Holographic Residual Dark Matter IV: Cosmic Voids as Hill-like Residual Geometric Perturbations

This technical preprint presents Paper IV of the Holographic Residual Dark Matter (HRDM) series. Papers I--III formulated HRDM as a non-particle interpretation of the gravitational phenomena conventionally modeled as cold dark matter, developed a galaxy-scale phenomenology, and interpreted merging-cluster lensing-gas offsets as baryonic displacement from a persistent residual gravitational well. The present note extends the framework from residual wells to residual hills. In HRDM, the residual component X is not restricted to attractive well-like structures. More generally, X is treated as a residual geometric perturbation field with both well-like and hill-like branches. Well-like residual geometry can retain baryons and appear as galaxies, filaments, clusters, and positive lensing convergence. Hill-like residual geometry does not efficiently retain baryonic matter and can appear observationally as baryon-poor regions, with cosmic voids representing the most prominent large-scale expression of this branch. The proposal is not that standard cosmic voids are absent from conventional cosmology. In the standard picture, voids arise from initially underdense regions whose matter flows toward surrounding overdensities. HRDM reinterprets the ontology of those underdensities: the seed of a void may be a hill-like residual geometric perturbation rather than only a particle-density deficit. This version emphasizes the observational tests that can distinguish this interpretation: a broad negative-convergence hill field, lensing-defined versus galaxy-defined void centers, void convergence profiles, hill-to-well transition regions, and the relation between void lensing and ISW imprints. The note remains phenomenological and does not present a full void-lensing or structure-formation simulation.