808988764) = 1.676004 AU. Optimistic inner = sqrt(1.0 / 1.7763) = sqrt(0.562969089) = 0.750312 AU. Optimistic outer = sqrt(1.0 / 0.32) = sqrt(3.125) = 1.767767 AU."
}
````

## 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-tranche7/tranche7-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`