Aggregated relational data (ARD) record how many ties sampled respondents have to predeclared groups without revealing individual dyads. We ask whether such counts can falsify a pure additive-activity network model for one predeclared form of residual cross-group association. When the groups form an exhaustive partition, respondent degree is observed exactly. For arbitrary fixed activity values under an independent-Bernoulli additive-logit null, conditioning two respondents on equal degree yields a finite nonpositive sign restriction for their two disjoint group-count differences. Operational inference is narrower: on a regular repeated-cell array, analyst-randomized pair thinning gives a conservative one-network test with graph-independent sampled respondents. Finite and growing matched-law constructions establish that the target contains bivariate information absent from a collapsed binary count, while a declared rank-one path gives pointwise power. A deterministic marked-profile contract and a fixed-dimensional lattice local-limit argument make the design and conditioning requirements explicit. These results define a target- and design-specific specification diagnostic, not recovery of a labeled probability matrix, latent geometry, or arbitrary residual dependence.

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