The Recursive Structure of Perfect Numbers – A New Mathematical Invariant

Perfect numbers have long been studied in number theory for theirunique divisor properties. In this paper, we reveal a hidden recursivestructure within perfect numbers, demonstrating that they exhibit a self-stabilizing cycle when processed through sequential division and multi-plication. This recursive law remains consistent across known and newlypredicted perfect numbers, implying a deeper structural relationship be-tween them that has not been previously documented.