This paper presents a catalogue of the largest under-dense and over-dense regions in the local Universe. The authors use galaxy distance data from the CosmicFlows-4++ Zone of Avoidance (CF4++ ZOA) catalogue out to redshift z = 0.1 to identify 37 cosmic voids and 42 converging “knot” regions. The voids have effective radii between about 13 and 38 h⁻¹ Mpc. The knot volumes range from about 10^4 to 3.3×10^5 h⁻3 Mpc^3.

Instead of defining voids by where galaxies are missing, the team used the V-web method, a dynamically motivated classifier. It starts from the reconstructed three-dimensional peculiar velocity field of matter. The method computes the velocity shear tensor — a measurement of how nearby flows stretch or squeeze space — and finds its three eigenvalues at each point. Where all three eigenvalues are positive, the flow is expanding in all directions and the region is called a void. Where all three are negative, the flow is converging and the region is called a knot. Intermediate signs correspond to sheets and filaments.

To get the velocity field they applied a Bayesian reconstruction using Hamiltonian Monte Carlo (HMC) sampling. HMC is a statistical method that explores many possible reconstructions consistent with the distance data. They ran more than 10,000 HMC steps and used both the individual realizations and the overall mean field. The analysis used a grid of 128^3 cells spanning 1000 h⁻¹ Mpc, so each voxel is 7.8 h⁻¹ Mpc on a side. Candidate void centres were found by locating minima in a hierarchical field of the V-web classification. Regions were grown with a flood-fill algorithm, minima were kept at least 20 h⁻¹ Mpc apart, and a structure was accepted only if it appeared in at least 68% of the HMC realizations and did not have more than 50% of its volume outside the survey boundaries.

This work matters because it ties the large-scale map of the cosmic web to dynamics. Voids and knots identified from velocity flows are directly linked to the underlying gravitational motion, rather than only to the distribution of visible galaxies. Such a dynamical catalogue can help studies of how structure grows, tests of gravity on large scales, and investigations of how galaxy properties depend on their environment.