Optical Relativity and Gravitation - Supplementary Materials

Following an operationalist protocol grounded in SR null exchange, the paper reconstructs relativity and gravitation as flat-background ray optics on a Euclidean slice Σ. Rather than taking Lorentz symmetry as primitive, it postulates a single-speed geometry from which SR kinematics follow as theorems. Persistent structure requires internal cycling; partitioning the single speed budget between drift and cycling is the mechanism by which mass and observers are mechanically embedded into the instantaneous slice Σ, yielding rest frames, clocks, and the self-relative intervals by which embedded observers reconstruct a curved geometry from their null exchanges.

Vacuum field equations — three harmonic constraints on flat ℝ³ — are established via the null protocol. These, together with an algebraic assembly map, are sufficient to derive exact Schwarzschild and Kerr without using the Einstein field equations as input; the Kerr derivation identifies the oblate source geometry and complex shift as consequences of spin-induced single-speed arena geometry. Inserting the speed-budget commitment into the ADM decomposition of GR confirms consistency with EFE. Post-Newtonian, dynamical, sourced, and cosmological results are further developed and catalogued. Because the primitive variables are phase advance and null comparison, the formulation aligns naturally with wave-mechanical descriptions of matter.