  We consider a simplified model of double scaled SYK (DSSYK) in which the
Hamiltonian is the position operator of the Harmonic oscillator. This model
captures the high temperature limit of DSSYK but could also be defined as a
quantum theory in its own right. We study properties of the emergent geometry
including its dynamics in response to inserting matter particles. In
particular, we find that the model displays de Sitter-like properties such as
that infalling matter reduces the rate of growth of geodesic slices between the
two boundaries. The simplicity of the model allows us to compute the full
generating functional for correlation functions of the length mode or any
number of matter operators. We provide evidence that the effective action of
the geodesic length between boundary points is non-local. Furthermore, we use
the on-shell solution for the geodesic lengths between any two boundary points
to reconstruct an effective bulk metric and reverse engineer the dilaton
gravity theory that generates this metric as a solution.
