The majority of baryons reside beyond the optical extent of a galaxy in the circumgalactic and intergalactic media (CGM/IGM). Gaseous halos are inextricably linked to the appearance of their host galaxies through a complex story of accretion, feedback, and continual recycling. The energetic processes, which define the state of gas in the CGM, are the same ones that 1) regulate stellar growth so that it is not over-efficient, and 2) create the diversity of todays galaxy colors, SFRs, and morphologies spanning Hubbles Tuning Fork Diagram. They work in concert to set the speed of growth on the star-forming Main Sequence, transform a galaxy across the Green Valley, and maintain a galaxys quenched appearance on the Red Sequence. Most baryons in halos more massive than 10^12 Msolar along with their high-energy physics and dynamics remain invisible because that gas is heated above the UV ionization states. We argue that information on many of the essential drivers of galaxy evolution is primarily contained in this missing hot gas phase. Completing the picture of galaxy formation requires uncovering the physical mechanisms behind stellar and SMBH feedback driving mass, metals, and energy into the CGM. By opening galactic hot halos to new wavebands, we not only obtain fossil imprints of >13 Gyrs of evolution, but observe on-going hot-mode accretion, the deposition of superwind outflows into the CGM, and the re-arrangement of baryons by SMBH feedback. A description of the flows of mass, metals, and energy will only be complete by observing the thermodynamic states, chemical compositions, structure, and dynamics of T>=10^6 K halos. These measurements are uniquely possible with a next-generation X-ray observatory if it provides the sensitivity to detect faint CGM emission, spectroscopic power to measure absorption lines and gas motions, and high spatial resolution to resolve structures.
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