Percentage difference between alternative DM theories (ADM) and CDM power spectra. The power spectra data for FDM and WDM are from May & Springel (2023) and Viel et al. (2012) with a DM mass parameter of 2.5 × 10⁻²² eV and 2 keV at z = 3 and z = 0, respectively. The cut-offs observed in WDM and FDM, similar to those in the Monge-Ampère model but occurring at different scales, are expected to induce differences in halo connectivity compared to CDM.