Volume and Mass Fractions of the Cosmic Web's Four Components: Mean Overdensities and the Warm Share They Imply

Classifications of the cosmic web into voids, walls, filaments, and nodes return two sets of numbers — the fraction of space each component occupies and the fraction of mass it holds — and the ratio of the two is each component's mean overdensity. This paper takes stated census values in the range of published NEXUS and tidal-web classifications — volume shares 0.72 for voids, 0.19 for walls, 0.085 for filaments and 0.005 for nodes; mass shares 0.13, 0.24, 0.42 and 0.21 respectively — and derives the consequences. Mean overdensities are 0.181 for voids, 1.26 for walls, 4.94 for filaments and 42.0 for nodes. Filaments and walls together hold 0.66 of the mass in 0.275 of the volume. Applying stated warm fractions per component gives a warm share of 0.409 of all baryons — the classification route to the same warm-hot reservoir that dispersion, absorption, and stacking measure directly. Both share sets sum to 1.0 and 1.0 respectively, as they must; the paper's content is in the ratios and in what they oblige any consistent picture of the web to satisfy.