SDRIS: The Geometric Origin of Inertia and the Equivalence Principle - Deriving Newton's Laws of Motion ($F=ma$) from the Information Latency of the Recursive Vacuum Grid

The equivalence of inertial mass ($m_i$) and gravitational mass ($m_g$) is one of the foundational pillars of physics, yet its microscopic origin remains unexplained by the Standard Model. Classical mechanics accepts Inertia as an axiom, while General Relativity postulates it as a consequence of spacetime geometry without identifying the underlying information-theoretic mechanism. In this paper, we derive Newton's Laws of Motion and the Weak Equivalence Principle from the axioms of the Static-Dynamic Recursive Information Space (SDRIS) framework. We model the vacuum not as a continuous void, but as a discrete, recursive processing grid with finite information throughput. We demonstrate that "Mass" corresponds to the Recursive Complexity ($\mathcal{C}$) of a topological knot, effectively representing the "refresh rate" required to maintain its existence. Uniform motion is identified as a unitary, energy-free "Shift Operation" (Newton's First Law). In contrast, acceleration introduces a predictive mismatch between the grid's address pointer and the particle's trajectory. We derive Newton's Second Law ($F=ma$) as the energy cost required to overcome the Write-Latency of the vacuum grid during non-linear updates. Finally, we resolve the Equivalence Principle by showing that Gravity (passive grid scrolling) and Inertia (active grid traversal) involve the exact same computational cost: relocating the information content of the object. Thus, $m_i \equiv m_g$ is derived as a necessary identity of information processing. Includes Computational Verification: This publication includes a Python simulation (SDRIS_Inertia_Simulation_Code_v1.0.ipynb) that numerically validates the latency mechanism. It demonstrates that the linear relationship $F=ma$ emerges statistically from the resource constraints of a discrete processing grid, strictly adhering to the Law of Large Numbers.