Work-Induced Specialization and Trade-offs in Future Capabilities of Adaptive Physical Networks

Mandatory activity can change the organization of an adaptive physical network even when its current input--output function is restored. We ask what this activity necessarily leaves available for future functional changes. For a declared class of controlled conductance networks, we compare the true minimum times of future tasks from the initial carrier and from the terminal carrier after the same mandatory work. Under explicit physical regularity, material saturation and absolute terminal-selection conditions, every sufficiently efficient execution has both strict improvements on a positive-radius cap of a fixed future-task sphere and strict deterioration on another such cap. The deterioration region is common to all such executions; an improvement region is selected from a fixed finite menu and may depend on the terminal organization. A material-demand bound supplies the obstruction, while an inward native lift converts a directional speed advantage into a feasible finite-task improvement. All controllers may learn, prepare and take admissible detours, and the future request is disclosed only after work ends. Separate results give exact zero readiness overhead for reflected work and positive absolute overhead for a different directed family. The family theorem applies at a small but fixed future amplitude; it does not provide a complete future profile or a universal law of plasticity.