Paper 1 established quantum mechanics as the mathematics of partial closure within Atomic Continuum Ontology. Paper 2 interpreted the Schrodinger equation as phase-preserving partial-closure evolution. Paper 3 interpreted measurement as the boundary-conditioned reclosure of partial closure into atomic-object residue. This fourth paper extends the framework to entanglement. Entanglement is here interpreted not as spooky action between already separated objects, but as shared closure prior to completed separability. The entangled state is not reducible to independently closed parts: ψAB ≠ ψA ⊗ ψB In ACO translation, this means that systems A and B remain jointly disclosed through a distributed partial closure relation. Measurement does not transmit influence between completed objects; it reclosures a shared relation into correlated atomic-object residues. Bell-type correlations therefore reveal the failure of completed object separability, not the existence of faster-than-light object signaling. A worked singlet-state example demonstrates how anti-correlated measurement outcomes arise as residues of a shared closure structure. The paper concludes that entanglement is distributed partial closure, and that separability belongs to the reclosed AO residue rather than to the pre-measurement ACO state.
Philip Lilien (Thu,) studied this question.