Entanglement Without Shared Space: A DAG-Based Account in Temporal Rate Ontology

We argue that quantum entanglement is best understood as the structural non-factorizability of joint continuation measures in a pregeometric framework — one that presupposes neither a background Hilbert space nor a background spacetime. This thesis has direct implications for the interpretation of Bell non-locality, the debate between ontic and epistemic structural realism, and the question of whether entanglement is a fundamental feature of reality or an artifact of quantum-mechanical representation. Within Temporal Rate Ontology (TRO), physical systems are modelled as directed acyclic graphs (DAGs) of continuation events, and entanglement is defined as the non-existence of a product decomposition of the joint continuation measure — a purely combinatorial condition that requires no wavefunction and no shared configuration space. We prove that this structural condition entails the standard correlated measurement outcomes of quantum mechanics, under a mild non-degeneracy condition on the joint DAG that is generically satisfied. The quadratic probability rule is derived from an aggregation-stability argument within the CLT regime rather than postulated. Bell non-locality is reinterpreted as global DAG coherence rather than superluminal influence. Decoherence is modelled as constraint-induced suppression of continuation multiplicity. The framework is situated against relational quantum mechanics, causal set theory, and ontic structural realism, and philosophical objections concerning subsystem identity, underdetermination, and the emergence of the Hilbert space are addressed directly.