The Null Cone Is Enough: Geometric Unification of Massless Fields

We prove that the null cone is enough: at every event in Minkowski spacetime, the null cone carries a two-dimensional conformal field theory with spectrum \Delta_{\ell} = \ell +1 , unifying all massless fields of spin \ell = 0,\frac{1}{2},1,\frac{3}{2},2 through pure geometry. The framework is classical throughout. From two postulates—four-dimensional Minkowski spacetime and the Isometric Sampling Condition (the requirement that field sampling on a lattice be a unitary isomorphism)—the unique Lorentz-invariant propagator is G(x,y) = \sin (\Omega \sqrt{-\sigma^2 - i\epsilon}) / (\Omega \sqrt{-\sigma^2 - i\epsilon}) , where the Feynman i\epsilon prescription selects the unique L^2 branch in the spacelike region. The RKHS normalisation K(x,x) = 1 forces G = 1 on the null cone, so the full two-point function is controlled entirely by a 2D CFT on the transverse S^2 , yielding \Delta_{\ell} = \ell +1 . Fermionic statistics arise from the \mathbb{Z}_2 holonomy of an \mathrm{SL}(2,\mathbb{C}) fibre bundle without any additional postulate. Seven independent paths—spanning operator algebra, tractor calculus, antenna theory, and celestial holography—converge on this result. At large angular scales (\ell \lesssim 30) , the condition G = 1 forces the CMB angular power spectrum C_{\ell} toward a geometric constant, consistent with the Planck anomaly.