Three Domains, One Direction: Reasoning-Calibration Steering Transfers Across Domains

Steering vectors are compact artifacts of a trained model: directions extracted from its internal representations that, added back to the residual stream, change its behavior. Reasoning-calibration steering uses one such artifact to reduce overthinking in reasoning language models (Chen et al., 2025), and the vector is typically extracted from a single reasoning domain (Chen et al., 2025; Nguyen & Le, 2026), as if each domain required its own. We treat these vectors as data and ask whether that is so. We extract calibration vectors from mathematics, code, and logic, together with two domain-general vectors built by different merging routes: a pooled vector, extracted from the union of the three activation sets, and a combined vector, obtained by averaging the three finished domain vectors. Analyzed as a population, the artifacts are nearly rank one: 87.0% of the domain vectors' squared variation lies along one singular direction on DeepSeek-R1-Distill-Qwen-1.5B, against 35.1% for random vectors of the same dimension, and the two merging routes agree to cosine 0.981 despite weighting the domains differently. The behavior is consistent with this geometry. On MATH-500, APPS, and LogiQA2, all pairwise McNemar comparisons among the five vectors are non-significant, no domain vector has a measurable advantage on its home domain, and every learned vector shortens generations while improving accuracy. A norm-matched random direction instead lengthens responses and yields no accuracy benefit, so the effect belongs to the learned direction. The same geometry and the same behavior replicate on the 7B model of the family, extracted independently in a residual stream more than twice as wide. These results suggest a shared, domain-general reasoning-calibration direction in activation space, common across mathematics, code, and logic, and they illustrate that the geometry of a set of steering vectors, measured before any generation is run, can be informative about how those vectors will behave. Code, vectors, and per-problem outcomes are available at https://anonymous.4open.science/r/SEAL-EB7E/.