Predicted total mass of the LG of galaxies based on the proper motion of M 31 towards us (TA) with the simulation calibrations. The figure compares masses inferred from different embedding with ä/a vs. pure Λ, and from different methods in the literature: the virial theorem (Diaz et al. 2014), Hubble flow (Peñarrubia et al. 2014), TA + Λ + LMC (Benisty et al. 2022), artificial neural networks on simulated pairs (McLeod et al. 2017), and Gaussian processes on simulated pairs (Sawala et al. 2023b). The red area shows the uniform range M_MW + M₃₁ ∈ [1.9, 3.3]×10¹² M_⊙ which is based on complementary total mass estimate of the MW and M 31 galaxies (Wang et al. 2020; Sawala et al. 2023b). The total LG virialized mass should be higher then the total halo masses.