A Geometric Framework for Fundamental Parameters: Investigating the Dimensional Information Cascade (SFT v3600)

While the Standard Model (SM) provides an unparalleled description of particle dynamics, the origin of its fundamental parameters and mass hierarchies remains a central question in theoretical physics. This paper introduces the SFT v3600 framework, which explores a geometric derivation of these constants through a concept termed the Dimensional Information Cascade.

Rather than treating physical constants as independent input parameters, this model investigates their potential emergence from layered topological constraints:

• Dimensional Transitions: We explore the hypothesis that information density shifts from a fractal UV-background ($d_s \approx 1.2$) to localized 3D resonances.

• Planar Correlations: Utilizing Principal Component Analysis (PCA) on quark-related metrics, we identify a statistical preference for planar (2D) configurations, suggesting a geometric basis for the quark sector.

• Topological Coupling: By applying constants derived from vacuum symmetries—specifically the $O_h$ (octahedral) symmetry and an instanton-based bridge to the Vacuum Expectation Value (VEV)—the model seeks to calculate the mass ratios of the lepton and boson sectors.

The accompanying Python protocol (SFT_v3600.py) provides a transparent computational environment to reproduce these numerical correlations. Preliminary results show that the values derived from these geometric axioms align closely with CODATA experimental data, offering a heuristic perspective on the "why" behind the Standard Model's parameter space.