Quantum Entanglement in the U-Cell Model: Spinor Structure of Transverse Substrate Modes and Exact Reproduction of Bell Correlations

Quantum entanglement has no explanation in terms of local hidden variables (Bell 1964). The U-Cell Model (UCM) is an elastic lattice substrate — naively a local theory. We show that the UCM is in fact a non-local theory: entangled particles share a global pattern in the substrate network, not a local hidden variable. The transverse substrate modes ψᵃ transform as spin-1/2 spinors under spatial rotations, a consequence of the cubic lattice symmetry and the Helmholtz decomposition. From this we derive that the UCM substrate reproduces the quantum-mechanical Bell correlation C (α, β) = −cos (α−β) exactly, including the maximum CHSH violation |S| = 2√2. The physical mechanism is the global substrate pattern maintained through the cell membranes, which propagate correlations instantaneously without carrying a usable signal. The UCM thus satisfies Bell's theorem, the no-communication theorem, and special relativity simultaneously. An open question is whether the membrane stiffness κₘem/κcell is finite or infinite. If finite but very large, the UCM predicts a preferred frame — the substrate rest frame — as a testable departure from strict Lorentz invariance. Analysis code (ucmbell. py) included for reproducibility. Part of the UCM preprint series (ORCID 0009-0005-5088-4339, records 19387201–19430524).