High probe accuracy does not by itself establish that a language model computes and uses the decoded value. We examine this inference in a syntax-sensitive arithmetic testbed: Llama-3.1-8B often fails multiplication when an operand is wrapped in parentheses or an additive identity. In the primary operand band, an input-only linear baseline nearly matches the original hidden-state probe’s regression R² ≈ 0.96. A classical variance decomposition gives an analytical headroom of only 0.031 for this baseline class. In wider bands, selection-separated reanalysis instead finds positive activation advantages, which increase with regularization tuning; joint input-and-activation probes also improve over the baseline. These predictive gains are distinct from exact integer recovery and causal use. In the primary band, tested answer-site steering and state transplants produce small average output shifts and no observed donor-answer emissions, whereas operand-site interventions produce large effects. Operand access is necessary, with a strong bottleneck at one attention layer. The causal tests do not cover the wider-band predictive gains. We advocate explicit input baselines, matched causal tests, and positive controls, with conclusions restricted to the distributions, representations, and interventions actually examined.