Enabling Cosmic Web Analysis at Gigaparsec Scales: A Multi Block Approach for DisPerSE
Cosmic filaments are the longest structures in the Universe and the dominant element of the cosmic web, channelling matter onto clusters and shaping the environments in which galaxies form and evolve. Accurate reconstructions of this network across gigaparsec volumes are increasingly important for cosmology and galaxy evolution. However, the most commonly used topological filament finder, DisPerSE (Discrete Persistent Structures Extractor), faces a memory bottleneck: it requires a Delaunay tessellation of the full input point set, preventing application to large simulations. Naively splitting the volume fails, as different sub-volumes yield inconsistent tessellations and filament networks. We present a frozen-core method that overcomes this bottleneck while preserving the global topology. The volume is decomposed into overlapping blocks whose tessellations are filtered by a circumsphere criterion retaining only globally valid tetrahedra; a post-processing pipeline merges the tiled outputs through core filtering, deduplication, and boundary stitching. Validation against a monolithic reference on a $300\,h^{-1}\,\mathrm{Mpc}$ MDPL2 subvolume shows 99.6% total length recovery, 100% recovery of density maxima and minima, and 94.7% individual filament matching (the ${\sim}$5% of unmatched filaments are predominantly short, low-significance structures). We apply the method to the full $(1\,h^{-1}\,\mathrm{Gpc})^3$ MDPL2 box (92 million haloes), producing a gigaparsec-scale filament catalogue. As a first application, we measure the connectivity ($\kappa$) for 22,900 haloes spanning $M_{200\mathrm{c}} = 10^{12}$-$10^{15.5}\,h^{-1}\,\mathrm{M}_\odot$, finding a power-law mass-connectivity relation that extends from group to cluster scales, providing the first confirmation in an $N$-body halo catalogue that the theoretically predicted scaling holds across three decades in halo mass.