Necessary, Decodable and Reversible, Yet Not Transferable: A Stress Test for Attention-Head Role Claims

Mechanistic studies often assign a component a role when removing it damages a behavior, its activation linearly encodes task information, and restoring that activation repairs the damage. We test the stronger implication: can the same activation carry the requested computation into another prompt? In the roughly 8 of 15 model-family cells receiving our full matched-control transfer assay, covering three 7-8B instruction-tuned models and 5 single-step computation families, tested attention-head states did not produce clean computation transfer. Same-answer and matched-context controls instead exposed inert or broad effects. Positive controls bound this result rather than eliminating its caveats: the instrument recovers known function vectors when writing into an underspecified prompt, and recovers a compact override-capable residual state in one of three controlled-model seeds. Neither control proves sensitivity to the object carried by real-model attention during prompt override. On two composed forms in Qwen, a strongly decodable operation direction also failed to steer the generated answer under passing gates; the corresponding cross-model test was invalid. These results show that necessity, decodability, same-prompt repair, and cross-prompt transfer are separable evidence. They do not establish that a portable selection state is absent from untested components or settings.