Context Selection as a Partial Order: A Blackwell Framework and Verified LLM Evidence

Context selection for large language models (LLMs) requires distinguishing source informativeness from the performance a fixed model can realize. We develop a framework separating the Blackwell order under optimal decision rules from a model-specific performance order, with finite-sample certificates for source comparisons. The framework establishes why no task-independent scalar ranking preserves all optimal preferences between incomparable sources. For declared source families, we prove structural incomparability. Under the sampled-state design and proved guessing caps, measurements from all six LLMs provide positive lower bounds on Le Cam deficiency in both directions for two source pairs, at 95% simultaneous confidence. Separately, constructed coding tasks with executable tests verify crossing source preferences and harm from adding correct information. Randomized replication confirms both effects; three further pairs exhibit verified crossings in 16 of 18 model–pair combinations, and some harm persists after explicit contract clarification. On HotpotQA and MuSiQue, listwise reranking retrieves complete evidence for 82% and 80% of questions within supplied pools, versus 23–47% and 7–32% for baselines; advantages narrow on retrieved candidates. These results make the gap between available information and realized model utility statistically testable and support task-conditioned context evaluation.