The nature of dark matter remains unknown. This paper proposes a geometric model: dark matter is a primordial, slowly evolving foam — a continuous, fractal scaffold that constitutes the skeleton of the universe. Ordinary matter does not clump under pressure but instead fills the voids of this foam without resistance. This filling process explains the observed cosmic web (JWST COSMOS-Web map, 2026) as a ghost trace of the underlying foam. The foam is not strictly timeless; it evolves on timescales far longer than the current age of the universe, making it effectively static over cosmic history. Time dilation emerges from matter's position within the foam, with limits that avoid singularities and respect causality. Gravitational waves propagate through the foam walls analogously to pressure waves through Earth's atmosphere (Hunga Tonga 2022). The model accounts for redshift asa cumulative path effect, for large-scale structure without dark energy, and for the "tree ring" appearance of the cosmic web. The Local Void — a 150—300 Mly underdense region adjacentto the Local Group — provides a nearby laboratory. Observational predictions include:a quantitative gradient in stellar age and metallicity across the Local Sheet (∆[Fe/H]∼0.1− 0.2 dex per 10 Mpc), gravitational wave echoes from foam walls, and small-scale CMBanisotropies matching a fractal pattern.