  In our earlier paper "Corrections to the Bekenstein-Hawking entropy and the
Hawking radiation spectrum", arXiv:0910.2755, we provided two concrete
numerical evidences for the new area spectrum based on the Einstein-Kaufman
pseudo tensor as opposed to the Ashtekar variables: namely, the reproduction of
the Bekenstein-Hawking entropy without fixing Immirzi parameter and the
reproduction of the Hawking radiation spectrum. In this article, we provide
another concrete, numerical evidence for this new area spectrum; there was a
constant in our earlier article, which was inversely proportional to the
density of state, and which we could not fix a priori. Nevertheless, in our
earlier article, we obtained this constant to be around 172~173 by fitting it
to the Planck radiation spectrum. In this article, we calculate this value
using another method. We obtain 172.87...which implies consistency.
