  An elementary topological error in Bell's representation of the EPR elements
of reality is identified. Once recognized, it leads to a topologically correct
local-realistic framework that provides exact, deterministic, and local
underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The
correlations exhibited by these states are shown to be exactly the classical
correlations among the points of a 3 or 7-sphere, both of which are closed
under multiplication, and hence preserve the locality condition of Bell. The
alleged non-localities of these states are thus shown to result from
misidentified topologies of the EPR elements of reality. When topologies are
correctly identified, local-realistic completion of any arbitrary entangled
state is always guaranteed in our framework. This vindicates EPR, and entails
that quantum entanglement is best understood as an illusion.
