Why Growth Stops Before Saturation: Elemental Throughput Limits in Deep Time

This paper develops a steady-state material ceiling for long-lived technological systems based on closed-loop atomic throughput. Even when stellar energy is abundant, persistent infrastructure must replace degraded material inventory. Because irrecoverable loss is non-zero over gigayear timescales, sustainable scale is bounded by replenishment-to-loss ratios of critical elements. A general upper bound on infrastructure population is derived as a minimum-operator constraint across required elements. The tightest bottleneck determines the system-level ceiling. This mechanism provides a physical route to sub-saturation equilibria without invoking coordination failure, collapse, or deliberate restraint. This work forms the material constraint layer of the Deep-Time Structural Constraints series.