Q-Prime: Structured Embeddings for Rule-Bearing Knowledge: Formal Readouts, Semantic Binding and Reported Results

Q-Prime is the embedding component described in QGI’s existing model card and previously unpublished position paper. This manuscript develops a mathematical account of its semantic requirements: preserving polarity, scope, conditions, modality and inter-rule bindings under named readouts. It distinguishes direct-sum semantic views from tensor-product joint states, derives query and update preservation conditions, and relates a polarity-weighted score to an interference cross term. It includes the earlier Q-Prime paper’s reported conflict scores and supporting QGI structural-ablation and cross-domain results with separate provenance. Preliminary preprint; not peer reviewed. Numerical results are previously reported aggregates, not new model runs. QGI website: https://www.qgi.dev