The Feedback-based knowledge Repository for IntegrateD Assessments (FRIDA) v3.1 is a fully coupled climate-human systems model designed to explore the global long-term co-evolution of environmental, technological, economic, financial, and social processes under deep uncertainty. While many integrated assessment models represent climate damages primarily through aggregate economic impacts, important feedbacks among human behaviour, energy systems, land use, climate impacts, technological change, and financial stability remain weakly represented or exogenous. FRIDA v3.1 addresses this limitation through a system dynamics framework that embeds these processes within a unified feedback-rich structure, enabling emergent dynamics to arise from interactions across sectors rather than from externally prescribed assumptions. Building on earlier model versions, FRIDA v3.1 introduces representations of climate-driven wildfire dynamics, endogenous fertilizer use, sectorally disaggregated and behaviourally-informed energy demand, climate impacts on wind energy productivity, endogenous life expectancy, carbon capture and storage technologies, and macro-financial policy mechanisms designed to reduce climate-related financial risks. The model integrates these additions with existing representations of the climate system, carbon cycle, hydrology, population, economy, agriculture, land use, and energy supply. Calibration and evaluation against a large historical dataset and extensive uncertainty ensembles show that the updated model reproduces history while generating novel feedbacks that influence future development pathways. FRIDA v3.1 advances the capacity of integrated assessment modelling to investigate how behavioural, biophysical, technological, and financial processes jointly shape climate outcomes, providing a transparent and computationally efficient platform for uncertainty analysis, scenario exploration, and policy assessment in a rapidly changing world.