Gradient Mechanics: The Dynamics of the Inversion Principle - Corpus Paper XIII - The Necessity of Interaction: The Derivation of Mass (Ω), Gravity (γ), and Light (c) as Artifacts of Processing Load

Papers I through XII constructed the Kinetic Engine (∆, Θ, η) and the Kinetic Stage (d = 3, τ0, σ). The stage is complete: three-dimensional clearance geometry, discrete spacetime, irreversible temporal flow, structural mechanical tolerance. This paper populates the stage by deriving the three observable artifacts of processing load strictly from the triadic primitives E = 0. 8, C = 0. 7, F = 0. 6 and their kinetic derivatives (∆, Θ, η, Φ). Mass (Ω) is derived as the ratio of local to baseline processing demand—the Computational Density imposed when recursive complexity saturates the grid. Gravity (γ) is derived as the gradient of that density—the differential update lag that refracts the worldline. Light (c) is derived as the unimpeded propagation of the update cycle at the causality limit already established in Paper XI. Each artifact is derived twice: first as a Logical Necessity from the internal structure of G = (E × C) /F, then as a Computational Instantiation from the algebraic values of the triad. No external theories serve as derivational premises. External frameworks appear only in Part IV as isomorphic confirmation of results already obtained. The three artifacts complete the operational dynamics of the Veldt: the stage runs, the load distributes, the signal propagates.