Electron Entanglement (EE) - Spectral and Topological Structures

Abstract

This document presents Version V03 of Electron Entanglement (EE): Spectral and Topological Structures, a core contribution within the broader Monistic Continuum Model (MCM) research program. The EE framework explores how quantum‑mechanical two‑electron configurations emerge from deeper geometric and spectral structures inherent to the continuum substrate. Rather than treating entanglement as an abstract algebraic construct, this work situates it within a physically motivated, vortex‑mode‑based geometry that underlies the MCM. Version V03 consolidates and extends earlier formulations by refining the spectral projection formalism, clarifying the role of continuum modes Wn, and strengthening the correspondence between coupling geometries and observable quantum‑mechanical states. The present version also integrates updated operator structures, expanded glossary sections, and a more systematic treatment of emergent Hilbert‑space behavior within the continuum. The goal of this release is to provide a stable, citable reference for ongoing theoretical development, interdisciplinary discussion, and future extensions of the MCM/UPC framework. By archiving this version with a permanent DOI on Zenodo, the document becomes part of a long‑term, openly accessible scientific record intended to support reproducibility, transparency, and collaborative research. Researchers, students, and readers interested in foundational physics, geometric approaches to quantum theory, or emergent‑structure models are invited to use this version as the authoritative reference for EE within the MCM context.