This research preprint introduces an alternative arithmetic framework for evaluating number divisibility, focusing specifically on the structural characteristics and numeric ratios of the prime number 7. Volume 4 details a novel heuristic that connects the properties of prime 3 and prime 7 to map spatial digit distributions and "2:1 ratio" splits. By establishing distinct organizational classification nodes—classified here as Super Nodes and Master Nodes—this methodology provides a systematic tracking grid. This allows for the direct determination of divisibility and the extraction of resulting multi-digit multipliers without the complexity or operational overhead of standard long division.