Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase

General relativity (GR) and quantum mechanics (QM) rest on incompatible geometries: GR on hyperbolic Lorentz boosts, QM on circular unitary phase rotations. This paper proposes both as projections of a deeper, pre-geometric entanglement structure. Building on a dual-domain ontology in which spacetime emerges from a timeless Quantum Domain (QD) of pure entanglement, the entanglement-strain angle θ is introduced as the fundamental geometric variable bridging the two domains. All relativistic effects—time dilation, length contraction, energy increase, and gravitational redshift—are expressed as elementary functions of θ, which links relativistic kinematics, gravitational effects, and quantum phase evolution. θ is identified with the complement of the Gudermannian function, the classical bridge between hyperbolic and circular angles. The Lorentz factor and Schwarzschild metric become direct functions of θ, revealing hyperbolic geometry as a projection of circular entanglement geometry. The speed of light c is reinterpreted as the maximum rate at which the internal quantum phase Φ_P synchronizes with θ, while the standard Compton–Schwarzschild crossover—the equality of Compton wavelength and Schwarzschild radius—acquires an interpretation as the scale where quantum coherence and gravitational strain become inseparable. Gravity's dual role—local attraction versus global expansion—follows from scale-dependent behavior of the same θ-field. The formalism modifies no empirical prediction of GR or QM, but reinterprets them as manifestations of entanglement strain, offering a unified geometric language in which motion and gravity are two sides of the same coin, pointing toward a deeper ontology where entanglement is fundamental. Keywords: entanglement‑strain angle; quantum entanglement; general relativity; quantum mechanics; quantum gravity; dark energy