  Elastic moduli and dislocation core energy of the triangular solid of hard
disks of diameter $\sigma$ are obtained in the limit of vanishing dislocation-
antidislocation pair density, from Monte Carlo simulations which incorporates a
constraint, namely that all moves altering the local connectivity away from
that of the ideal triangular lattice are rejected. In this limit, we show that
the solid is stable against all other fluctuations at least upto densities as
low as $\rho \sigma^2 = 0.88$. Our system does not show any phase transition so
diverging correlation lengths leading to finite size effects and slow
relaxations do not exist. The dislocation pair formation probability is
estimated from the fraction of moves rejected due to the constraint which
yields, in turn, the core energy E_c and the (bare) dislocation fugacity y.
Using these quantities, we check the relative validity of first order and
Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) melting scenarios and obtain
numerical estimates of the typical expected transition densities and pressures.
We conclude that a KTHNY transition from the solid to a hexatic phase preempts
the solid to liquid first order transition in this system albeit by a very
small margin, easily masked by crossover effects in unconstrained
``brute-force'' simulations with small number of particles.
