MSP² and the Generator Table: Structural Recurrence, Two Construction Methods, and Supporting Tables

This research deposit presents the structural recurrence of the MSP² Generator Table, developed by Mario Sousa Pereira and Enzo Mazzoni in the context of the Syracuse (Collatz) problem. The work describes two complementary approaches to the recursive construction of the Generator Table: the structural organization of its blocks and walls, and the method based on parent-child relationships, cousin families, and recurrence parameters. The deposit includes the original French document, its English version, and five supporting Excel tables illustrating the structure and recursive rules of the Generator Table. These materials were prepared as part of the authors' mathematical correspondence with Trevor Morris concerning the examination and formalization of the MSP² approach in Lean. The purpose of this deposit is to make the mathematical constructions, supporting data, and proposed recurrence methods publicly accessible for independent examination and verification. Related research: Mario Sousa Pereira and Enzo Mazzoni, MSP² / Generator Table, DOI: 10.5281/zenodo.22555969.