  We establish the Lorentzian AdS$_2$/CFT$_1$ correspondence from a
reconstruction of all bulk points through the kinematic-space approach. The OPE
block is exactly a bulk local operator. We formulate the correspondence between
the bulk propagator in the non-interacting scalar field theory and the
conformal block in CFT$_1$. When we consider the stress tensor, the variation
probes the variation of AdS$_2$ metric. The reparameterization provides the
asymptotic boundary of the bulk spacetime as in the derivation of the
Schwarzian theory from two-dimensional dilaton gravity theory. Finally, we find
the AdS$_2$ Riemann curvature tensor based on the above consistent check.
