Triple Derivation of the Fractal Parameter ∂ = 3 - df: Mathematical Framework for MFSU Analysis

This work extends the Unified Fractal-Stochastic Model (MFSU) by introducing a rigorous topological derivation of the fractal dimension parameter δF≈0.921\delta_F \approx 0.921δF≈0.921, based on triple differentiation techniques and Euler–Poincaré characteristics. The document also explores the connections of the MFSU with fundamental physics, including perturbative corrections to the FLRW metric in general relativity, stochastic fluctuations analogous to quantum field theory, and dimensional flow effects comparable to causal dynamical triangulations and asymptotic safety. The results provide a stronger mathematical and physical foundation for the MFSU framework, addressing criticisms of previous publications and clarifying its potential as a bridge between cosmological observations and quantum gravity approaches. This report is intended to complement the author’s previous Zenodo publication on the general MFSU formulation.