Dimensional Mismatch: The Structural Conflict between High-Dimensional Manifolds and Linear Computing

NOTE: This paper is part of a 4-part research series (tetralogy) on database systems: structural trade-offs in modern data architectures and quantum-augmented techniques for robust query optimization and OLAP execution. Other parts (Zenodo DOIs):- 10.5281/zenodo.17797276- 10.5281/zenodo.17796162- 10.5281/zenodo.17796302 Research positioning:- This is an unpublished research manuscript intended for open dissemination and community feedback.- The work emphasizes explicit assumptions/limitations and model- or simulation-based evidence where applicable. Reproducibility (current status):- The current release focuses on the manuscript and experimental description.- Code/data packaging will be added in subsequent releases (new versions) as a reproducibility bundle. License:- Please see the license field of this Zenodo record for reuse terms. We formalize metric distortion induced by projecting high-dimensional structure into linear representations, and demonstrate a resulting “findability collapse” in similarity-based retrieval.