What is completed

Hawking's original result is a semiclassical field-theory calculation, not a theorem of nonperturbative quantum gravity Hawking1975. The present paper is an explicit identification and calculation of one fixed-background observable. It is not a novelty claim for the Hawking effect.

The mathematical release is:

The temperature is not supplied as calibration data. It emerges from the affine-to-Killing coordinate relation after surface gravity has been computed. The greybody factor is not supplied as a numerical table. It is defined constructively by the same metric's radial scattering equation.

The choice of state is nevertheless essential. This paper does not claim that a metric and a classical wave equation uniquely determine a quantum emission law.