arXiv2026
Dynamic query processing keeps query answers up to date during insertions and deletions. For conjunctive queries (CQs) under set semantics, the classes maintainable in constant amortized time are known exactly: the $q$-hierarchical CQs under arbitrary updates, and the free-connex CQs under insertion-only updates. Many analytics tasks, including \textsf{SUM}/\textsf{COUNT} aggregations, provenance, and access control, are captured by evaluating a CQ over a positive commutative semiring. We thus ask whether aggregation changes what can be maintained efficiently, and if so, when. Under \emph{insertion-only} updates, it does: the boundary retreats from free-connex to a new class we call \emph{strong-connex}, with $q\text{-hierarchical} \subsetneq \text{strong-connex} \subsetneq \text{free-connex} \subsetneq \text{acyclic}$. For every \emph{strictly monotone} semiring, including the sum-product and tropical semirings, no free-connex but non-strong-connex CQ is maintainable in $O(|D|^{1/2-ε})$ time under the OuMv and OMv conjectures, whereas every strong-connex CQ is maintainable in $O(1)$ amortized time over every semiring. Under \emph{arbitrary} updates, the boundary stays at the $q$-hierarchical CQs for every semiring with $O(1)$-deletable aggregates, and maintenance over any semiring is at least as hard as over the Boolean semiring. We further strengthen the lower bounds to semirings that fall outside the class and to query with different \emph{height} and \emph{dimension}, under the combinatorial $k$-clique and generalized OuMv conjectures. All upper bounds come from a single framework, obtained by adapting CROWN to annotated relations; together with the lower bounds, they yield dichotomies parameterized by both the query and the semiring, recovering the Boolean results as a special case.