Archaeological investigation of galaxies' evolutionary history in the cosmic middle ages

The cosmic Middle Ages, spanning the last 8-10 Gyr of the Universe, is a critical period in which massive early-formed systems coexist with global star formation quenching in less massive galaxies, yet galaxies experience further dynamical, morphological and chemical evolution. Understanding the relative role of internal drivers and of interaction with the evolving large-scale structures remains a highly complex and unsettled issue. To make transformative progress on these questions we must characterize the physical and kinematic properties (integrated and spatially resolved) of stellar populations in galaxies, fossil record of their past star formation and assembly histories, together with gas properties, across a wide range of masses and environmental scales, over this critical cosmic epoch. Volume-representative samples of 10^6 galaxies down to 10^9 solar masses are essential to fully trace the complex interplay between physical processes and to physically connect progenitor and descendant galaxy populations. This demands a deep and extensive survey with high signal-to-noise, medium-resolution, rest-frame optical spectroscopy. Current and planned facilities in the 2020-2030s cannot simultaneously achieve the required sample size, spectral quality, mass limit, and spatial coverage. A dedicated large-aperture spectroscopic facility with wide-area high-multiplex MOS and large field-of-view IFU is needed to provide transformative insights into the physical mechanisms regulating star formation and galaxy evolution.