STEER for Law: Cross-Domain Algebraic Retrieval on Brazilian Legal Text

STEER (Semantic Transformation for Embedding-space Exploration in Retrieval) was validated on English-language BEIR benchmarks, where it demonstrated controllable cross-domain retrieval via embedding rotation and identified isotropy as the hidden variable governing operation efficacy. An open question remained: does STEER generalize to non-English text and to the structurally distinct domain of law? We report a dedicated benchmark on 100 Brazilian legal ementas (judicial headnotes) across five legal domains (tax, labor, civil, criminal, constitutional), using six embedding models on Modal GPU (T4) infrastructure. Four findings emerge: (1) the isotropy-effectiveness correlation replicates in Portuguese legal text (r=-0.370); (2) all six models showed positive cross-domain shift on Brazilian legal text; (3) the optimal rotation parameter is substantially higher for law (alpha=0.30-0.40); (4) an English-only model achieved the highest cross-domain shift (+2.75) on Portuguese text. These findings extend STEER to a new language and a legally significant application: automating cross-domain analogical reasoning that Brazilian law constitutionally mandates (Art. 4, LINDB).