Paper 63: Cosmic Web Emergence from Phase Gradient Flow: Filaments, Voids, and Walls in Holosphere Theory

We propose a structural mechanism for the formation of the cosmic web—its filaments, voids, walls, and junctions—based on angular phase gradient flow in the Holosphere lattice. In this framework, space is composed of discrete, spinning units (Holospheres) that propagate coherence across nested shells. Filaments emerge where angular phase gradients align constructively, while voids form in regions of destructive interference and coherence suppression. A universal percolation slope of beta = 3/2 limits angular strain propagation, setting a maximum extent for filaments and a coherence-based cutoff for void size. This framework predicts filament length scaling with angular seed strength and exponential suppression of large voids. Observational forecasts from the Euclid mission support this model, showing a steep decline in the number of voids above 40 h⁻¹ Mpc and typical void spacing between 100 and 300 Mpc—consistent with Holosphere Theory’s strain saturation threshold. This percolation limit also appears in prior Holosphere papers explaining galaxy rotation curves, redshift, and gravitational memory, suggesting it functions as a universal design constant. Unlike standard cosmology, no dark matter, inflation, or initial density seeds are required. Cosmic structure arises deterministically from recursive angular coherence flow in a rotating lattice. This coherence-based view unifies the architecture of the universe across scales and offers falsifiable predictions for filament widths, void spacing, and network topology.