Prime-Relational Substrate

Prime-Relational Substrate Nonfactorizable Prime Structure as a Hypothesis for Quantum Correlations and Emergent Spacetime Preprint — Hypothesis / Conceptual Framework Abstract We propose a pre-geometric hypothesis in which Prime structure is not assigned to physical objects as an individual hidden code, but instead constitutes an irreducible relational substrate from which local objects, correlations, adjacency, and eventually spacetime geometry may emerge . The central distinction is between a naïve shared-label relation, Π A = Π B A= B , and a genuinely nonfactorizable joint structure, Π A B ≠ Π A ⊗ Π B . {AB} A B. The former reduces naturally to a local hidden-variable picture and therefore cannot reproduce Bell-inequality violations. The latter instead treats spatially separated subsystems as local projections of a single relational object. We introduce a minimal graph-theoretic rea