How Do Recursive Numeric Residues and Base-2 Modular Offsets Naturally Mirror the 57-Cell's Structural Symmetry?

Abstract

The research examines how recursive numeric residues, base-2 modular symmetry, and offset normalization naturally generate numeric patterns closely aligned with the structural symmetries of high-dimensional geometries, particularly the 57-cell. Employing a fibristic and Mohandase methodological framework, the study systematically traces numeric relationships emerging from simple recursive operations and decimal residues, notably around prime offsets such as 19. By explicitly analyzing numeric normalization and diagonal offsets, the investigation reveals harmonic proportions and numeric alignments that inherently reflect established geometric and group-theoretic configurations, including PSL(2,19). Rather than positing theoretical novelties, this exploration transparently synthesizes observed numerical alignments that closely resonate with known polytope structures. Comprehensive numeric analyses, along with detailed appendices, clarify these naturally arising structural resonances, establishing a clear, jargon-free basis for further empirical visualization and computational validation presented in subsequent research.