Embeddings, Geometry and Entanglement: Formal Relations and Reported Semantic Results

We formalize the relation between semantic embeddings, scalar retrieval, tensor-product states and phase-sensitive readouts. A one-parameter family has constant query similarity while its entanglement varies from zero to maximal. We derive its reduced spectrum, relate normalized squared-overlap classification to valid quantum measurements, and state the information preserved by reversible spectral transforms. Previously reported QGI results are consolidated: category accuracy on 812 structured states, calibration differences across five embedding models, role ablations and four additional domains. Numerical tables are source-reported aggregates, not new experiments. Preliminary preprint; not peer reviewed. QGI website: https://www.qgi.dev