The Geometry of Evolving Viability: Nested Constraints, Corrective Capacity, and Food-System Continuation

This exploratory research preprint develops a mathematical and conceptual synthesis within Living Information Systems Dynamics (LISD), investigating how interacting systems preserve or lose their capacity for continued viable evolution. The framework connects three established mathematical concepts: barycentric geometry, constrained three-body dynamics, and viability theory. Together, they motivate a distinction between a system's apparent stability, its dynamically reachable states, and its capacity to maintain viable trajectories through time. A geometric construction demonstrates how pairwise compatibility can persist after joint feasibility disappears. A stronger bounded-steering model establishes that every instantaneous constraint set and every pairwise trajectory can remain feasible while no jointly admissible trajectory exists below an exact minimum correction rate. The paper extends this analysis to an illustrative food-system model, examining how increasing technological productivity can coexist with declining ecological resources and shrinking safety margins for future food production. An updated LISD operator language organizes these relationships across physical, biological, technological, and collective systems, emphasizing feedback, correction, and evolving boundaries. The central proposition is that present performance does not necessarily reveal the loss of future viability, and continued alignment depends on sufficient corrective capacity. The manuscript distinguishes established mathematics from proposed cross-domain interpretations and identifies directions for empirical validation.