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Non-line-of-sight reconstruction (NLoS) is a novel indirect imaging modality that aims to recover objects or scene parts outside the field of view from measurements of light that is indirectly scattered off a directly visible, diffuse wall. Despite recent advances in acquisition and reconstruction techniques, the well-posedness of the problem at large, and the recoverability of objects and their shapes in particular, remains an open question. The commonly employed Fermat path criterion is rather conservative with this regard, as it classifies some surfaces as unrecoverable, although they contribute to the signal. In this paper, we use a simpler necessary criterion for an opaque surface patch to be recoverable. Such piece of surface must be directly visible from some point on the wall, and it must occlude the space behind itself. Inspired by recent advances in neural implicit representations, we devise a new representation and reconstruction technique for NLoS scenes that unifies the treatment of recoverability with the reconstruction itself. Our approach, which we validate on various synthetic and experimental datasets, exhibits interesting properties. Unlike memory-inefficient volumetric representations, ours allows to infer adaptively tessellated surfaces from time-of-flight measurements of moderate resolution. It can further recover features beyond the Fermat path criterion, and it is robust to significant amounts of self-occlusion. We believe that this is the first time that these properties have been achieved in one system that, as an additional benefit, is trainable and hence suited for data-driven approaches.