Why the Northern Hemisphere Needs a 30-40m Telescope and the Science at Stake: Ultra-Low-Mass Dwarf Galaxies Across the Boreal Cosmic Web

Dwarf galaxies dominate the galaxy population in the nearby Universe and occupy the regime where feedback, reionization, and environment exert their strongest influence on galaxy formation. Despite their importance, detailed spectroscopic constraints on the faintest dwarfs are currently limited to a handful of systems in the Local Volume, leaving the role of large-scale environment essentially unexplored at ultra-low stellar masses. A northern 30-40m class telescope equipped with a multiplexed optical integral-field spectrograph will enable a systematic, spatially resolved spectroscopic census of dwarf galaxies with $M_\star \sim 10^{5}-10^{7} M_\odot$ across a wide range of environments. A deep survey of the Coma Cluster, combined with targeted observations of dwarfs in clusters, groups, filaments, and low-density regions, will map star formation histories, chemical enrichment, and internal kinematics at unprecedented depth. This program will directly test models of dark-matter physics, early-Universe feedback, and environmental quenching in the lowest-mass galaxies, establishing dwarf galaxies as precision probes of both galaxy formation and fundamental physics.