Climbing the $N$-point Ladder Part I: Information in the Higher-Order Configuration-Space Clustering of Dark Matter Halos

We quantify the information content of the configuration-space two-, three-, and connected four-point correlation functions of Quijote dark-matter haloes at $z=0$ and fixed number density. We build Fisher forecasts for $\{Ω_m, Ω_b, h, n_s, σ_8, M_ν\}$ in real and redshift space from ${\sim}38{,}000$