Luminosity from Radius & Temperature mechanism

Model scope

The mathematical formula is standard and correct, but the catalog entry needs explicit input units, numerical constants and precision conventions, and an honest label such as bolometric luminosity under the spherical blackbody/effective-temperature assumption.

• The Stefan-Boltzmann formula L = 4πR²σT⁴ is correct for bolometric luminosity of an approximately spherical radiating body when T is effective temperature.
• The specification does not state whether radius is supplied in metres or solar radii, nor whether temperature is in kelvin.
• The L_sun output requires a defined solar-luminosity convention; the specification names L_sun but does not provide its numerical value or standard.

Units and conventions

• For SI luminosity in watts, radius R must be in metres, temperature T must be in kelvin, and σ = 5.670374419×10^-8 W m^-2 K^-4.
• Test vectors use R_sun = 6.957×10^8 m and L_sun = 3.828×10^26 W, the IAU nominal solar radius and luminosity conventions.
• L_sun output is computed as luminosity in watts divided by 3.828×10^26 W.
• The result is bolometric luminosity, not luminosity in a particular photometric band.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "radius_m": 695700000,
    "effective_temperature_K": 5772
  },
  "expected_outputs": {
    "luminosity_W": 3.82799e+26,
    "luminosity_L_sun": 0.999996
  },
  "working": "R² = (6.957×10^8 m)² = 4.8399849×10^17 m². T² = 5772² = 33,315,984 K², so T⁴ = 33,315,984² = 1.10995479×10^15 K⁴. 4πR²σ = 12.566370614 × 4.8399849×10^17 × 5.670374419×10^-8 = 3.448776×10^11 W K^-4. L = 3.448776×10^11 × 1.10995479×10^15 = 3.82799×10^26 W. L/L_sun = 3.82799×10^26 / 3.828×10^26 = 0.999996."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme-magnitude vector produces Infinity in ordinary JavaScript arithmetic because T⁴ overflows binary64, and the specification provides no stated overflow handling or input validation. A secondary hazard is unit ambiguity because the formula requires metres and Kelvin but the input schema does not specify units.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json