Four Null Spacetime Theory III: Propagation and Classical Gravity: the Huygens Law, its Causal Selection and the Finite Cell Einstein Interactio

This is the third paper of a series on Four Null Spacetime Theory, in which spacetime is built from finite cells spanned by four lightlike vectors in perfect balance. The first two papers established the geometry of one cell and how cells meet; this one asks how radiation and gravity act on them. On a light front gravity separates by spin into the Raychaudhuri and Damour constraints and two radiative polarizations, and the cell preserves the separation: its scalar sector has only a double root, its vector sector a positive dressing, and its finite step corrections have unique covariant forms. Symmetry and locality alone do not fix the finite cell law, as explicit counterexamples show; causality does, given one premise, that the law’s principal part depends on the reconstructed metric alone and not on the cell’s clock; observation bounds the speed difference such a coupling would produce at long wavelengths to about one part in 1015, but does not establish that the coupling vanishes. For a reversible two step law whose kernel stays within its causal reach and which is stable at every momentum, Bernstein’s inequality bounds every propagation speed by the reach, and equality forces Kirchhoff’s law on the sphere one cell away, with quartic coefficient one twelfth; the shell family that earlier work left open reaches beyond the light cone and is excluded, and scale invariance under blocking independently selects the same law. On the Regge lattice of the cell the Fierz Pauli graviton appears with the correct normalization. Requiring the propagation law on curved backgrounds to come from one action fixes the Einstein coupling to one and, through order of the cell size squared in the transverse traceless sector, a unique completion whose coefficients are exact rationals, with the extrinsic coefficient two thirds, all certified in exact a rithmetic. The constraints remain first class, their lattice forms are preserved to fourth order along rays, and the ray network radiates by the quadrupole formula. Every result is stated with its status, and every verified result is reproduced by the archived package.