Quantum Entanglement as a Manifestation of Pregeometric Connectivity

This paper reinterprets quantum entanglement from a pregeometric perspective in which connectivity precedes distance, metric, and continuous space. At the lowest layer, objects are represented solely by sets of relations. It is assumed that the addition of physical interaction to a two-element relation generates an elementary length, while three- and four-element relations generate elementary area and volume, respectively. Macroscopic distance, area, and space are interpreted as emergent quantities obtained by coarse-graining or integrating large ensembles of these elementary relations. A complete four-element connection is represented by the tetrahedral graph K₄ and interpreted as a fundamental object. The line graph L(K₄) is the octahedral graph, providing a natural mathematical model of a relational space generated from the connections of tetrahedral objects. Octahedral geometry contains three mutually orthogonal directions together with the normalized diagonal directions (x±y)/√2, and is geometrically compatible with the 45° measurement configuration associated with maximal CHSH violation. This paper does not claim to derive the quantum correlation E(a,b)=−cosθ. Rather, it presents a discrete geometry compatible with the known CHSH geometry and interprets quantum entanglement as a possible observable manifestation of a connectivity layer underlying ordinary spacetime. Rotation and phase coupling are further introduced as candidate dynamical ingredients for a future derivation of the angular correlation law. The model suggests that Bell nonlocality need not represent propagation across pre-existing space, but may instead expose the relational structure from which spatial distance itself emerges. Keywords: quantum entanglement, pregeometry, tetrahedron, octahedron, line graph, emergent space, CHSH, phase, rotation, fine-structure constant