Universal Entanglement from the Unity of the Continuous Field in UD Theory

We derive universal quantum entanglement from the unity of the continuous field in UD theory. Matter formation converts the U attribute in space (Uᵤ) into the U attribute in matter (Dᵤ) via the vertex λ Uᵤ Dd; all Dᵤ excitations are perturbations of the same underlying Uᵤ field. The correlation function of these perturbations inherits the connectedness of space. Because the physical observable SA SB∝ e^-meffr, this background correlation does not yield observable Bell violation; a conditionally normalized E=cosΔθ is a formal construct. When two (or more) particles originate from the same matter formation event, their Dᵤ excitations share the same Uᵤ source, and momentum conservation ₐ=0 elevates the weak background correlation to strong, distance-independent multi-particle entanglement, with =2√2. The measurement process is the unitary coupling of Dᵤ to Dd via Hₘₑₐₛ=(m₀²/8)∫ d³x\,φDᵤφDd; the Born rule follows from the reduced density matrix. All results are derived from first principles without collapse postulates or adjustable parameters.