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 λUUDD; 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 ⟨ŜAŜB⟩ ∝ e^(-meff r), this background correlation does not yield observable Bell violation; a conditionally normalized E = cos Δθ 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 ∑ka = 0 elevates the weak background correlation to strong, distance-independent multi-particle entanglement, with ⟨B⟩ = 2√2. The measurement process is the unitary coupling of DU to DD via Ĥmeas = (m0²/4) ∫d³x φ̂DU φ̂DD; the Born rule follows from the reduced density matrix. All results are derived from first principles without collapse postulates or adjustable parameters.