An Arithmetic Heuristic for Atomic Number Interpolation in Homologous Groups of the Extended Periodic Table

This preprint presents an empirical arithmetic heuristic for interpolating atomic numbers within homologous groups of the extended periodic table. It shows that the simple arithmetic mean between atomic numbers of homologous elements located in different periods systematically deviates due to the insertion of internal electronic subshells (d, f, and, theoretically, g blocks) between successive periods. A corrective constant, defined as half of the electronic capacity of the highest-energy internal subshell crossed, is introduced to compensate for this numerical displacement. The method reproduces known atomic numbers across light and heavy groups and provides a consistent qualitative framework for discussing extrapolations toward superheavy elements. The approach is explicitly heuristic and descriptive in nature, is fully compatible with the Madelung (n + l) rule, and does not propose modifications to established quantum mechanical theory. It is intended as a structural and conceptual analysis of periodic table organization rather than as a predictive physical model.