Preprint Frames Planetary Sustainability as Coupled Finite-Buffer Dynamics

The paper constructs a minimal nonequilibrium dynamical system linking a regenerative resource stock, an accumulating waste stock, and an aggregate activity variable. It distinguishes a soft waste threshold that suppresses growth while processing remains possible from a hard threshold at which waste production exceeds maximum removal capacity. The framework explicitly incorporates recycling efficiencies, multiple resource and waste classes, and an analogy to cellular, organismal, and planetary scales of life-support function.

Gazeau positions the work against the 1972 Limits to Growth report, the 2009 planetary-boundaries framework, and stock-pollution economic models, arguing that carrying capacity is an emergent, time-dependent property rather than a fixed number. The dominant constraint shifts according to the relative reserve times of each buffer, a principle illustrated by a toy numerical example showing how technological or institutional changes can alter which threshold is encountered first.

The approach remains purely theoretical; no empirical calibration or validation against global datasets is presented. Strengthening would require coupling the model to observed time series of resource depletion rates and waste-removal capacities, then testing whether predicted threshold crossings align with historical or projected trajectories under different policy scenarios.