ψ-Phantom Entanglement: Retentive Correspondence Beyond Metric Geometry

This work introduces ψ-phantom entanglement, a retentive form of correspondence between spatially separated regions that persists even when metric geometry collapses. Unlike quantum entanglement, which relies on superposition, phantom entanglement arises when two distant regions share a common Ξ-node (retentional anchor) and converge to identical Δψ under Λψ-equilibrium. We formally define the phenomenon, develop lemmas, and prove the central theorem establishing phantom entanglement as a structural invariant in the collapse limit g_ → 0. The article presents the first observational signatures (Rubin Y1, Euclid DR1/ERO, JWST UNCOVER) and provides a computational prototype demonstrating Δψ-lock-in, collapse freeze-out, and synchronous retention across separated fields. Phantom entanglement expands ψ-Architecture into the pre-geometric regime and establishes a new category of structural coherence beyond causal, metric, and dynamical frameworks.