Modulus Matrix is an 85-home social-rental building in Cornellà (Barcelona metropolitan area) conceived as a low-carbon, low-energy prototype for dense urban housing—and in 2024 it won the RIBA International Prize, the overall winner of the RIBA International Awards cycle. Its primary sustainability lever is embodied carbon. Around 8,300 m² of locally sourced timber was used in the superstructure, delivered through prefabricated, dry assemblies that reduce waste, shorten construction time and lower site impacts, while cutting embodied CO₂ compared with conventional heavy structures. Timber use was also economically optimised (around 0.24 m³ per m² built) to keep high environmental performance compatible with social-housing budgets. Operational demand is reduced to a minimum through passive comfort. A central planted courtyard acts as a shaded microclimate and social neighbourhood square; four corner stair cores make it the shared point of arrival, reducing enclosed internal corridors. Open galleries and private balconies add intermediate buffer zones that temper heat, provide outdoor space and shade and encourage everyday use. Every dwelling is dual-oriented, enabling cross-ventilation and night purging in summer, and façades integrate screens and Barcelona shutters to combine solar control, daylight and privacy. By prioritising shade, airflow and robust envelopes over mechanical complexity, the building supports stable comfort with minimal energy. Sustainability is also social and long-term: generous shared spaces foster neighbourliness, improve perceived safety and care, and support interdependence in daily routines. Flexible room sizes allow changing household needs over decades, extending service life and reducing future refurbishment impacts. Modulus Matrix demonstrates how carbon, comfort and community can be delivered together on a very low budget.