Partial Identification of Network Causal Effects under Structural Support Deficiency

Repeated network experiments can leave policy contrasts unidentified even as sampling error vanishes: operational constraints assign zero probability to relevant exposures. We characterize this limitation through a compact completion polytope combining outcome bounds, scientific linear restrictions, and bidirectional transformation distances respecting one-way operational boundaries. Under the finite-population mean-response model, its target image is a sharp identified set: diameter $\omega$ implies worst-case squared-error risk at least ${\omega }^2/4$ for every point estimator under any number of unchanged-design repetitions. Optimal dual faces characterize when these bounds coincide and their local sensitivity to supported means and restrictions. To infer this set, we project a design-based confidence polytope for supported means, obtaining finite-sample full-set coverage; independent stable waves permit affine refinement through exact common-dual vertex certification. Matching upper and block-experiment lower bounds give minimax expected interval length of order $D_0+M\sqrt{(1+\Delta )/(Np)}$ for the specified fixed-dimensional classes with uniformly bounded endpoint sensitivity, identification-diameter bound $D_0$, supported-cell probabilities $\ge p$, and dependency degree $\le \Delta$. In 600-repetition experiments, widths approach the $0.20$ identification plateau, while projection attains $0.9917$–$0.9967$ full-set coverage versus $\le 0.0067$ for raw optimization. The predicted dependence scaling appears in a variance log–log slope of $0.9976$ against $1+\Delta$; across 4,000 end-to-end runs, dependence-calibrated full-set coverage is $1.000$, versus $0.910$–$0.918$ with a unit-iid radius. In a six-cell insurance-network audit, descriptive projection spans all held-out empirical means at average width $0.922$, versus unrestricted width $1.000$. These results connect the limits of causal learning to experimental design and specify when greater precision requires new identifying information.