Context compaction finally has a theory, and summarizing provably beats selecting.

arXiv 2608.01326 models compaction as two games: a Context Selection Game (retain a subset) and a Context Generation Game (summarize into a bounded message). It proves the generation game is equivalent to one-way communication complexity, so the minimum compaction budget for answering a query set within a target error is exactly that complexity. Then it proves a strict separation: generation-based compaction outperforms selection-based for certain query classes. Summarize-then-drop beats retrieve-and-keep on a provable set of workloads. They demonstrate by measuring Anthropic's own compaction endpoint on set-membership queries, which gives you a way to score a deployed algorithm against the optimum instead of eyeballing whether it "feels lossy."