Large language model assistants increasingly remember users across sessions by storing unstructured text summaries. Such a summary behaves like an unindexed heap. Every stored fact carries the same retrieval priority, and nothing signals which facts matter most right now.

We present Asterism, a local-first system that builds a weighted, decaying knowledge graph from conversation history. At inference time it injects a ranked subset of that graph into the model’s context. Our central design claim is architectural. The graph acts as a priority index over flat memory, in the same sense that a B-tree indexes an ordered file. Node weight is the salience signal, and it plays the role of an index key.

We evaluate five retrieval conditions on two independently authored personal graphs, using 100 priority queries per graph and five assistant models from four vendors. Decoding is held fixed, and the graph is reseeded before every call.

We report three findings. First, the deployed system is a weighted graph injected together with a prioritization instruction. It makes models more decisive under ambiguity than a flat list of the same facts. We score decisiveness with a pre-registered commit/hedge metric that was validated on held-out data. Every model commits to a weight-justified answer more often under the graph, in nearly every run.

Second, that decisiveness is also more accurate than flat memory, in every model. Absolute accuracy stays low, however. The best model identifies the true top priority only about 40% of the time, and most models do far worse. The graph therefore delivers a large relative gain on a problem that is far from solved.

Third, we separate the two ingredients with two further conditions: the graph with its instruction removed, and a flat list with that instruction added. Decisiveness does not distinguish them. The instruction alone raises commitment in all ten model and graph cells, by 11.2 points on average. That is as much as the structure alone achieves, at 10.7 points. A commit-rate gap is therefore not by itself evidence of a structural effect. Accuracy does distinguish them. Structure alone improves correctness over a flat list in all nine measured cells, and separably from zero in seven of them, against five of ten cells for the instruction alone. Among committed answers, structure alone is also more precise than the instruction alone in all nine measured cells, by 5.1 to 31.4 points, with four cells separable from zero. The two ingredients are complementary rather than redundant. The correctness gain of the deployed system matches or exceeds the better single ingredient in all ten cells, and strictly exceeds it in nine.

An earlier twelve-query pilot read this decomposition as purely structural. At one hundred queries the supportable reading is narrower. The instruction buys decisiveness, and the weighted structure is what makes that decisiveness accurate.

We also report the reliability of our own instrument. Agreement between the scorer and a human annotator is kappa = 0.64, and its errors bias the measured gap toward the null. We then measure two components that any automatically populated index needs. The first is an entity-resolution layer, whose accuracy ceiling we quantify. The second is a supersession mechanism that demotes contradicted facts. Retrieval latency scales approximately linearly and stays near 34 ms at 10,000 nodes. We release the full system, both benchmark graphs, and all negative results.