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A high-dynamic-range view of the growth of structure and the warm/hot Universe

Baryons heat to temperatures above $>\!\!10^5\,\mathrm{K}$ as they accrete onto massive overdensities -- galaxies, groups, clusters, and filaments -- where they ionize and become optically transparent. Deep mm-wave observations such as those with ALMA have begun to probe a handful ($\sim\,$4) of massive systems at $z\!\sim\!2-4$, while low-resolution mm-wave surveys have detected thousands of objects at arcminute resolution out to $z\!\approx\!2$. To truly advance the field of the evolution of large-scale structures, mapping the warm/hot distribution of ionized gas out to the redshift of their formation, the ESO community requires a large-aperture single-dish (sub-)mm telescope. This will need to provide several orders of magnitude higher mapping speeds than currently available while preserving the few arcsecond resolution required for imaging the gas and removing contaminating radio and dusty thermal signals across the full (sub-)mm wavelength range.