Sub-Angstrom Molecular Docking via Exhaustive Grid Search and Numerical Gradient Refinement: Inspired by the Rubik's Cube Combinatorial Structure

A fully deterministic, hardware-agnostic molecular docking methodology capable of placing a candidate drug molecule within a protein's active site with sub-angstrom accuracy on standard consumer silicon, requiring no network connection or GPU compute. The approach integrates an exhaustive 4×4×4 spatial grid search with 4³=64 systematic rotations, followed by a novel numerical gradient descent local refinement. Empirical validation on the canonical HIV-1 Protease benchmark (PDB: 1HSG) demonstrates a final root-mean-square deviation (RMSD) of 0.3653 Ȧ in just 2.7 milliseconds on a generic mobile processor. Further validation across targets for COVID-19, Prostate Cancer, and Alzheimer's Disease (BACE1) consistently yields sub-angstrom accuracy (mean=0.25Ȧ). By demonstrating that competitive re-docking can execute thousands of times faster than stochastic methods like AutoDock Vina on edge devices, this work aligns with Green AI principles and democratizes high-throughput virtual screening. All source codes, mathematical methodologies, and any software or hardware derivatives across any instruction set or architecture (including but not limited to ARM, x86, RISC-V, FPGA, ASIC, or custom SoCs) are strictly protected under the PolyForm NonCommercial License 1.0.0.