When Solutions Do Not Exist: Physical Limits on Planetary Futures

This study presents a constraint-driven computational framework for evaluating the physical feasibility of planetary-scale futures under realistic limits, without presupposing the existence of viable interventions, materials, or optimization pathways. Unlike conventional global risk models that operate within an assumed solution space, the framework eliminates predefined technologies, material libraries, and risk weightings, allowing future trajectories to survive or collapse based solely on physical realizability, resource boundedness, scalability, and cross-domain self-consistency. Applied to a coupled Earth system model spanning climate, biosphere, infrastructure, logistics, energy systems, and human mobility over a 20-year horizon, the framework demonstrates that nearly all candidate futures fail due to physical infeasibility rather than policy or economic insufficiency. A single convergent solution topology emerges, exhibiting zero topological variance across viable trajectories. This solution cannot be realized using known material capabilities. The framework therefore identifies the necessity of a previously undefined class of matter, specified by functional and structural requirements rather than chemical identity, as a prerequisite for planetary-scale stability under the modeled conditions. These findings reposition materials capability as an upstream determinant of global feasibility and introduce a falsifiable method for mapping hard physical limits on future planetary interventions.