Status and Dependency

This paper dissolves the quantum entanglement paradox. Entanglement is not a mysterious connection between distant particles but the actualisation of a single pre-state entity.

The apparent non-locality arises because the pre-state (AP09) has no spatial structure — distance is a property of the manifold (the accumulation of records), not of the probability state that precedes it.

Three formal results. Lemma 1 (Local Interaction, Global Actualisation) establishes why a local measurement on any subsystem of an entangled state necessarily actualises the global state.

Proposition 1 (Single Record) shows that the actualisation of an entangled state is a single record-writing event with no signal propagation between subsystems.

Proposition 2 (Bell Prediction) shows that Bell’s theorem is predicted by the axioms: Axiom R structurally forbids pre-existing value assignments, the non-spatial pre-state dissolves the locality presupposition, and the Born rule (AP09) yields the quantitative violation.

Axiom C is safe because its scope is the manifold, not the transition from pre-state to manifold.

The dependency chain: AP09 (complex Hilbert space, Born rule, no spatial pre-state; measurement as actualisation) → Axiom R (record-writing, irreversibility) → Axiom C (Constraint) → this paper (entanglement as single actualisation, Bell predicted, relativistic covariance dissolved).

Epistemic status per section. 1 (Problem of Entanglement): historical — summary of the entanglement puzzle, Bell’s theorem, and the tension with Axiom C. 2 (Distance is a Property of the Record): established — follows from AP09 and AP17. 3 (Single Entity): derived — the entangled state is one mathematical object in the pre-state. 4 (Single Actualisation): derived — Lemma 1 + Proposition 1. 5 (Axiom C Safe): derived — scope clarification; no-signalling derived from axioms. 5.1 (Relativistic Covariance): derived — actualisation has no spacetime location. 6 (Bell Predicted): derived — Proposition 2 + quantitative CHSH verification.