Activation steering often averages activation differences between positive and negative prompts to construct a steering vector. This difference-in-means (DiM) estimator is simple, but a contrast pair can coactivate the intended concept together with topic, style, length, refusal, or truthfulness-related nuisance features. We model each pair as revealing the target vector through a quotient that removes its active nuisance span. The resulting polysemantic information operator determines which target components are identifiable and the number of contrast pairs needed to recover them. We establish identifiability, sample-complexity bounds, a coactivation phase diagram, and sparse-dictionary recovery guarantees. Synthetic and controlled experiments support the predicted quotient-recovery behavior. Public-data and Pythia-410M pilots instead evaluate recovery of the quotient estimand induced by chosen nuisance supports, not an externally validated semantic target. A controlled TruthfulQA counter-confounder illustrates the main NLP lesson: raw behavioral margin can reward a style-entangled DiM vector even when quotienting removes the injected style component.

The Subregular Hypothesis posits that phonological patterns in natural languages occupy a restricted region of the formal language hierarchy, yet the cognitive basis for this restriction remains unclear. We propose an information-theoretic characterization: Strictly Local languages, when formalized as shifts of finite type, are exactly those admitting stationary Markov sources, which exhibit zero conditional mutual information between distant positions given intervening symbols. We prove that certain non-subregular patterns such as first-last assimilation admit no such Markov realization, explaining their unlearnability. Empirical validation on English phonotactics versus Finnish, Turkish, and Hungarian vowel harmony confirms that MI profiles statistically distinguish SL-like from TSL-like patterns (p < 0.001, r = 0.84). This work bridges formal language theory and information theory, offering a unified framework for understanding computational restrictions on natural language phonology.