Emergent Cosmic Web and Dark Matter Halos in a Background-Free Quantum Graph

In standard cosmology, the ``CDM model posits that dark matter halos form the structural scaffolding of the cosmic web, gravitationally anchoring visible baryonic matter. In this paper we test whether a similar large-scale partition can emerge spontaneously in the QGEFT framework from geometry alone. On a thermalized `N=1024` graph background, we define three sectors using only local graph observables: a triangle-rich visible sector capable of supporting gauge fields, a high-degree but triangle-free dark sector representing massive but gauge-blind topological halos, and a low-degree vacuum bulk. We find a sharp spontaneous mass partition: `85. 23%` of the connectivity mass lies in the vacuum bulk, `14. 26%` in dark halos, and only `0. 51%` in the visible sector, corresponding to an effective dark-to-visible mass ratio of about `28: 1`. The topological proximity test is even sharper: `100%` of the visible nodes lie exactly one graph hop from the nearest dark halo and also one hop from the corresponding halo core, while random bulk nodes sit farther away with mean distance `2. 0`. The narrow claim supported by the current benchmark is that the QGEFT surrogate naturally generates a ``CDM-like cosmic web as a purely topological feature of the cooling spacetime graph, without introducing a separate dark-matter particle sector.