We show that the qubit Bloch sphere, the relativistic celestial sphere, and the projective line CP¹ are one and the same manifold, identified by the rank-one factorization of a null vector, and that the antipodal map on this sphere is simultaneously the EPR singlet condition and the BMS boundary-matching condition. The positivity that Information Causality (IC) imposes on quantum correlations and the positivity that Lorentz unitarity imposes on celestial correlators are shown to be two physical sources of one mathematical condition, Schoenberg positivity, connected by an antipodal translation rooted in the singlet structure. On this basis, the first-order entanglement variation reproduces the linearized Einstein equation and the second order the positive canonical energy (both verified numerically); the finite curvature coefficient is derived as a topological (Gauss-Bonnet) invariant. In the nonlinear sector, Schoenberg positivity pins the zonal three-graviton vertex uniquely; the Weinberg soft theorem then fixes the extended vertex V = −cΔ up to a single coupling c, and the Bondi-Sachs formalism reconstructs the vacuum Einstein equation from the boundary data, under explicitly stated structural assumptions (perturbative factorization, spectral dictionary, and the equivalence-principle input). New in Version 5: The construction is extended to de Sitter spacetime (S³ boundary), yielding Gµν + Λgµν = 0 under three axioms; the former masslessness axiom is derived from the geometric identification. The framework is organized in two tiers. Tier 1 (A1–A3 alone) yields emergent classical gravity and predicts a null result for gravitationally induced entanglement experiments of the BMV type, the framework's first falsifiable statement, conditional exactly on the tier choice. Tier 2 (bulk quantization as an additional postulate) is degenerate with perturbative quantum gravity; within it, the one-loop counterterm structure is proven rigid (Counterterm Rigidity Lemma: exactly (δG, δΛ), no new couplings possible), and the beta function of the single running coupling c is computed, validated against the known de Sitter one-loop coefficient 571/90 and the Gibbons-Hawking entropy. The critical point c → 1 is shown to be dynamically unreachable (~10²⁴⁴ e-folds), a strong-coupling singularity, not an attractor. A proven limitation is stated plainly: IC is an upper bound on correlations and cannot force a boundary interaction (Gallego et al., PRL 107, 210403); bulk quantization is a postulate, not a consequence of IC. All numerical claims are reproduced by the accompanying open verification suite (21 scripts, MIT license; see related identifiers). Discarded approaches and corrected errors from earlier versions are documented in a dedicated section
Daniel Süß (Fri,) studied this question.