This paper addresses the problem of defining the non-perturbative bulk Hilbert space in $2d$ JT gravity, both with and without matter. The authors provide the first explicit definition of a non-perturbative Hilbert space specified in terms of metric variables, where states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. They identify null states and discuss their importance for defining operators non-perturbatively. To highlight the power of their formalism, they study two bulk linear operators that serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge, and the other captures the center-of-mass collision energy between two particles falling from opposite sides. They track the behavior of these operators up to times of order \(e^{S_{\text{BH}}}\), at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, their results indicate an \(O(1)\) probability of detecting a firewall at late times that is self-averaging and universal.This paper addresses the problem of defining the non-perturbative bulk Hilbert space in $2d$ JT gravity, both with and without matter. The authors provide the first explicit definition of a non-perturbative Hilbert space specified in terms of metric variables, where states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. They identify null states and discuss their importance for defining operators non-perturbatively. To highlight the power of their formalism, they study two bulk linear operators that serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge, and the other captures the center-of-mass collision energy between two particles falling from opposite sides. They track the behavior of these operators up to times of order \(e^{S_{\text{BH}}}\), at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, their results indicate an \(O(1)\) probability of detecting a firewall at late times that is self-averaging and universal.