Electron Entanglement (EE) - Spectral and Topological Structures

Electron Entanglement (EE‑V04) presents a continuum‑geometric formulation of two‑electron entanglement within the Monistic Continuum Model (MCM). In this framework, electrons are modeled as vortex‑like excitations of a continuous substrate, characterized by geometric, spectral, and topological invariants. Entanglement arises from non‑separable correlation kernels generated by the continuum field C(x,λ) and its dynamical operator D. The study introduces a precise formulation of the correlation kernel K(x,y;λ), establishes a geometric mechanism for two‑mode coupling, and derives an effective Hilbert‑space structure through coarse‑graining over the evolution parameter λ. Linear quantum dynamics and spectral decomposition emerge naturally from the continuum behavior. EE‑V04 consolidates the mathematical foundations, operator constructions, vortex‑mode analysis, and structural results required for a continuum‑based description of electron entanglement, and outlines experimentally accessible signatures of continuum‑mediated coherence.