Abstract

This paper studies networks of bounded evaluators in which the interface graph itself is not fixed but may be synthesized subject to declared communication permissions. Building on prior fixed-point composition and interface-commensuration results, it asks four ordered questions: whether declared demands are realizable, what capability closure follows from a chosen augmentation, which augmentations minimally realize the demands, and how a separately declared objective may select among those realizations. For finite fixed-carrier systems with reusable full-disclosure interfaces, capability closure is shown to be exactly the meet of the initial kernels of all reachable ancestors. Consequently, capability factors through the network’s reachability preorder. Existence of a realizing augmentation reduces to a single reachability computation followed by the corresponding realizability test. The central separation is that attainability does not determine realization. Minimal realizing augmentations may form a nontrivial antichain, their intersection may realize nothing, and distinct minimal realizations may induce different excess capability even while satisfying the same declared demand. Thus feasibility and the consequences of any fixed realization are canonical, while the realizing network generally is not. Selection among realizations therefore requires an independently declared objective rather than following from capability closure itself. The paper further proves objective-relativity, gives a displayed counterexample to locally greedy interface synthesis, and separates reusable-edge confluence, relay depth, single-use order dependence, and cyclic iteration cost. The results locate a formal boundary between what network structure determines and what remains a matter of declared policy, objective, and authority. Scope is finite, deterministic, static, set-level, and fixed-carrier.