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This paper studies whether, once a strong teacher representation space and corpus index are fixed, repeated neural query encoding can be replaced by a substantially lighter and analytically explicit estimator. We formulate fixed-teacher lexical-to-semantic encoding as a conditional-mean estimation problem in which the target semantic vector is represented as a noisy mixture of semantic prototypes weighted by posterior cluster probabilities. Kernel Affine Hull Machine (KAHM) geometry is used to estimate these posterior weights from inexpensive lexical features in an explicitly identified RKHS hypothesis space, and the semantic prototypes are refined by normalized least-mean-squares updates from noisy teacher embeddings. 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Kernel Affine Hull Machine (KAHM) geometry is used to estimate these posterior weights from inexpensive lexical features in an explicitly identified RKHS hypothesis space, and the semantic prototypes are refined by normalized least-mean-squares updates from noisy teacher embeddings. 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