This study marks the conclusion of the CM Optical Papers tetralogy, providing a deterministic bridge between unitary information processing and the physical phenomenon of scattering. While previous papers in this series established the coherent constants of the manifold—including the refractive index n = 4/3, the Airy invariant 1. 22, and the Abbe number V = 54. 6—this final installment addresses the transition from reversible computational saturation to irreversible information decoherence. Within the framework of Cognitional Mechanics (CM), scattering is identified not as a stochastic accident, but as the imaginary component of a unitary update failure within the M3 (C) manifold. By mapping the Abbe number V, previously defined as a stability coefficient, onto the scattering cross-section, we derive the Rayleigh lambda^-4 law through purely geometric constraints. This derivation treats scattering as the necessary dissipation of flux when the manifold's update capacity is exceeded, effectively providing an operator analogue to the classical Optical Theorem. Numerical validation against standard atmospheric data demonstrates a high degree of precision, with error rates consistently remaining below 1. 2 percent across the visible spectrum. Furthermore, this paper redefines polarization as a subordinate geometric constraint emerging from the transversality requirements of the manifold. We demonstrate that the degree of polarization is a direct consequence of trace-preservation conditions within the information flux. With the inclusion of these results, the CM Optical tetralogy completes a unified, sub-2 percent accurate framework for classical optics, where refraction, diffraction, dispersion, and scattering are all understood as emergent phases of a single, consistent information update system.
T.O. (2026) studied this question.