A Multi-Lattice Framework for Robotics: Navigating the Complexity-Efficiency Pareto Frontier

1. Title A Multi-Lattice Framework for Robotics: Navigating the Complexity-Efficiency Pareto Frontier This version has been withdrawn by the author for further refinement. Please refer to the updated 6D proof in Record. 2. Abstract / Description This preprint introduces a unified theoretical framework for selecting $N$-dimensional mathematical lattices ($A_n$, $E_n$) to optimize robotic control manifolds. While randomized sampling methods are standard, they often lack geometric interpretability. We propose a Pareto-optimal approach that balances computational complexity—scaled as $O(K \log K)$—against kinematic efficiency. Key Contributions: The Dimensionality Frontier: A formal model identifying the…