This research identifies the qubit Bloch sphere, the relativistic celestial sphere, and the projective line CP¹ as a single manifold, proven via rank-one factorization of null vectors. It establishes that Information Causality (IC) on S² and Lorentz unitarity on celestial correlators are distinct physical manifestations of Schoenberg positivity, bridged by a canonical antipodal translation derived from the EPR singlet structure. The work provides a rigorous analytical derivation of the Einstein Field Equations (EFE) as a "State Equation of Information Causality. " Key results include: 1. First-order variation: Reproduction of the linearized Einstein equation (S/ K 1). 2. Second-order variation: Recovery of positive canonical energy (Fisher structure). 3. Nonlinear Resummation: Assembly of a flat-spacetime entanglement-geometry dictionary using a Dyson-resummed propagator, where the three-graviton vertex is uniquely pinned to V = (3E² - 1) /2 by Schoenberg positivity. 4. Topological Invariance: Derivation of the curvature coefficient (-1/90) as a Gauss-Bonnet invariant. The theory is validated against lattice simulations, quantitatively matching the predicted non-Gaussian deviations and the spin-2 graviton pole.
Daniel Süß (Mon,) studied this question.