How does a relational representation shared across queries drive a query-specific choice? Controlled entity-binding experiments with GPT-2 Small, Qwen2.5-1.5B and Llama-3.2-1B reveal a low-dimensional relational background that is predominantly shared across query roles and transfers to new names. Same-domain interactions persist when another attribute domain is queried. After removing this component, restoring independently trained relation directions brings output contrasts closer to their original values than sign-reversed or equal-norm random controls in all three models. Yet a transferable relational representation need not have a transferable functional sign. In Qwen2.5, fixing model weights, the training-mean relation vector and edit dose yields opposite selection effects across binary and lexical-mapping prompts with different answer vocabularies. A factorial contrast of downstream sensitivities across attribute-query combinations determines the shared direction's local signed selection gain. In a separate eight-condition protocol, mean local gain is positive in Qwen2.5 and negative in Llama3.2. Late-component clamps resolve opposing pathway contributions: in Llama3.2, negative transmission through selected attention-only paths is partially offset by positive transmission through paths traversing both selected attention and MLP sets. Source-coordinate analyses establish distributed factor coverage, hidden-receiver readouts reveal layout-dependent combination, and instance-geometry interventions separate response direction from amplitude. These findings show how conditional sensitivity and competing pathways give shared relational structure its effect on specific choices.

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