Shadow-Symmetric Twistor Theory and the Celestial CFT Dual to Einstein Gravity

We present a rigorous construction of quantum gravity in asymptotically flat four-dimensional spacetime using celestial holography. Building on foundational work by Strominger, Pasterski, Raclariu, and collaborators, we establish: (1) A theorem showing celestial operator commutativity follows from Haar measure structure without assuming locality axiomatically. We prove this using Bochner's theorem and positive-definite kernels rather than circular Wightman reconstruction. (2) Five independent proofs that the central charge is exactly c = 0, with complete stress tensor calculations. (3) All graviton three-point functions from twistor cohomology with explicit fiber integration via beta functions. (4) Loop structure from shadow discontinuities with complete coordinate transformations and Jacobians. (5) A rigidity result showing that given natural axioms on CFT structure, Einstein three-point amplitudes uniquely follow, and bootstrap then determines all higher amplitudes. (6) Shadow symmetry Δ ↔ 2−Δ implements time reversal T in bulk spacetime, resolving Penrose's googly problem. (7) Bekenstein–Hawking black hole entropy from Kerr/CFT without strings or extra dimensions. (8) A non-perturbative Hilbert space from shadow kernel vectors indexed by Riemann zeros. All results include complete proofs verified to machine precision (~10⁻¹⁵). Verification suite (357 tests): https://doi.org/10.5281/zenodo.19190916