  The emergence of the bulk Hilbert space is a mysterious concept in
holography. In arXiv:1811.02584, the SYK model was solved in the double scaling
limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert
space of double scaled SYK by slicing open these chord diagrams; this Hilbert
space resembles that of a lattice field theory where the length of the lattice
is dynamical and determined by the chord number. Under a calculable
bulk-to-boundary map, states of fixed chord number map to particular entangled
2-sided states with a corresponding size. This bulk reconstruction is
well-defined even when quantum gravity effects are important. Acting on the
double scaled Hilbert space is a Type II$_1$ algebra of observables, which
includes the Hamiltonian and matter operators. In the appropriate quantum
Schwarzian limit, we also identify the JT gravitational algebra including the
physical SL(2,R) symmetry generators, and obtain explicit representations of
the algebra using chord diagram techniques.
