A Cold-Remnant Temperature Law: Where the Specific Heat of an Evaporating Hole Changes Sign

The turnover sits at 1.500e+11 kilograms by the analytic route and 1.499e+11 kilograms by the numerical scan, agreement at the quoted precision. The maximum temperature is 5.454e+11 kelvin. At ten remnant masses the model gives 1.403e+11 kelvin against the uncorrected Hawking value 1.417e+11 kelvin, a one-percent correction, so the law is invisible until the end-stage and decisive only there, exactly the behaviour a candidate endpoint law should have. Below the turnover mass the specific heat is positive: losing mass lowers the temperature, evaporation throttles itself, and the approach to the remnant is asymptotic and gentle rather than explosive. Computed from stated assumptions, not measured.