Hartle-Hawking wavefunction in double scaled SYK

We compute the transition amplitude between the chord number $0$ and $\mathrm{\ell }$ states in the double scaled SYK model and interpret it as a Hartle-Hawking wavefunction of the bulk gravitational theory. We observe that the so-called un-crossed matter correlators of double scaled SYK model are obtained by gluing the Hartle-Hawking wavefunctions with an appropriate weight.