FourNull_Supplementary_Derivations_Verification

This supplement to Four Null Spacetime Theory, Part 1, shows how its key formulas arise, which results are exact, and which are certified by numerical integrability with stated bases, residuals and negative controls. It derives the regular four null geometry, its exact tetrahedral incidence decomposition and the self dual structure of the six channels; the composite relational clock, unique by strict convexity; the two shell Huygens law, its exact composition and the fixed point 1/12; the finite step Raychaudhuri correction and finite cell Damour equation, exact through order L_c², with the continuum constraint algebra verified symbolically; and the nonlinear radiative completion, with the Einstein coupling κ = 1, a unique order L_c² transverse traceless completion and x = 8a₄, confirmed by independent implementations. It establishes two polarizations without birefringence, causal propagation in every direction, stability for all data, a Maxwell sector with photon and graviton dispersion identical and κ_A = 1, and the universal null plane cell area. Every claim carries an explicit status, and a closing matrix records the boundaries of the present results. Calculations were carried out with AI assistance under the author’s direction.