This paper develops a foundational mechanics layer within the Sobolev-Ozok Lattice (SOL) framework by reinterpreting motion as directional coherence-resolution flow on a discrete relational substrate. Starting from a scalar coherence field defined on a Planck-scale lattice, the paper derives velocity, momentum, inertial mass, rest energy, and a modified acceleration law from local coherence redistribution and finite update constraints. The framework does not assume Newtonian momentum, relativistic energy, or mass-energy equivalence a priori; instead, these emerge from the internal structure of coherence propagation. Within this interpretation: momentum corresponds to directed coherence flux, mass corresponds to total coherence content, inertia corresponds to resistance against coherence redirection, and rest energy corresponds to the update cost required to maintain coherent structure. The paper also introduces a transitional inertia term arising from temporal coherence variation and explores possible phenomenological implications in decoherence-dominated regions, including potential connections to coherence instability and Void Black Hole (VBH) structures within the broader SOL framework. In contrast to rigid-lattice approaches, relativistic consistency is maintained through a relational coherence interpretation in which the Planck scale acts as a local update-resolution bound rather than a preferred geometric frame. Lorentz covariance is treated as an emergent large-scale property of isotropic coherence propagation. This work forms part of the broader Sobolev-Ozok Lattice research program, which investigates the emergence of spacetime, gravity, quantum behavior, and kinematics from discrete coherence dynamics and Sobolev-order resolution structure. Declaration of Tools Used: This manuscript was prepared and typeset using LaTeX via Overleaf. Language refinement and stylistic polishing were assisted by the Overleaf AI Editor. All scientific content, mathematical derivations, conceptual development, and conclusions are original and authored by the undersigned. This paper is part of the Sobolev-Ozok Lattice (SOL) research program. Project webpage (papers, figures, updates): https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/
Ozcan Ozok (Tue,) studied this question.