Solving the Three-Generation Problem in E8

The Standard Model of particle physics exhibits exactly three generations of chiral fermions with identical gauge quantum numbers but widely separated mass scales. Attempts to derive this structure from the exceptional Lie group E₈, particularly via the triality of its D₄ ≅ so(8) subalgebra, have historically failed. The no-go theorem of Distler and Garibaldi rigorously demonstrates that three chiral generations cannot be obtained from a single, static E₈ representation without introducing unphysical mirror fermions. This article presents a resolution to the three-generation problem within the Fractal-Enhanced Timeless Quantum Substrate Hypothesis (F-TQSH) by introducing a Fractal Inheritance Operator acting on the E₈ subalgebra chain