Abstract: In this talk I will discuss an entropic puzzle in pure JT gravity and its resolution, which requires taking into account (doubly) non-perturbative effects in the gravitational path integral. In JT gravity, which is dual to a random matrix ensemble, the gravitational thermal entropy becomes negative at very low temperatures. This puzzle arises when computing the annealed (instead of quenched) entropy, corresponding to an incorrect averaging procedure in the dual matrix model. After defining an “intermediate” quantity, the semi-quenched entropy, I will explain how the positivity of entropy can be rescued. From the bulk perspective, both a resummation of higher-genus topologies and wormhole effects are crucial. From the matrix model perspective, the resolution relies on the statistics of eigenvalues near the edge, governed, in different regimes, by the Airy distribution or by 1-eigenvalue instantons. I will also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit. Based on arXiv:2507.10657. A related, interesting puzzle and its resolution will be described in part II by Patrick Tran on September 3rd.