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. From two postulates—four-dimensional Minkowski spacetime and the Isometric Sampling Condition—the unique Lorentz-invariant propagator is G(x,y) = \mathrm{sinc}(\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, and 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. We provide the microscopic foundation for Jacobson's thermodynamic Einstein equation and Verlinde's entropic gravity. We extend the framework to \mathrm{SU}(N) gauge theories and derive asymptotic freedom: b_{\ell} = (12\ell^2 - 1)C_2(G) / (12\pi) > 0 for all \ell \geq 1 , reproducing the Gross-Wilczek-Politzer result for \ell = 1 . We develop the structural correspondence between the sinc kernel and the Riemann zeta function, construct a mathematical bridge to the non-trivial zeros of \zeta (s) , and identify the precise step separating the ISC framework from a proof of the Riemann Hypothesis.It is worth noting that the BSS theorem establishes not merely the unitarity of the sampling map, but a categorical equivalence between \mathrm{PW}_{\Omega} and \ell^2(\mathbb{Z}) — which implies that the ISC is an intrinsic property of the Paley-Wiener space structure, rather than an externally imposed postulate. This observation is crucial for understanding the inevitability of the ISC in its four-dimensional generalization.