Compute the Interactions, Not the Attributes: What a Fact Layer Must Supply in the Chinese Sexagenary System

Language-model systems in rule-governed domains often pair the model with a deterministic fact layer, but which facts that layer should supply is rarely measured. We measure it in the Chinese sexagenary system underlying BaZi chart analysis, where every fact has one table-checkable value: 682 items over twelve fact categories and 160 transit--natal collision items, posed closed-book, with the reference table, and with computed facts at increasing levels. In eleven open-weight models answering directly, errors concentrate where attributes must be combined: none gets more than 4\% of sexagenary days or 1\% of collisions right. Static attributes have no consistent effect, and the complete relation list leaves most direct-answering models near zero although it contains the answer. A query-filtered layer (exploratory) raises Qwen3-8B and Qwen3-32B to 78--92\% and four further models to 96--100\%. Three proprietary reasoning models compute 68--95\% of collisions unaided. On chess positions, under predictions locked in advance, attributes again do not substitute for relations and listed distractors are misattributed. The fact layer must supply computed interactions; how they are presented depends on the model and the domain.