Evaporation Time to the Remnant: How the Density Cap Shortens the Hawking Lifetime

For an initial mass of 1e12 kilograms the full lifetime is 8.411e+19 seconds and the time to reach the remnant is 8.406e+19 seconds; the saved fraction is 6.493e-04, utterly negligible, because the remnant mass of 8.659e+10 kilograms is about one order of magnitude below the initial mass and the cube of that ratio suppresses the saved tail. Even at 1e15 kilograms the saved fraction is only 6.494e-13. The cap therefore leaves the familiar lifetime essentially untouched for every hole heavy enough to discuss observationally. A negative result of this cleanliness is useful. Computed from stated assumptions, not measured.