Quantum Mechanics Within the Cartesian Relativity Framework: Resolving Double-Slit Anomalies through Algorithmic Rendering, Probabilistic Pruning, and the Energetic Lattice Tax

Abstract This paper resolves the wave-particle duality and the measurement problem of the double-slit experiment by applying the Cartesian Relativity Framework 1, 2. We posit that quantum superposition exists strictly as an unrendered probability distribution within the "Backend" of spacetime—a domain devoid of geometric volume and physical time. The physical detection of a particle is a forced "Render Event" onto a discrete, integer-based coordinate topology. By defining the wave function as a continuous Gaussian probability curve mapping to a quantized physical lattice—governed by a fundamental "Resolution Limit" that removes the reliance on mathematical infinity—we provide a deterministic mechanism for Quantum Dithering, Probabilistic Pruning, and the energetic "Lattice Tax" required to maintain non-rendered states. We address potential critiques regarding non-local domains and the energy costs of entanglement, demonstrating how this framework provides superior macro-to-micro coherence over standard interpretations. Finally, we propose falsifiable observational metrics: the laboratory Jitter Shadow, Render Exclusion Zones, and the measurable energetic overhead of logical address synchronization. Footnotes / References: 1 Kerr, A. J. (2026). Cartesian Relativity and the Zeno Non-singularity: A Unified Theory of Quantum Rendered Spacetime and Elastic Coordinate Topology. Zenodo. https://doi.org/10.5281/zenodo.20046745 2 Kerr, A. J. (2026). Cartesian Spacetime and Macroscopic Gravity: Topological Gradients, Data Collisions, and Planetary Hydrostatic Equilibrium. Zenodo. https://doi.org/10.5281/zenodo.20078172