Cosmic Web Formalism

This paper develops the mathematical and geometric formalism underlying the cosmic web within the MID/QC framework. Instead of treating large‑scale structure as the emergent outcome of gravitational collapse seeded by primordial fluctuations, the analysis derives filamentary networks as coherence‑tension ridges formed by substrate‑level flow and gradient alignment. The formalism introduces ridge operators, coherence‑gradient tensors, and tension‑flow equations that generate filament morphology, void expansion, and multi‑scale alignment as natural solutions. This substrate‑first approach provides a unified mathematical basis for cosmic web structure, guided lensing behavior, and the emergence of ultra‑large coherent features that challenge ΛCDM expectations.