The analogy between Multi-scale Entanglement Renormalization Ansatz (MERA) and the spatial slice of three-dimensional anti-de Sitter space (AdS3) has motivated a great interest in tensor networks among holographers. I discuss a way to promote this analogy to a rigorous, quantitative, and constructive relation. A key quantitative ingredient is the way the strong subadditivity of entanglement entropy is encoded in MERA and in a holographic spacetime. The upshot is that the map between MERA and the spatial slice of AdS3 is mediated through an additional integral transform. Interpreted directly, MERA is a discretization not of the spatial slice of AdS3, but of the space of geodesics on the spatial slice of AdS3.