  In loop quantum gravity the quantum states of a black hole horizon are
produced by point-like discrete quantum geometry excitations (or {\em
punctures}) labelled by spin $j$. The excitations possibly carry other internal
degrees of freedom also, and the associated quantum states are eigenstates of
the area $A$ operator. On the other hand, the appropriately scaled area
operator $A/(8\pi\ell)$ is also the physical Hamiltonian associated with the
quasilocal stationary observers located at a small distance $\ell$ from the
horizon. Thus, the local energy is entirely accounted for by the geometric
operator $A$.
  We assume that: In a suitable vacuum state with regular energy momentum
tensor at and close to the horizon the local temperature measured by stationary
observers is the Unruh temperature and the degeneracy of `matter' states is
exponential with the area $\exp{(\lambda A/\ell_p^2)}$---this is supported by
the well established results of QFT in curved spacetimes, which do not
determine $\lambda$ but asserts an exponential behaviour. The geometric
excitations of the horizon (punctures) are indistinguishable. In the
semiclassical limit the area of the black hole horizon is large in Planck
units.
  It follows that: Up to quantum corrections, matter degrees of freedom
saturate the holographic bound, {\em viz.} $\lambda=\frac{1}{4}$. Up to quantum
corrections, the statistical black hole entropy coincides with
Bekenstein-Hawking entropy $S={A}/({4\ell_p^2})$. The number of horizon
punctures goes like $N\propto \sqrt{A/\ell_p^2}$, i.e the number of punctures
$N$ remains large in the semiclassical limit. Fluctuations of the horizon area
are small while fluctuations of the area of an individual puncture are large. A
precise notion of local conformal invariance of the thermal state is recovered
in the $A\to\infty$ limit where the near horizon geometry becomes Rindler.
