Habitable-Zone Distance (rough)

Inspectable records

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