Remark: Thermal calibration is not a derivation

Choosing $p_j$ proportional to $e^{-\beta e_j}$ makes the selected $B$ marginal a finite Gibbs state. It does not derive a Hawking spectrum, greybody factors, dimensional emission rates, geometry, or transfer dynamics. Those separations are explicit in Hawk01-A, Hawk02-A, and Em03-E CHawk01A,CHawk02A,CEm03E.