Metric-Independent Phase Invariance: Resolving Quantum Non-Locality without Superluminal Signaling

Quantum non-locality and entanglement correlations pose a persistent conceptual conflict with relativistic causality, traditionally requiring either physical non-local collapse mechanisms or hidden-variable frameworks. In this work, we present a self-contained mathematical formulation operating over a composite Hilbert space Hsys ∼= HA ⊗ HT to resolve this tension from first principles. We define spatial separation r and the background metric gμν as emergent field properties of the realized manifestation space HT , governed by local informational density gradients I(x) ≡ Imax − svN(x). In contrast, maximally entangled quantum states are derived as metricindependent spectral phase invariants within the unobserved potential space HA, mediated by a self-adjoint recognition operator Kˆ. We demonstrate that local measurement operations execute deterministic internal phase alignment (∆K2 = 0) obeying strict local unitarity, preserving exact relativistic causality without physical energy-momentum or signal propagation through spacetime geometry. Finally, we derive from Lindblad master dynamics an explicit, testable expression for entanglement dephasing as a function of environmental informational gradients ∆Ienv along spatial geodesics.