Quantum Entanglement as Topological Phase Constraint in T7 Spacetime — Version 2.0 (corrected)

We prove that quantum entanglement — specifically the non-factorizability of the joint probability distribution of two particles and the violation of Bell's inequalities — follows necessarily from the axioms of the T7 model, a seven-dimensional toroidal spacetime defined by four geometric axioms. The central result is the T7 Entanglement Theorem: for any two particles born at the same event on T7, the topological phase constraint imposed by Axiom A1 (a straight line is a circle S1 whose two ends meet at a single point at infinity) produces a non-separable joint walk distribution whose correlations satisfy E(a,b) = −cos(a−b), yielding a CHSH parameter S = 2√2 > 2, thereby violating Bell's bound. This extends the Hassan-T7 theorem (Bibote, 2026, DOI: 10.5281/zenodo.20617431), which derived relativistic time dilation as an emergent statistical law from Planck-scale random walks, to the quantum domain. Non-locality is not postulated — it is a structural consequence of the compact topology of T7.