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Hydrogen oscillation into a dark-sector state $H'$ has recently been proposed as a novel mechanism through which hydrogen can be cooled during the dark ages -- without direct couplings between the Standard Model and dark matter. In this work we demonstrate that the requisite mixing can appear naturally from a microphysical theory, and argue that the startling deviations from standard cosmology are nonetheless consistent with observations. A symmetric mirror model enforces the necessary degeneracy between $H$ and $H'$, and an additional twisted $B+L'$ symmetry dictates that $H$-$H'$ mixing is the leading connection between the sectors. We write down a UV completion where $\sim$ TeV-scale leptoquarks generate the partonic dimension-12 mixing operator, thus linking to the energy frontier. With half of all $H$ atoms oscillating into $H'$, the composition of the universe is scandalously different during part of its history. We qualitatively discuss structure formation: both the modifications to it in the Standard Model sector and the possibility of it in the mirror sector, which has recently been proposed as a resolution to the puzzle of early supermassive black holes. While the egregious loss of SM baryons mostly self-erases during reionization, to our knowledge this is the first model that suggests there should be missing baryons in the late universe, and highly motivates a continued, robust observational program of high-precision searches for cosmic baryons.