Terraeon is not a building, but a time-based architectural system. Located on the Red Hook waterfront, it responds to heat, flooding, impermeable ground, and carbon-intensive construction by transforming urban waste into a living material infrastructure. Inspired by Korea’s Joseon Dynasty toseokdam, Terraeon reinterprets stone and earth as incomplete, repairable, and collective architecture. Salvaged stone, soil, biochar, and lime accumulate over time to form dry-stacked compression walls, arches, cross vaults, and rib networks shaped by load flow rather than formal design. Above the structure, soil and biochar create an ecological roof that retains water, supports vegetation, stores carbon, and moderates heat. Built through public funding, research institutions, trained citizens, and cooperative labor, Terraeon grows, decays, and repairs itself continuously. It proposes architecture not as a finished object, but as a long-term system of accumulation, maintenance, ecology, and shared time.