The True Coset Structure of IGPS and the Z₃ Replacement of the k=1 Approximation (IGPS VIII)

This paper resolves the precise algebraic identity of the vertex operator algebra (VIGPS) underlying the Information-Geometric Physics System (IGPS) framework. It formally replaces the SU(3)₁ Wess-Zumino-Witten (WZW) $k=1$ approximation used in Papers IV–VII with a rigorous structural theorem, identifying a genuinely new $c=2$ Rational Conformal Field Theory (RCFT). By establishing the exact Goddard-Kent-Olive (GKO) coset structure, this work extracts the true conformal weights of the quark sectors, yielding a topological correction that resolves the previous 1.8σ discrepancy in the Standard Model CP-violating phase prediction. Key Findings & Breakthroughs: Discovery of a New $c=2$ RCFT (Theorem VIII.1): The paper proves that the IGPS vertex algebra is the GKO coset VIGPS = SU(3)₁⊗ 3/SU(3)₃. Exhaustive verification confirms this is a new $c=2$ RCFT, distinguished by a unique "denominator-9" conformal weight fingerprint ($h = 1/9, 4/9$) originating from its SU(3)₃ heritage, alongside 30 primaries and a total quantum dimension of D² = 108. The Z₃ Fusion Ring (Theorem VIII.2): The $k=1$ minimality assumption of previous papers is rigorously replaced. The framework mathematically proves that the fusion algebra restricted to Z₃ triality sectors is isomorphic to Z₃, preserving the necessary superselection sector structure, triality charges, and generation count (Ngen = 3). Exact CP Phase Correction (Theorem VIII.3): The true coset conformal weights of the charged sectors (h₁ = 1/9 ≠ h₂ = 1/6) introduce a natural T-matrix asymmetry. Under Z₃ holonomy transport, this yields an exact, topological phase correction of Δδ = -6.67^∘. The corrected CP phase prediction is δ = 110.53^∘, deviating from the Particle Data Group (PDG) world average by only 0.67^∘ (< 0.1σ). Yukawa Quartic Coupling Prediction: As an additional physical application, the paper derives the Yukawa quartic coupling λYukawa = 1.886 directly from the Schwinger-Dyson equation coefficient. Significance: This paper acts as a profound structural upgrade to the IGPS series. It proves retroactively why the previous $k=1$ approximation succeeded at leading order, while successfully utilizing the true coset's fractional conformal weights to achieve unprecedented, sub-degree precision in predicting CP violation without the introduction of free parameters.