LH$μ$C: A high energy, high luminosity muon-hadron collider at CERN

The latest developments regarding the feasibility of muon-hadron collisions, achieved through the major reuse of LH$e$C infrastructure, are presented - at the LH$μ$C, a 1 or 2 TeV $μ^+$ beam collides with a 7 TeV proton beam, resulting in the $μ^+p$ centre-of-mass energy of 5.3 or 7.5 TeV, respectively, at an average luminosity close to $10^{34}$cm$^{-2}$s$^{-1}$. First, a concise scientific motivation is given, including exceptional prospects for neutrino science, and is followed by a presentation of the LH$μ$C concept in a nutshell - from the source of ultra-cold anti-muons, through the muon booster, to the main muon ring. Basic considerations regarding the machine-detector interface and the general-purpose detector are also presented. The paper concludes with an outlook underlying unique and powerful synergies between the LH$μ$C, LH$e$C, FCC and Muon Collider projects.